# Exam 2014 Year 10( includes Answers at the bottom)

```NAME:
TEACHER:
Your​ ​school​ ​name
Year​ ​10​ ​Mathematics
2014​ ​Examination
Time:​ ​2​ ​hours
Sections
1​ ​Number
Page​ ​number
2
2​ ​Algebra
5
3​ ​Graphs
8
MHJC
Page​ ​1
Result
2014​ ​EOY​ ​Year​ ​10​ ​(104)
4​ ​Measurement
11
5​ ​Trigonometry
15
6​ ​Geometry
19
7​ ​Angles
24
8​ ​Statistics
27
9​ ​Probability
31
Answer​ ​ALL​ ​questions​ ​in​ ​the​ ​spaces​ ​provided​ ​in​ ​this​ ​booklet.​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Show​ ​ALL​ ​working.
NAME:
TEACHER:
YEAR​ ​10​ ​MATHEMATICS,​ ​2014
Section​ ​1​ ​Number
Answer​ ​ALL​ ​questions​ ​in​ ​the​ ​spaces​ ​provided​ ​in​ ​this​ ​booklet.​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Show​ ​ALL​ ​working.
For​ ​Assessor’s​ ​use​ ​only
MHJC
Page​ ​2
2014​ ​EOY​ ​Year​ ​10​ ​(104)
Curriculum​ ​Level
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(c) Tina’s​ ​parents​ ​pay​ ​for​ ​500​ ​mB​ ​of​ ​data​ ​on​ ​her​ ​new​ ​phone.​ ​ ​Tina​ ​uses
SKILLS​ ​QUESTIONS
this​ ​up​ ​in​ ​4​ ​days!​ ​ ​How​ ​much​ ​data​ ​will​ ​she​ ​need​ ​per​ ​month​ ​(30​ ​days)
if​ ​she​ ​uses​ ​it​ ​at​ ​this​ ​rate?
QUESTION​ ​ONE
Tina’s​ ​parents​ ​will​ ​finally​ ​let​ ​her​ ​get​ ​a​ ​smart​ ​phone.​ ​ ​She​ ​wants​ ​a​ ​phone
that​ ​costs​ ​\$300.​ ​ ​Her​ ​parents​ ​will​ ​only​ ​give​ ​her​ ​\$75,​ ​enough​ ​to​ ​buy​ ​a
budget​ ​model.
(a) Tina​ ​decides​ ​to​ ​buy​ ​the​ ​\$300​ ​phone.​ ​ ​What​ ​percentage​​ ​of​ ​the​ ​cost
does​ ​her​ ​parents’​ ​money​ ​cover?
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(b) Tina​ ​sometimes​ ​babysits​ ​for​ ​\$8/hr.​ ​ ​How​ ​many​ ​hours​ ​of​ ​babysitting
will​ ​she​ ​need​ ​to​ ​do​ ​to​ ​raise​ ​the​ ​extra​ ​money​ ​she​ ​needs​ ​for​ ​the​ ​phone?
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(d) 1​ ​Gb​ ​of​ ​data​ ​is​ ​1024​ ​mB.
The​ ​phone​ ​company​ ​Tina​ ​is​ ​with​ ​offers​ ​the​ ​following​ ​data​ ​packs:
● 3Gb​ ​for​ ​\$50
● 1​ ​gB​ ​for​ ​\$20
● 500​ ​mB​ ​for​ ​\$10​ ​and
● 50​ ​mB​ ​for​ ​\$6
Using​ ​your​ ​answer​ ​to​ ​part​ ​(c),​ ​what​ ​data​ ​packs​ ​should​ ​Tina​ ​buy​ ​to​ ​get
a​ ​month’s​ ​data​ ​as​ ​cheaply​ ​as​ ​possible?​ ​ ​Justify​ ​your​ ​answer.
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Page​ ​3
2014​ ​EOY​ ​Year​ ​10​ ​(104)
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(c) CheapSellaz​ ​holds​ ​a​ ​20%​ ​off​ ​sale​ ​and​ ​lists​ ​the​ ​phone’s​ ​sales​ ​price​ ​as
\$782.​ ​ ​What​ ​is​ ​their​ ​non-sale​ ​price​ ​for​ ​the​ ​phone?
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QUESTION​ ​THREE
Some​ ​students​ ​weighed​ ​their​ ​phones.​ ​ ​Here​ ​are​ ​the​ ​weights​ ​(in​ ​g).​ ​ ​Write
them​ ​in​ ​order​ ​from​ ​smallest​ ​to​ ​largest:
QUESTION​ ​TWO
110.7,​ ​112.0,​ ​110.08,​ ​111.3,​ ​110.309
A​ ​new​ ​smart​ ​phone​ ​has​ ​a​ ​recommended​ ​retail​ ​price​ ​of​ ​\$1049.
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(a) Shady​ ​Sam​ ​says​ ​he​ ​can​ ​get​ ​it​ ​for​ ​65%​ ​of​ ​the​ ​recommended​ ​price.
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(b) Techfilla​ ​Company​ ​sells​ ​the​ ​phone​ ​at​ ​its​ ​recommended​ ​price…but
then​ ​holds​ ​a​ ​“30%​ ​off​ ​everything​ ​sale”.​ ​ ​What​ ​is​ ​the​ ​sale​ ​price​ ​of​ ​the
phone?
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Page​ ​4
2014​ ​EOY​ ​Year​ ​10​ ​(104)
QUESTION​ ​FOUR
Tina’s​ ​teacher​ ​tells​ ​the​ ​class​ ​that​ ​they​ ​are​ ​not​ ​allowed​ ​to​ ​use​ ​their​ ​phones
as​ ​calculators!​ ​ ​Tina​ ​did​ ​not​ ​remember​ ​to​ ​bring​ ​her​ ​calculator​ ​to​ ​class.
Show​ ​how​ ​these​ ​questions​ ​could​ ​be​ ​solved​ ​without​ ​a​ ​calculator​ ​(show
working).
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2
5
+
3
4
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(e) Find​ ​the​ ​lowest​ ​common​ ​multiple​ ​of​ ​6​ ​and​ ​8.
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(a) Find​ ​20%​ ​of​ ​800
(b)
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=
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(f) 5.2&times;103 &times; 4&times;105
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□​​ ​=​ ​77​ ​–​ ​1
(c) 62​ ​+​ ​
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QUESTION​ ​FIVE
Complete​ ​the​ ​rounding​ ​table
Number
Rounded​ ​to…
Nearest​ ​100 2​ ​d.p.
4768.207
5211.367
4
59.0099
3​ ​s.f.
QUESTION​ ​SIX
3
(d) 2 − (4 + 2) + √16
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A​ ​phone​ ​cost​ ​a​ ​retailer​ ​\$530​ ​to​ ​get​ ​into​ ​the​ ​store.​ ​ ​72%​ ​profit​ ​is​ ​added​ ​to
get​ ​the​ ​GST​ ​exclusive​ ​selling​ ​price,​ ​then​ ​15%​ ​GST​ ​is​ ​added.
(a) What​ ​will​ ​the​ ​GST​ ​inclusive​ ​selling​ ​price​ ​be?
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2014​ ​EOY​ ​Year​ ​10​ ​(104)
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NCEA​ ​STYLE​ ​QUESTION
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Tina​ ​hopes​ ​to​ ​save​ ​for​ ​an​ ​iPad,​ ​now​ ​that​ ​she​ ​has​ ​her​ ​phone.
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(b) If​ ​the​ ​price​ ​in​ ​(i)​ ​is​ ​then​ ​discounted​ ​30%,​ ​what​ ​will​ ​the​ ​new​ ​selling
price​ ​be?
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Explain​ ​what​ ​you​ ​are​ ​calculating​ ​at​ ​each​ ​step.
● She​ ​now​ ​has​ ​a​ ​paper​ ​run.​ ​ ​She​ ​delivers​ ​430​ ​papers​ ​twice​ ​per​ ​week
at​ ​5c​ ​per​ ​paper​ ​delivered.
● Her​ ​parents​ ​tell​ ​her​ ​that​ ​for​ ​every​ ​\$5​ ​she​ ​saves,​ ​they​ ​will​ ​give​ ​her
● The​ ​ipad​ ​cost​ ​724​ ​when​ ​she​ ​first​ ​starts​ ​saving.​ ​ ​Its​ ​price​ ​will​ ​have
come​ ​down​ ​by​ ​15%​ ​by​ ​the​ ​time​ ​she​ ​is​ ​ready​ ​to​ ​go​ ​shopping.
How​ ​long​ ​will​ ​it​ ​take​ ​Tina​ ​to​ ​save​ ​enough​ ​to​ ​buy​ ​the​ ​iPad?
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(c) What​ ​is​ ​the​ ​percentage​ ​decrease​ ​between​ ​the​ ​original​ ​GST​ ​exclusive
price​ ​and​ ​the​ ​discount​ ​price​ ​in​ ​(ii)?
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(d) Another​ ​phone​ ​has​ ​a​ ​GST​ ​inclusive​ ​price​ ​of​ ​\$870.​ ​ ​What​ ​is​ ​the​ ​GST
exclusive​ ​price?​ ​ ​(GST​ ​is​ ​15%)
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Page​ ​6
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2014​ ​EOY​ ​Year​ ​10​ ​(104)
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Page​ ​7
2014​ ​EOY​ ​Year​ ​10​ ​(104)
NAME:
TEACHER:
YEAR​ ​10​ ​MATHEMATICS,​ ​2014
Section​ ​2​ ​Algebra
Answer​ ​ALL​ ​questions​ ​in​ ​the​ ​spaces​ ​provided​ ​in​ ​this​ ​booklet.​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Show​ ​ALL​ ​working.
For​ ​Assessor’s​ ​use​ ​only
Curriculum​ ​Level
==========================================================================
QUESTION​ ​ONE
(a) These​ ​scales​ ​balance.​ ​ ​Therefore,​ ​a​ ​bag​ ​weighs​ ​the​ ​same​ ​as​ ​how​ ​many
blocks?
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2014​ ​EOY​ ​Year​ ​10​ ​(104)
(b) If​ ​the​ ​first​ ​two​ ​scales​ ​are​ ​in​ ​perfect​ ​balance,​ ​what​ ​needs​ ​to​ ​be​ ​added​ ​(in
place​ ​of​ ​the​ ​question​ ​mark)​ ​to​ ​balance​ ​the​ ​third​ ​set?
QUESTION​ ​TWO
Solve​ ​the​ ​following​ ​equations:
(a) 10​ ​+
=​ ​32​ ​–​ ​4
(b) 53​ ​–
=​ ​41
(c) 2n​ ​+​ ​5​ ​=​ ​29
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(d) 6n​ ​–​ ​4​ ​=​ ​3n​ ​+​ ​8
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(e) 5(n​ ​–​ ​3)​ ​=​ ​35
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(f)​ ​(n​ ​–​ ​4)(n​ ​+​ ​3)​ ​=​ ​0
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QUESTION​ ​THREE
Simplify​ ​the​ ​following​ ​expressions:
(a) p​ ​&times;​ ​p​ ​&times;​ ​p​ ​&times;​ ​p
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2014​ ​EOY​ ​Year​ ​10​ ​(104)
=​ ​______________
(b) 4n​ ​–​ ​n
=​ ​______________
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(c) 5n​ ​+​ ​4p​ ​–​ ​3n​ ​+​ ​p =​ ​______________
(d) 7n​ ​&times;​ ​8n
=​ ​______________
(e) (3n​4​)​2
=​ ​______________
(f)
(g)
2y
5
+
(ii) How​ ​many​ ​biscuits​ ​will​ ​be​ ​needed​ ​for​ ​20​ ​people?
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(iii) How​ ​many​ ​people​ ​were​ ​there​ ​at​ ​the​ ​last​ ​party​ ​if​ ​they​ ​provided​ ​175
biscuits?
y
3
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14n4 x
35nx
(b) The​ ​interest​ ​earned​ ​on​ ​an​ ​investment​ ​that​ ​pays​ ​interest​ ​annually​ ​can​ ​be
calculated​ ​using​ ​the​ ​formula
=​ ​______________
QUESTION​ ​FOUR
I=
(a) To​ ​cater​ ​an​ ​afternoon​ ​tea,​ ​it​ ​was​ ​decided​ ​to​ ​provide​ ​3​ ​biscuits​ ​per
person​ ​and​ ​supply​ ​an​ ​extra​ ​10​ ​biscuits​ ​in​ ​case​ ​of​ ​greedy​ ​people!
The​ ​following​ ​formula​ ​was​ ​used:
b​ ​=​ ​3n​ ​+​ ​10
P RT
100
Where​ ​I​ ​=​ ​amount​ ​of​ ​interest​ ​earned,
P​ ​=​ ​“principal”​ ​ ​(amount​ ​of​ ​money​ ​invested),​ ​R​ ​=​ ​the​ ​interest​ ​rate​ ​(as​ ​a
%)​ ​and​ ​T​ ​=​ ​amount​ ​of​ ​time​ ​in​ ​years.
(i) How​ ​much​ ​interest​ ​would​ ​be​ ​earned​ ​on​ ​a​ ​3​ ​year​ ​investment​ ​of​ ​\$30
000​ ​at​ ​4%​ ​per​ ​annum?
(i) Explain​ ​what​ ​b​ ​and​ ​n​ ​stand​ ​for
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2014​ ​EOY​ ​Year​ ​10​ ​(104)
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(ii) ​ ​If​ ​\$450​ ​interest​ ​was​ ​earned​ ​on​ ​a​ ​2​ ​year​ ​investment​ ​of​ ​\$2​ ​400,​ ​what
was​ ​the​ ​interest​ ​rate?
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(g) (p​ ​–​ ​6)​2​​ ​+​ ​6p
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QUESTION​ ​FIVE
Expand​ ​the​ ​following,​ ​simplify​ ​if​ ​necessary.
Fully​ ​factorise​ ​the​ ​following​ ​expressions
(h) 5p​ ​+​ ​10​ ​=​ ​_______________________
(a) 5(b​ ​+​ ​c)​ ​=​ ​ ​________________________
(i) 42n​ ​–​ ​12​ ​=​ ​______________________
(b) 12(n​ ​+​ ​4)​ ​=​ ​________________________
(j) x​2​​ ​–​ ​6x​ ​+​ ​8​ ​=​ ​____________________
(c) p(5p​ ​+​ ​1)​ ​=​ ​________________________
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(d) n(6​ ​–​ ​n)​ ​+​ ​2(n​ ​+​ ​3)
QUESTION​ ​SIX
For​ ​the​ ​following​ ​questions,​ ​write​ ​an​ ​algebraic​ ​equation
that​ ​fits​ ​the​ ​problem.​ ​ ​Solve​ ​it​ ​to​ ​find​ ​the​ ​answer.
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(a) ​ ​Given​ ​that​ ​the​ ​angles​ ​in​ ​a​ ​triangle​ ​add​ ​to​ ​180
degrees,​ ​what​ ​size​ ​(in​ ​degrees)​ ​is​ ​x​ ​in​ ​this​ ​triangle?
(e) 4(y​ ​+​ ​3)​ ​–​ ​3(y​ ​–​ ​1)
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(f) (x​ ​+​ ​4)(x​ ​–​ ​2)
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2014​ ​EOY​ ​Year​ ​10​ ​(104)
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(b) Jessica​ ​is​ ​given​ ​\$15​ ​per​ ​week​ ​and​ ​also​ ​got​ ​\$100​ ​from​ ​her​ ​Grandma​ ​for
her​ ​birthday.​ ​ ​If​ ​all​ ​of​ ​this​ ​money​ ​is​ ​put​ ​into​ ​her​ ​bank​ ​account,​ ​how
long​ ​has​ ​she​ ​been​ ​saving​ ​if​ ​she​ ​has​ ​\$520?
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(c) James’​ ​two​ ​friends’​ ​ages​ ​multiply​ ​to​ ​154.​ ​ ​One​ ​of​ ​them​ ​is​ ​two​ ​years
older​ ​than​ ​James​ ​and​ ​one​ ​of​ ​them​ ​is​ ​one​ ​year​ ​younger​ ​than​ ​James.
How​ ​old​ ​is​ ​James?
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(d) Find​ ​the​ ​sizes​ ​of​ ​both​ ​x​ ​and​ ​y,​ ​showing​ ​all​ ​working.
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Page​ ​12
2014​ ​EOY​ ​Year​ ​10​ ​(104)
NAME:
TEACHER:
YEAR​ ​10​ ​MATHEMATICS,​ ​2014
Section​ ​3​ ​Graphs
Answer​ ​ALL​ ​questions​ ​in​ ​the​ ​spaces​ ​provided​ ​in​ ​this​ ​booklet.​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Show​ ​ALL​ ​working.
For​ ​Assessor’s​ ​use​ ​only
Curriculum​ ​Level
==========================================================================
joining​ ​them​ ​in​ ​the​ ​order​ ​they​ ​are​ ​given.
SKILLS​ ​QUESTIONS
The​ ​first​ ​point​ ​and​ ​last​ ​point​ ​of​ ​each​ ​missing​ ​section​ ​has​ ​already​ ​been
plotted.
QUESTION​ ​ONE
Part​ ​of​ ​a​ ​dot-to-dot
graph​ ​picture​ ​is
shown​ ​above,​ ​but
two​ ​sections​ ​are
missing.​ ​ ​Complete
them​ ​by​ ​plotting
the​ ​points​ ​listed​ ​and
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Page​ ​13
Section​ ​1:​ ​ ​(3,​ ​1),​ ​(7,​ ​-2),​ ​(5,​ ​-3),​ ​(9,​ ​-7),​ ​(2,​ ​-7),​ ​(3,​ ​-10)
Section​ ​2:
(-5,​ ​-3),​ ​(-7,​ ​-2),​ ​(-3,​ ​1),​ ​(-6,​ ​2),​ ​(0,​ ​7)
QUESTION​ ​TWO
Give​ ​the​ ​next​ ​two​​ ​terms​ ​in​ ​each​ ​of​ ​these​ ​patterns
2014​ ​EOY​ ​Year​ ​10​ ​(104)
(a) 6,​ ​10,​ ​14,​ ​18,​ ​_____​ ​,​ ​______
(a) Complete​ ​the​ ​table​ ​for​ ​pattern​ ​numbers​ ​and​ ​numbers​ ​of​ ​matches.
Pattern​ ​(P)
1
2
3
4
5
(b) 15,​ ​30,​ ​45,​ ​60,​ ​______​ ​,​ ​______
(c) 11,​ ​8,​ ​5,​ ​2,​ ​______​ ​,​ ​______
Matches​ ​(M)
4
7
(b) Write​ ​a​ ​rule​​ ​linking​ ​the​ ​number​ ​of​ ​matches​ ​to​ ​the​ ​pattern​ ​number.
(d) ​ ​4,​ ​6,​ ​10,​ ​16,​ ​24,​ ​_______​ ​,​ ​_______
M​ ​=​ ​_____________________________
(e) n​ ​+​ ​4,​ ​2n​ ​+​ ​1,​ ​3n​ ​–​ ​2,​ ​4n​ ​–​ ​5,​ ​_________,
(c) How​ ​many​ ​matches​ ​would​ ​be​ ​required​ ​to​ ​make​ ​the​ ​tree​ ​that​ ​is​ ​Pattern
number​ ​23?
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QUESTION​ ​THREE
pattern​ ​out​ ​of​ ​matches.
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(d) What​ ​pattern​ ​number​ ​would​ ​require​ ​244​ ​matches​ ​to​ ​make?
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(e) If​ ​the​ ​rule​ ​in​ ​part​ ​(b)​ ​was​ ​plotted​ ​on​ ​a​ ​graph,​ ​what​ ​would​ ​its​ ​y​ ​intercept
be?
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2014​ ​EOY​ ​Year​ ​10​ ​(104)
QUESTION​ ​FOUR
Colin​ ​believes​ ​his​ ​pattern​ ​is​ ​MUCH​ ​better​ ​than​ ​Ellen’s.
4
5
(c) Work​ ​out​ ​a​ ​rule​ ​that​ ​connects​ ​the​ ​number​ ​of​ ​squares​ ​required​ ​to​ ​the
pattern​ ​number.
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(a) Draw​ ​the​ ​pattern​ ​4​ ​tree.
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QUESTION​ ​FIVE
(b) Complete​ ​the​ ​table​ ​showing​ ​the​ ​number​ ​of​ ​squares​ ​required​ ​for​ ​each
pattern.
Pattern​ ​(P)
1
2
3
MHJC
Squares​ ​(S)
6
12
Give​ ​the​ ​gradients​ ​of​ ​the​ ​lines​ ​shown​ ​above
Page​ ​15
2014​ ​EOY​ ​Year​ ​10​ ​(104)
At​ ​2pm​ ​one​ ​day,​ ​Petra​ ​left​ ​her​ ​house​ ​to​ ​walk​ ​and​ ​visit​ ​Anna.​ ​ ​Anna​ ​left​ ​her
house​ ​to​ ​go​ ​on​ ​a​ ​walk.​ ​ ​Kelly​ ​stayed​ ​home.​ ​ ​The​ ​graph​ ​shows​ ​the​ ​three
girls’​ ​movements.
QUESTION​ ​SIX
(a) Give​ ​the​ ​equations​ ​of​ ​each​ ​girl’s​ ​line.
Petra:
Anna:
Kelly:
(b) How​ ​fast​ ​does​ ​Petra​ ​walk?
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Here​ ​is​ ​the​ ​graph​ ​of​ ​the​ ​equation​ ​y​ ​=​ ​x​
2
On​ ​the​ ​same​ ​grid,​ ​draw​ ​and​ ​label​ ​the​ ​graphs​ ​of
(c) How​ ​far​ ​away​ ​from​ ​Anna​ ​does​ ​Kelly​ ​live?​ ​ ​How​ ​is​ ​this​ ​shown​ ​on​ ​the
graph?
(a) y​ ​=​ ​x2​​ ​ ​+​ ​3
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(b) y​ ​=​ ​-x​2​​ ​–​ ​2
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(c) If​ ​all​ ​the​ ​points​ ​on​ ​the​ ​graph​ ​y​ ​=​ ​x2​​ ​were​ ​moved​ ​1​ ​unit​ ​to​ ​the​ ​right,​ ​give
the​ ​equation​ ​of​ ​the​ ​new​ ​graph​ ​that​ ​would​ ​be​ ​formed.
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(e) Explain​ ​why​ ​Anna​ ​and​ ​Petra​ ​do​ ​not​ ​necessarily​ ​meet​ ​each​ ​other.
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QUESTION​ ​SEVEN
MHJC
(d) How​ ​fast​ ​does​ ​Anna​ ​walk?
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2014​ ​EOY​ ​Year​ ​10​ ​(104)
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2014​ ​EOY​ ​Year​ ​10​ ​(104)
NAME:
TEACHER:
YEAR​ ​10​ ​MATHEMATICS,​ ​2014
Section​ ​4​ ​Measurement
Answer​ ​ALL​ ​questions​ ​in​ ​the​ ​spaces​ ​provided​ ​in​ ​this​ ​booklet.​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Show​ ​ALL​ ​working.
For​ ​Assessor’s​ ​use​ ​only
Curriculum​ ​Level
========================================================================
SKILLS​ ​QUESTIONS
QUESTION​ ​ONE
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2014​ ​EOY​ ​Year​ ​10​ ​(104)
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(b) Cylinder
_________________
_________________
(a) The​ ​dimensions​ ​of​ ​Cherie’s​ ​bath​ ​towel​ ​are​ ​given​ ​above.​ ​ ​What​ ​is​ ​the
area​ ​of​ ​Cherie’s​ ​towel?
_________________
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(b) A​ ​towel​ ​weighs​ ​500g​ ​per​ ​square​ ​metre.​ ​ ​What​ ​does​ ​Cherie’s​ ​towel
weigh?
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QUESTION​ ​TWO
QUESTION​ ​THREE
Cherie​ ​doesn’t​ ​like​ ​her​ ​bath​ ​too​ ​hot.​ ​ ​She​ ​took​ ​the​ ​temperature​ ​of​ ​the​ ​bath
water​ ​before​ ​and​ ​after​ ​adding​ ​some​ ​cold​ ​to​ ​it​ ​(thermometer​ ​reads​ ​in
degrees​ ​Celsius).​ ​ ​What​ ​were​ ​the​ ​temperature​ ​readings?
Cherie​ ​is​ ​considering​ ​several​ ​different​ ​toothbrush​ ​holders.​ ​ ​Calculate​ ​the
volume​ ​of​ ​each​ ​one.
(a) Rectangular​ ​prism​ ​(cuboid)
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2014​ ​EOY​ ​Year​ ​10​ ​(104)
(b) Unusually,​ ​Cherie’s​ ​bath​ ​is​ ​a​ ​prism​ ​(it​ ​does​ ​not​ ​get​ ​narrower,​ ​change
shape​ ​or​ ​curve​ ​towards​ ​the​ ​bottom).​ ​ ​If​ ​Cherie​ ​gets​ ​into​ ​the​ ​bath,​ ​the
water​ ​level​ ​rises​ ​by​ ​22​ ​cm.​ ​ ​What​ ​volume​ ​does​ ​the​ ​part​ ​of​ ​Cherie
submerged​ ​by​ ​water​ ​have?
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First​ ​temperature:​ ​_________________
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Second​ ​temperature:​ ​ ​______________
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QUESTION​ ​FOUR
Cherie’s​ ​bath​ ​is​ ​shaped​ ​like​ ​a
semi-circle​ ​at​ ​either​ ​end.
rectangle​ ​with​ ​a
(a) If​ ​Cherie​ ​filled​ ​her
bath​ ​right​ ​to​ ​the​ ​top,
what​ ​would​ ​the
surface​ ​area​ ​of​ ​the
water​ ​be?
(c) Cherie​ ​decides​ ​to​ ​fill​ ​her​ ​bath​ ​to​ ​a​ ​depth​ ​of​ ​28​ ​cm​ ​(without​ ​her​ ​in​ ​it!).
She​ ​has​ ​read​ ​that​ ​her​ ​tap’s​ ​flow​ ​rate​ ​is​ ​0.8​ ​L/second.​ ​ ​How​ ​long​ ​will​ ​it
take​ ​her​ ​to​ ​fill​ ​her​ ​bath?
QUESTION​ ​FIVE
Give​ ​the​ ​conversions​ ​for​ ​these​ ​metric​ ​units:
(a) 49​ ​cm​ ​=​ ​_____________​ ​m
(b) 1.02​ ​kg​ ​=​ ​____________​ ​g
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(c) 154​ ​mm​ ​=​ ​____________​ ​cm
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(d) 24​ ​mL​ ​=​ ​______________​ ​L
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QUESTION​ ​SIX
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Circle​ ​the​ ​most​ ​sensible​ ​measurement
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(a) Width​ ​of​ ​a​ ​bathroom​ ​sink​ ​might​ ​be:
2014​ ​EOY​ ​Year​ ​10​ ​(104)
47​ ​m​ ​ ​ ​ ​ ​ ​ ​ ​47​ ​cm​ ​ ​ ​ ​ ​ ​ ​47​ ​mm​ ​ ​ ​ ​ ​ ​ ​ ​47​ ​L
(b) A​ ​bath​ ​soap​ ​might​ ​weigh:
90​ ​cm​ ​ ​ ​ ​ ​ ​90​ ​kg​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​90​ ​g​ ​ ​ ​ ​ ​ ​ ​ ​ ​90​ ​mg
(c) Height​ ​of​ ​the​ ​bathroom​ ​door​ ​might​ ​be:
190​ ​cm​ ​ ​ ​ ​ ​190​ ​kg​ ​ ​ ​ ​ ​ ​190​ ​mm​ ​ ​ ​ ​ ​190​ ​m
(d) The​ ​area​ ​of​ ​a​ ​face​ ​cloth​ ​might​ ​be:
​ ​ ​ ​ ​625​ ​m2​​ ​ ​ ​ ​ ​ ​ ​625​ ​mL​ ​ ​ ​ ​ ​625​ ​cm​2​​ ​ ​ ​ ​625​ ​mm
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2014​ ​EOY​ ​Year​ ​10​ ​(104)
QUESTION​ ​SEVEN
Cherie​ ​is​ ​planning​ ​to​ ​get​ ​a​ ​new​ ​surface​ ​covering​ ​for​ ​her​ ​bathroom​ ​floor.​ ​ ​It
is​ ​only​ ​laid​ ​on​ ​the​ ​shaded​ ​area​ ​of​ ​the​ ​floor​ ​plan​ ​(not​ ​under​ ​the​ ​bath​ ​area​ ​or
vanity).​ ​ ​All​ ​measurements​ ​are​ ​in​ ​mm.
(a) ​ ​What​ ​is​ ​the​ ​perimeter​ ​of​ ​Cherie’s​ ​whole​ ​bathroom?
________________________________________
________________________________________
(c) Cherie’s​ ​flooring​ ​options​ ​are​ ​vinyl​ ​and​ ​laminate.
Vinyl​ ​comes​ ​in​ ​2m​ ​wide​ ​rolls​ ​and​ ​is​ ​priced​ ​at​ ​\$90​ ​for​ ​every​ ​linear
metre,​ ​plus​ ​\$120​ ​laying​ ​costs.​ ​ ​A​ ​single​ ​piece​ ​of​ ​vinyl​ ​would​ ​be​ ​used
(leaving​ ​some​ ​excess​ ​“off-cuts”)
Laminate​ ​costs​ ​\$180/m​2​​ ​of​ ​floor​ ​area.​ ​ ​This​ ​price​ ​includes​ ​installation.
Show​ ​(using​ ​calculations)​ ​which​ ​flooring​ ​option​ ​will​ ​be​ ​cheapest​ ​for
Cherie.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
(b) What​ ​is​ ​the​ ​area​ ​of​ ​the​ ​floor​ ​that​ ​is​ ​being​ ​resurfaced?
________________________________________
________________________________________
MHJC
Page​ ​22
________________________________________
________________________________________
________________________________________
QUESTION​ ​EIGHT
2014​ ​EOY​ ​Year​ ​10​ ​(104)
________________________________________
QUESTION​ ​NINE
Cherie’s​ ​friends​ ​know​ ​that​ ​she​ ​likes​ ​candles​ ​and​ ​soaps​ ​for​ ​her​ ​bathroom.
(a) One​ ​friend​ ​gave​ ​her​ ​this​ ​soap,​ ​which​ ​is​ ​a​ ​trapezium​ ​prism.
A​ ​toilet​ ​roll​ ​has​ ​the​ ​following​ ​dimensions:​ ​ ​width​ ​of​ ​11​ ​cm,​ ​diameter​ ​of
roll​ ​=​ ​10​ ​cm,​ ​diameter​ ​of​ ​cardboard​ ​tube​ ​=​ ​4​ ​cm.
(a) What​ ​is​ ​the​ ​volume​ ​of​ ​paper​ ​in​ ​the​ ​roll?
________________________________________
________________________________________
________________________________________
(b) The​ ​roll​ ​has​ ​200​ ​sheets​ ​of​ ​toilet​ ​paper,​ ​each​ ​12​ ​cm​ ​long.​ ​ ​If​ ​it​ ​was
unrolled,​ ​what​ ​would​ ​the​ ​total​ ​area​ ​of​ ​the​ ​toilet​ ​paper​ ​be?
________________________________________
MHJC
Page​ ​23
(i) What​ ​is​ ​the​ ​area​ ​of​ ​one​ ​of​ ​the​ ​soap’s​ ​trapezium​ ​shaped​ ​faces?
_____________________________________
_____________________________________
2014​ ​EOY​ ​Year​ ​10​ ​(104)
(c) Cherie​ ​and​ ​her​ ​friends​ ​have​ ​started​ ​making​ ​“bath​ ​bombs”.​ ​ ​These​ ​are
spherical​ ​in​ ​shape​ ​and​ ​have​ ​a​ ​diameter​ ​of​ ​7​ ​cm.
(ii) What​ ​is​ ​the​ ​volume​ ​of​ ​the​ ​soap?
_____________________________________
(b) Cherie​ ​was​ ​also​ ​given​ ​this​ ​candle.​ ​ ​It​ ​has​ ​a​ ​square​ ​base​ ​and​ ​is
pyramid-shaped.
(i)
What​ ​is​ ​the​ ​volume​ ​of​ ​each​ ​“bath​ ​bomb”?
_____________________________________
_____________________________________
(i) What​ ​is​ ​the​ ​volume​ ​of​ ​the​ ​candle?
_____________________________________
_____________________________________
_____________________________________
(ii) Sadly,​ ​the​ ​candle​ ​broke​ ​into​ ​pieces​ ​before​ ​Cherie​ ​could​ ​light​ ​it.​ ​ ​She
melted​ ​down​ ​the​ ​wax​ ​and​ ​created​ ​a​ ​new​ ​candle​ ​shaped​ ​like​ ​a​ ​cube.
What​ ​will​ ​the​ ​dimensions​ ​of​ ​the​ ​new​ ​candle​ ​be?
_____________________________________
(ii) Cherie​ ​has​ ​a​ ​cuboid​ ​shaped​ ​container​ ​of​ ​bath​ ​bomb​ ​mix.​ ​ ​Its
length​ ​and​ ​width​ ​are​ ​27​ ​cm​ ​and​ ​22​ ​cm​ ​respectively.​ ​ ​When​ ​the
mixture​ ​is​ ​level,​ ​the​ ​container​ ​is​ ​filled​ ​to​ ​a​ ​depth​ ​of​ ​10.4​ ​cm.
How​ ​many​ ​bath​ ​bombs​ ​can​ ​Cherie​ ​make?
_____________________________________
_____________________________________
_____________________________________
_____________________________________
_____________________________________
MHJC
Page​ ​24
2014​ ​EOY​ ​Year​ ​10​ ​(104)
NAME:
TEACHER:
YEAR​ ​10​ ​MATHEMATICS,​ ​2014
Section​ ​5​ ​Trigonometry
Answer​ ​ALL​ ​questions​ ​in​ ​the​ ​spaces​ ​provided​ ​in​ ​this​ ​booklet.​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Show​ ​ALL​ ​working.
For​ ​Assessor’s​ ​use​ ​only
Curriculum​ ​Level
==========================================================================
SKILLS​ ​QUESTIONS
___________________________________
QUESTION​ ​ONE
Use​ ​your​ ​calculator​ ​to​ ​find​ ​the​ ​values​ ​of​ ​n​ ​or​ ​A​.​ ​Record​ ​your​ ​working.
(a) 4​2​​ ​+​ ​72​​ ​ ​=​ ​n2​
___________________________________
___________________________________
(d) 9​ ​&times;​ ​n​ ​=​ ​cos​ ​52
___________________________________
(b) n2​​ ​ ​+​ ​82​​ ​ ​=​ ​12​2
MHJC
(c) n​ ​=​ ​sin​ ​35​ ​&times;​ ​8
Page​ ​25
2014​ ​EOY​ ​Year​ ​10​ ​(104)
Complete​ ​this​ ​diagram​ ​for​ ​a​ ​different​​ ​triangle.​ ​Use​ ​it​ ​to​ ​work​ ​out​ ​the​ ​size
of​ ​side​ ​x.
(e) 4​ ​&divide;​ ​7​ ​=​ ​tan​ ​A
___________________________________
QUESTION​ ​TWO
A​ ​teacher​ ​gave​ ​their​ ​student​ ​the
following​ ​diagram​ ​to​ ​reinforce
Pythagoras’​ ​theorem.
a​2​​ ​+​ ​b2​​ ​ ​=​ ​c2​
The​ ​values​ ​inside​ ​the​ ​triangle​ ​are​ ​side​ ​lengths.
MHJC
Page​ ​26
2014​ ​EOY​ ​Year​ ​10​ ​(104)
QUESTION
THREE
A​ ​boat​ ​is​ ​sailing
due​ ​East​ ​of​ ​a
plane​ ​is​ ​due
North​ ​of​ ​the
beacon.​ ​ ​The
plane​ ​and​ ​boat
are​ ​18​ ​km​ ​apart
and​ ​the​ ​boat​ ​is
10​ ​km​ ​from​ ​the
beacon.
_______________________________________
_______________________________________
_______________________________________
_______________________________________
QUESTION​ ​FOUR
A​ ​windsurfer​ ​sails​ ​a​ ​course​ ​marked​ ​by​ ​three​ ​buoys​ ​that​ ​form​ ​a​ ​right-angled
triangle.
The​ ​first​ ​leg​ ​of​ ​the​ ​course​ ​is​ ​35​ ​m.​ ​ ​Calculate​ ​x​ ​and​ ​y,​ ​the​ ​lengths​ ​of​ ​the
other​ ​two​ ​legs.
(a) How​ ​far​ ​North​ ​of​ ​the​ ​beacon​ ​is​ ​the​ ​plane?
_______________________________________
_______________________________________
(b) What​ ​is​ ​the​ ​angle​ ​between​ ​the​ ​boat’s​ ​path​ ​and​ ​a​ ​path​ ​that​ ​would​ ​take​ ​it
towards​ ​the​ ​plane?​ ​ ​(The​ ​angle​ ​indicated​ ​on​ ​the​ ​diagram)
_______________________________________
_______________________________________
(c) A​ ​bearing​ ​is​ ​an​ ​angle​ ​from​ ​north.​ ​ ​Calculate​ ​the
bearing​ ​of​ ​the​ ​boat​ ​from​ ​the​ ​plane’s​ ​position.
MHJC
Page​ ​27
_______________________________________
2014​ ​EOY​ ​Year​ ​10​ ​(104)
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
QUESTION​ ​FIVE
A​ ​kayak’s​ ​sail​ ​is​ ​shaped​ ​like​ ​an​ ​isosceles​ ​triangle.​ ​ ​If​ ​it​ ​is​ ​1.8​ ​m​ ​wide​ ​at​ ​the
top​ ​and​ ​the​ ​equal​ ​sides​ ​are​ ​3​ ​m,​ ​calculate​ ​the​ ​height​ ​of​ ​the​ ​sail.
(b) Calculate​ ​A,​ ​the​ ​angle​ ​at​ ​the​ ​top​ ​of​ ​the​ ​mainsail.
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
(c) Calculate​ ​y,​ ​a​ ​length​ ​on​ ​the​ ​smaller​ ​sail.
QUESTION​ ​SIX
_______________________________________
A​ ​boat​ ​has​ ​two
right-angled
triangle-shaped
sails.​ ​ ​The​ ​mainsail
is​ ​8m​ ​wide​ ​and​ ​the
smaller​ ​sail​ ​is​ ​12​ ​m
high.
_______________________________________
_______________________________________
(a) Calculate​ ​x,​ ​the
height​ ​of​ ​the
mainsail.
MHJC
Page​ ​28
2014​ ​EOY​ ​Year​ ​10​ ​(104)
QUESTION​ ​SEVEN
A​ ​student​ ​tried​ ​to​ ​design​ ​a​ ​triangular​ ​windsurfing​ ​sail​ ​(these​ ​are​ ​usually
curved!).​ ​ ​The​ ​placement​ ​of​ ​the​ ​boom​ ​splits​ ​the​ ​sail​ ​into​ ​two​ ​right-angled
triangles:​ ​ ​ABC​ ​and​ ​BDC.​ ​ ​AD​ ​=​ ​4.2​ ​m
NB:​ ​ ​this​ ​sail​ ​is​ ​unlikely​ ​to​ ​be​ ​practical​ ​in​ ​real​ ​life!
(a) Calculate​ ​AB,​ ​the​ ​length​ ​of​ ​the​ ​sail​ ​from​ ​the​ ​top​ ​to​ ​the​ ​outer​ ​edge​ ​on
the​ ​boom.
_______________________________________
height.​ ​ ​The​ ​base​ ​(BC)​ ​is​ ​2.39​ ​m,​ ​the​ ​perimeter​ ​of​ ​ABC
is​ ​8.2​ ​m​ ​and​ ​the​ ​area​ ​of​ ​ABC​ ​is​ ​1.61325​ ​m2​​ .​ ​ ​The​ ​angle
CAB​ ​is​ ​20​o​.​ ​ ​Calculate​ ​the​ ​lengths​ ​of​ ​AB​ ​and​ ​BC.
Clearly​ ​state​ ​what​ ​you​ ​are​ ​working​ ​out​ ​at​ ​each​ ​step​ ​and
show​ ​your​ ​calculations.
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
(b) Calculate​ ​angle​ ​CDB.​ ​ ​(Hint,​ ​you​ ​may​ ​find​ ​that​ ​first​ ​calculating​ ​the
length​ ​AC​ ​may​ ​help​ ​you).
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
QUESTION​ ​EIGHT
_______________________________________
Triangle​ ​ABC​ ​is​ ​a
non-right​ ​angled
triangle.​ ​ ​BD​ ​is​ ​its
MHJC
Page​ ​29
_______________________________________
2014​ ​EOY​ ​Year​ ​10​ ​(104)
QUESTION​ ​NINE
The​ ​angle​ ​of​ ​elevation​ ​from​ ​a​ ​boat​ ​to​ ​a​ ​plane​ ​is​ ​29​o​.​ ​ ​The​ ​relative​ ​positions
of​ ​the​ ​boat,​ ​plane​ ​and​ ​a​ ​radio​ ​beacon​ ​on​ ​the​ ​horizontal​ ​are​ ​given​ ​in​ ​the
second​ ​diagram.
Calculate​ ​the​ ​height
(altitude)​ ​at​ ​which​ ​the
plane​ ​is​ ​flying.
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
MHJC
Page​ ​30
2014​ ​EOY​ ​Year​ ​10​ ​(104)
NAME:
TEACHER:
YEAR​ ​10​ ​MATHEMATICS,​ ​2014
Section​ ​6​ ​Geometry
Answer​ ​ALL​ ​questions​ ​in​ ​the​ ​spaces​ ​provided​ ​in​ ​this​ ​booklet.​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Show​ ​ALL​ ​working.
For​ ​Assessor’s​ ​use​ ​only
Curriculum​ ​Level
===========================================================================
QUESTION​ ​ONE
(a) ​ ​Draw​ ​a​ ​different​ ​octomino​ ​that​ ​has​ ​one​ ​line​ ​of​ ​symmetry.
Here​ ​are​ ​three​ ​“octominoes”.​ ​ ​An​ ​octomino​ ​is​ ​made​ ​of​ ​8​ ​squares,​ ​all​ ​of
which​ ​are​ ​attached​ ​by​ ​a​ ​full​ ​side​ ​to​ ​at​ ​least​ ​one​ ​other
square.​ ​ ​These​ ​three​ ​all​ ​have​ ​one​ ​line​ ​of​ ​symmetry.
(b) ​ ​Draw​ ​an​ ​octomino​ ​that​ ​has​ ​two​ ​lines
of​ ​symmetry​ ​and​ ​show​ ​these​ ​lines.
MHJC
Page​ ​31
2014​ ​EOY​ ​Year​ ​10​ ​(104)
A​ ​different​ ​octomino​ ​is​ ​shown​ ​on​ ​the​ ​grid​ ​below.
(c)
Redraw​ ​this​ ​octomino​ ​to​ ​show​ ​what​ ​it​ ​would​ ​look​ ​like:
(i)
Rotated​ ​90​o​​ ​clockwise​ ​about​ ​point​ ​P
(ii)
Reflected​ ​in​ ​the​ ​mirror-line​ ​m
(iii) ​ ​Enlarged​ ​by​ ​a​ ​scale​ ​factor​ ​of​ -​​ 2​ ​with​ ​centre​ ​P.
QUESTION​ ​TWO
An​ ​aeroplane​ ​has
gone​ ​missing!​ ​ ​Use
compass
constructions​ ​and
different​ ​areas​ ​that
teams​ ​are​ ​searching.
Label​ ​these​ ​loci
A-C.
(a) Team​ ​A​ ​is
searching​ ​within
200​ ​km​ ​of​ ​Irakleion.
(b) Team​ ​B​ ​is
searching​ ​all​ ​the
places​ ​that​ ​are​ ​equal
distance​ ​from​ ​Patra
and​ ​Athens.
(c) Team​ ​C​ ​was​ ​told
either​ ​been​ ​travelling​ ​from​ ​Izmir​ ​to​ ​Volos​ ​or​ ​from​ ​Izmir​ ​to
Thessaloniki.​ ​ ​They​ ​have​ ​been​ ​told​ ​to​ ​search​ ​along​ ​the​ ​path​ ​halfway
between​ ​these​ ​two​ ​routes.
MHJC
Page​ ​32
2014​ ​EOY​ ​Year​ ​10​ ​(104)
D​ ​=​ ​___________________________
(d) Name​ ​the​ ​city​ ​that​ ​is​ ​nearly​ ​due​ ​North​ ​of​ ​Volos.
__________________________________
QUESTION​ ​FOUR
(e) Which​ ​city​ ​is​ ​approximately​ ​North-East​ ​of​ ​Athens?
(a) ​ ​How​ ​many​ ​cubes​ ​would​ ​it​ ​take​ ​to​ ​make​ ​this​ ​object?
__________________________________
__________________
QUESTION​ ​THREE
This​ ​Venn
diagram​ ​was
drawn​ ​up​ ​to
group
(b) Sketch​ ​an​ ​isometric​ ​drawing​ ​from​ ​the​ ​plan​ ​view​ ​below.
quadrilaterals​ ​(4​ ​sided​ ​shapes).​ ​ ​Try​ ​to​ ​identify​ ​a​ ​quadrilateral​ ​for​ ​each​ ​of
A​ ​–​ ​E.​ ​ ​Note​ ​that​ ​if​ ​a​ ​label​ ​is​ ​outside​ ​a​ ​circle,​ ​it​ ​does​ ​not​ ​fit​ ​the​ ​description
(e.g.​ ​D​ ​does​ ​NOT​ ​have​ ​parallel​ ​sides​ ​or​ ​right​ ​angles).
A​ ​=​ ​___________________________
B​ ​=​ ​___________________________
C​ ​=​ ​___________________________
MHJC
Page​ ​33
2014​ ​EOY​ ​Year​ ​10​ ​(104)
QUESTION​ ​FIVE
QUESTION​ ​SIX
In​ ​a​ ​fantasy​ ​computer​ ​game,​ ​there​ ​are
many​ ​dangers.​ ​ ​In​ ​this​ ​picture,​ ​1​ ​cm​ ​=​ ​1
m.
If​ ​you​ ​are​ ​within​ ​3m​ ​of​ ​the​ ​cave,​ ​a​ ​dragon
will​ ​attack​ ​you.
If​ ​you​ ​get​ ​closer​ ​to​ ​the​ ​robot​ ​than​ ​to​ ​the
cave,​ ​the​ ​robot​ ​will​ ​attack​ ​you.
The​ ​wizard​ ​shoots​ ​his​ ​spells​ ​at​ ​you​ ​when
you​ ​are​ ​within​ ​5​ ​m​ ​of​ ​him.
Use​ ​compass​ ​constructions​ ​to​ ​show​ ​the
places​ ​where​ ​you​ ​are​ ​threatened​ ​by​ ​two
dangers.
QUESTION​ ​SEVEN
Sketch​ ​a​ ​net​ ​for​ ​a​ ​triangular​ ​prism.
For​ ​the​ ​object​ ​above,​ ​the​ ​front​ ​view​ ​is​ ​drawn​ ​below.
Draw​ ​the​ ​Right​ ​and​ ​Top​ ​views.
MHJC
Page​ ​34
2014​ ​EOY​ ​Year​ ​10​ ​(104)
QUESTION​ ​NINE
An​ ​octomino​ ​shaped​ ​like​ ​the​ ​number​ ​one​ ​is​ ​used​ ​to​ ​make​ ​a​ ​design.
QUESTION​ ​EIGHT
(a) This​ ​octomino​ ​has​ ​rotational​ ​symmetry.​ ​ ​What​ ​is​ ​its​ ​order​ ​of​ ​rotation?
The​ ​original
shape​ ​is​ ​slightly
darker​ ​than​ ​the
others.
Write​ ​a​ ​set​ ​of
instructions​ ​for
how​ ​to​ ​generate
the​ ​WHOLE
design
step-by-step,
using
transformations.​ ​ ​You​ ​may​ ​draw​ ​on​ ​and​ ​label​ ​and​ ​points​ ​or​ ​mirror​ ​lines
you​ ​wish​ ​to​ ​use.​ ​ ​ ​ ​You​ ​may​ ​find​ ​it​ ​helpful​ ​to​ ​number​ ​each​ ​“1”​ ​to​ ​show
which​ ​order​ ​they​ ​should​ ​appear​ ​in.
____________________________
(b)
Draw​ ​a​ ​different​ ​octomino​ ​that​ ​has​ ​rotational​ ​symmetry​ ​and​ ​state
its​ ​order​ ​of​ ​rotation.
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
MHJC
Page​ ​35
2014​ ​EOY​ ​Year​ ​10​ ​(104)
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
MHJC
Page​ ​36
2014​ ​EOY​ ​Year​ ​10​ ​(104)
MHJC
Page​ ​37
2014​ ​EOY​ ​Year​ ​10​ ​(104)
NAME:
TEACHER:
YEAR​ ​10​ ​MATHEMATICS,​ ​2014
Section​ ​7​ ​Angles
Answer​ ​ALL​ ​questions​ ​in​ ​the​ ​spaces​ ​provided​ ​in​ ​this​ ​booklet.
Show​ ​ALL​ ​working
For​ ​Assessor’s​ ​use​ ​only
Curriculum​ ​Level
==========================================================================
QUESTION​ ​ONE
(a) Draw​ ​a​ ​cross​ ​inside​ ​one​ ​acute​​ ​angle.
(b) What​ ​size​ ​is​ ​angle​ ​ADC?
____________________________________
(c) The​ ​angle​ ​to​ ​the​ ​far​ ​right​ ​can​ ​be​ ​called​ ​ABC.​ ​ ​Give​ ​another​ ​three​ ​letter
name​ ​for​ ​this​ ​angle.
____________________________________
In​ ​the​ ​figure​ ​above…
MHJC
Page​ ​38
2014​ ​EOY​ ​Year​ ​10​ ​(104)
(d) Put​ ​a​ ​tick​ ​inside​ ​an​ ​obtuse​ ​angle.
(e) What​ ​would​ ​the​ ​angles​ ​inside​ ​the​ ​shape​ ​ABCD​ ​add​ ​to?
____________________________________
(c) Size​ ​of​ ​angle​ ​AOB?​ ​___________________
(d) Size​ ​of​ ​angle​ ​BOC?​ ​___________________
QUESTION​ ​THREE
Give​ ​the​ ​size​ ​of​ ​the​ ​marked​ ​angles.​ ​ ​Give​ ​a​ ​geometric​ ​reason​ ​for​ ​each​ ​one
if​ ​you​ ​can.
____________________________________
QUESTION​ ​TWO
(a)
A​ ​=
_________________
(a) Size​ ​of​ ​angle?​ ​ ​_____________________
because​ ​_______________________________________
_______________________________________
(b)
A​ ​=​ ​_________________
because​ ​_______________________________________
(b) Size​ ​of​ ​angle​ ​AOC?​ ​___________________
MHJC
Page​ ​39
_______________________________________
2014​ ​EOY​ ​Year​ ​10​ ​(104)
B​ ​=​ ​_________________
_______________________________________
because​ ​_______________________________________
_______________________________________
_______________________________________
_______________________________________
QUESTION​ ​FOUR
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
This​ ​diagram​ ​shows​ ​an​ ​isosceles​ ​triangle​ ​situated​ ​between​ ​parallel​ ​lines.
QUESTION​ ​FIVE
Calculate​ ​the​ ​size​ ​of​ ​angle​ ​E.​ ​ ​You​ ​may​ ​need​ ​to​ ​first​ ​work​ ​out​ ​some​ ​of​ ​the
angles​ ​marked​ ​a-d.​ ​ ​Give​ ​a​ ​geometric​ ​reason​ ​and​ ​clearly​ ​identify​ ​each
angle​ ​you​ ​calculate.
_______________________________________
_______________________________________
_______________________________________
MHJC
Page​ ​40
2014​ ​EOY​ ​Year​ ​10​ ​(104)
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
QUESTION​ ​SIX
Calculate​ ​the​ ​size​ ​of​ ​angle​ ​A.
You​ ​may​ ​need​ ​to​ ​calculate​ ​other​ ​angles​ ​in​ ​the​ ​diagram​ ​to​ ​do​ ​so.​ ​ ​Label​ ​any
angle​ ​that​ ​you​ ​use​ ​and​ ​give​ ​a​ ​geometric​ ​reason​ ​for​ ​its​ ​size.
Complete​ ​the​ ​proof​ ​to​ ​show​ ​that​ ​ABC​ ​and​ ​ADE​ ​are​ ​similar​ ​triangles.
Hint:​ ​You​ ​may​ ​need​ ​to​ ​extend​ ​the​ ​length​ ​of​ ​one​ ​of​ ​the​ ​existing​ ​lines.
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
MHJC
Page​ ​41
2014​ ​EOY​ ​Year​ ​10​ ​(104)
QUESTION​ ​SEVEN
Angles​ ​ABC​ ​and​ ​ADE​ ​are​ ​equal​ ​because:
______________________________________
______________________________________
Angles​ ​ACB​ ​and​ ​AED​ ​are​ ​equal​ ​because:
______________________________________
______________________________________
Angles​ ​BAC​ ​is​ ​also​ ​Angle
______________________________________
Because​ ​triangles​ ​ABC​ ​and​ ​ADE​ ​have
______________________________________
______________________________________
Some​ ​triangles​ ​have​ ​been​ ​created​ ​by​ ​connecting​ ​points​ ​A,​ ​B,​ ​C​ ​on​ ​the
circumference​ ​of​ ​a​ ​circle​ ​to​ ​the​ ​circle​ ​centre​ ​and​ ​also​ ​to​ ​each​ ​other.​ ​ ​Each
line​ ​to​ ​the​ ​centre​ ​is​ ​of​ ​equal​ ​length.
Two​ ​of​ ​the​ ​angles​ ​in​ ​this​ ​diagram​ ​have​ ​been​ ​given.​ ​ ​By​ ​calculating​ ​angles
a-e​ ​(with​ ​geometric​ ​reasons),​ ​show​ ​that​ ​angle​ ​e​ ​is​ ​twice​ ​as​ ​big​ ​as​ ​angle
ACB.
they​ ​are​ ​similar​ ​triangles.
a​ ​=​ ​__________​ ​because​ ​___________________
_______________________________________
b​ ​=​ ​__________​ ​because​ ​___________________
_______________________________________
MHJC
Page​ ​42
2014​ ​EOY​ ​Year​ ​10​ ​(104)
c​ ​=​ ​__________​ ​because​ ​___________________
QUESTION​ ​EIGHT
_______________________________________
d​ ​=​ ​__________​ ​because​ ​___________________
_______________________________________
e​ ​=​ ​__________​ ​because​ ​___________________
_______________________________________
Conclusion:​ ​ ​____________________________
_______________________________________
Given​ ​that​ ​angle​ ​EBD​ ​is​ ​size​ ​x​,​ ​give​ ​the​ ​sizes​ ​of​ ​the​ ​other​ ​angles​ ​in​ ​the
triangle​ ​in​ ​terms​ ​of​ ​x​.
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
MHJC
Page​ ​43
2014​ ​EOY​ ​Year​ ​10​ ​(104)
_______________________________________
_______________________________________
_______________________________________
_______________________________________
MHJC
Page​ ​44
2014​ ​EOY​ ​Year​ ​10​ ​(104)
NAME:
TEACHER:
YEAR​ ​10​ ​MATHEMATICS,​ ​2014
Section​ ​8​ ​Statistics
Answer​ ​ALL​ ​questions​ ​in​ ​the​ ​spaces​ ​provided​ ​in​ ​this​ ​booklet.​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Show​ ​ALL​ ​working.
For​ ​Assessor’s​ ​use​ ​only
Curriculum​ ​Level
==========================================================================
QUESTION​ ​ONE
_______________________________________
(a) Describe​ ​the
_______________________________________
long-term​ ​trend​ ​in
percentage​ ​of​ ​cars
exceeding​ ​the​ ​speed
limit​ ​in​ ​urban​ ​areas.
MHJC
Page​ ​45
_______________________________________
2014​ ​EOY​ ​Year​ ​10​ ​(104)
(b) Sam​ ​thinks​ ​the​ ​trends​ ​for​ ​the​ ​two​ ​speed​ ​limits​ ​show​ ​similar
movements.​ ​ ​What​ ​kind​ ​of​ ​graph​ ​could​ ​he​ ​use​ ​to​ ​look​ ​for​ ​a​ ​correlation
between​ ​the​ ​two​ ​sets​ ​of​ ​data?
_______________________________________
(c) Explain​ ​why​ ​the​ ​data​ ​for​ ​this​ ​graph​ ​is​ ​most​ ​likely​ ​based​ ​on​ ​samples​.
Suggest​ ​how​ ​it​ ​may​ ​have​ ​been​ ​collected.
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
(d) Explain​ ​why​ ​we​ ​can’t​ ​use​ ​this​ ​graph​ ​to​ ​find​ ​how​ ​many​ ​cars​ ​exceeded
the​ ​speed​ ​limit​ ​in​ ​2011.
Sam​ ​managed​ ​to​ ​obtain​ ​some​ ​data​ ​about​ ​car​ ​speeds​ ​in​ ​urban​ ​areas​ ​(where
the​ ​speed​ ​limit​ ​is​ ​50​ ​km/h).
(a) Is​ ​speed​ ​discrete​ ​or​ ​continuous​ ​data?
_______________________________________
(b) How​ ​does​ ​the​ ​graph​ ​show​ ​that​ ​all​ ​speeds​ ​were​ ​rounded?​ ​ ​ ​What​ ​were
they​ ​rounded​ ​to?
_______________________________________
_______________________________________
_______________________________________
(c) Describe​ ​features​ ​of​ ​the​ ​distribution​ ​of​ ​speeds.
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
(e) Estimate​ ​the​ ​percentage​ ​of​ ​cars​ ​that​ ​will​ ​break​ ​the​ ​rural​ ​speed​ ​limit​ ​in
2014.
_______________________________________
_______________________________________
_______________________________________
QUESTION​ ​TWO
MHJC
Page​ ​46
2014​ ​EOY​ ​Year​ ​10​ ​(104)
(d) In​ ​this​ ​sample,​ ​did​ ​the​ ​majority​ ​of​ ​cars​ ​stay​ ​within​ ​the​ ​speed​ ​limit?
Give​ ​evidence​ ​for​ ​your​ ​claim.
_______________________________________
_______________________________________
Mean
Mode
Lower​ ​quartile
Upper​ ​quartile
(c) Sketch​ ​a​ ​box​ ​plot​ ​of​ ​the​ ​data​ ​above​ ​the​ ​scale​ ​below
_______________________________________
_______________________________________
_______________________________________
QUESTION​ ​THREE
Sam’s​ ​school​ ​is​ ​loaned​ ​a​ ​speed​ ​radar​ ​which​ ​records​ ​car​ ​speeds​ ​to​ ​the
nearest​ ​km/h.​ ​ ​Sam​ ​uses​ ​it​ ​for​ ​10​ ​minutes​ ​at​ ​the​ ​school​ ​gate​ ​and​ ​records
the​ ​following​ ​speeds:
52,​ ​48,​ ​55,​ ​58,​ ​53,​ ​50,​ ​49,​ ​52,​ ​53,​ ​55,​ ​59,​ ​56,​ ​51,​ ​53,​ ​53,​ ​57,​ ​54,​ ​52,​ ​56,​ ​59,
51,​ ​50,​ ​49,​ ​50,​ ​53.
(a) Create​ ​a​ ​dot​ ​plot​ ​for​ ​the​ ​data​ ​given​ ​above,​ ​using​ ​the​ ​scale​ ​below
(d) Comment​ ​on
whether​ ​Sam’s
sample​ ​of​ ​cars​ ​is​ ​random.​ ​ ​For​ ​what​ ​reasons​ ​might​ ​you​ ​question
whether​ ​it​ ​is​ ​representative​ ​of​ ​all​ ​cars​ ​that​ ​pass​ ​by​ ​the​ ​school​ ​entrance?
_______________________________________
_______________________________________
_______________________________________
_______________________________________
(b) Complete​ ​the
table​ ​of​ ​summary
statistics​ ​for​ ​the​ ​data.
_______________________________________
_______________________________________
_______________________________________
Range
Median
MHJC
QUESTION​ ​FOUR
Page​ ​47
2014​ ​EOY​ ​Year​ ​10​ ​(104)
Sam’s​ ​friend​ ​Katrina​ ​suggested​ ​that​ ​cars​ ​may​ ​travel​ ​faster​ ​than​ ​Sam​ ​thinks
because​ ​they​ ​will​ ​slow​ ​down​ ​when​ ​they​ ​see​ ​the​ ​speed​ ​radar.​ ​ ​She​ ​proposes
an​ ​experiment:​ ​she​ ​and​ ​Sam​ ​will​ ​BOTH​ ​record​ ​the​ ​speed​ ​of​ ​the​ ​cars​ ​–​ ​Sam
standing​ ​where​ ​he​ ​is​ ​clearly​ ​visible​ ​and​ ​Katrina​ ​30​ ​m​ ​away,​ ​hiding​ ​behind
a​ ​bush.
(a) Describe​ ​in​ ​words​ ​the​ ​relationship​ ​between​ ​the​ ​two​ ​speed​ ​readings.
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
QUESTION​ ​FIVE
Sam​ ​decides​ ​to​ ​hold​ ​a​ ​survey​ ​to​ ​find​ ​out​ ​why​ ​a​ ​lot​ ​of​ ​people​ ​speed​ ​past​ ​the
school​ ​entrance.​ ​ ​He​ ​puts​ ​a​ ​survey​ ​in​ ​every​ ​letterbox​ ​he​ ​passes​ ​on​ ​his​ ​way
home​ ​from​ ​school.​ ​ ​The​ ​survey​ ​includes​ ​these​ ​questions:
_______________________________________
1. What​ ​speed​ ​do​ ​you​ ​normally​ ​drive​ ​at​ ​when​ ​passing​ ​Prince​ ​Albert
High​ ​School?
2. How​ ​often​ ​do​ ​you​ ​break​ ​the​ ​speed​ ​limit?
3. Why​ ​do​ ​you​ ​break​ ​the​ ​speed​ ​limit?
_______________________________________
Identify​ ​some​ ​problems​ ​with​ ​Sam’s​ ​sampling​ ​and​ ​question​ ​design.
_______________________________________
_______________________________________
(b) Draw​ ​a​ ​line​ ​of​ ​best​ ​fit​ ​onto​ ​the​ ​points.
(c) Using​ e​ vidence​ ​from​ ​the​ ​graph,​ ​comment​ ​on​ ​whether​ ​Katrina​ ​is​ ​correct
that​ ​the​ ​cars​ ​travel​ ​slower​ ​past​ ​Sam​ ​(where​ ​they​ ​can​ ​see​ ​the​ ​radar)​ ​than
they​ ​do​ ​past​ ​Katrina.
_______________________________________
_______________________________________
MHJC
Page​ ​48
_______________________________________
_______________________________________
_______________________________________
_______________________________________
2014​ ​EOY​ ​Year​ ​10​ ​(104)
_______________________________________
_______________________________________
_______________________________________
MHJC
Page​ ​49
2014​ ​EOY​ ​Year​ ​10​ ​(104)
NAME:
TEACHER:
YEAR​ ​10​ ​MATHEMATICS,​ ​2014
Section​ ​9​ ​Probability
Answer​ ​ALL​ ​questions​ ​in​ ​the​ ​spaces​ ​provided​ ​in​ ​this​ ​booklet.​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Show​ ​ALL​ ​working.
For​ ​Assessor’s​ ​use​ ​only
Curriculum​ ​Level
==========================================================================
QUESTION​ ​ONE
Put​ ​a​ ​dot​ ​on​ ​the​ ​scale​ ​to​ ​represent​ ​the​ ​likelihood​ ​of​ ​each​ ​event.
(a) Your​ ​teacher​ ​has​ ​a​ ​cat​ ​that​ ​can​ ​tap-dance​ ​and​ ​speak​ ​Mandarin.
(b) The​ ​next​ ​baby​ ​to​ ​be​ ​born​ ​in​ ​Auckland​ ​will​ ​be​ ​a​ ​boy.
MHJC
Page​ ​50
(c) It​ ​will​ ​rain​ ​in​ ​your​ ​town​ ​sometime​ ​in​ ​the​ ​next​ ​fortnight.
(d) All​ ​the​ ​kittens​ ​in​ ​a​ ​litter​ ​of​ ​5​ ​turn​ ​out​ ​to​ ​be​ ​males.
2014​ ​EOY​ ​Year​ ​10​ ​(104)
____________________________________
QUESTION​ ​TWO
Two​ ​superstitious​ ​models​ ​always​ ​pull​ ​one​ ​hairpin​ ​out​ ​of​ ​each​ ​other’s
hairstyle​ ​for​ ​luck.​ ​(For​ ​each​ ​model,​ ​ 12 ​ ​the​ ​hair​ ​pins​ ​are​ ​black,​ ​ 13 ​ ​are​ ​brown
and​ ​the​ ​rest,​ ​ 16 ​ ​,​ ​are​ ​silver).
(a) List​ ​all​ ​the​ ​colour​ ​combinations​ ​possible​ ​(hint:​ ​black/brown​ ​and
brown/black​ ​are​ ​two​ ​of​ ​them).
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
QUESTION​ ​THREE
One​ ​study​ ​found​ ​that​ ​the​ ​probability​ ​of​ ​a​ ​female​ ​being​ ​left​ ​handed​ ​is​ ​0.09,
but​ ​for​ ​a​ ​male​ ​it​ ​is​ ​0.12.
(a) Complete​ ​the​ ​tree​ ​diagram​ ​for​ ​this​ ​situation
(b) Calculate​ ​the
probability​ ​that​ ​a
randomly​ ​chosen​ ​person
is​ ​female​ ​and
left-handed.
(b) What​ ​is​ ​the​ ​probability​ ​that​ ​both​ ​models​ ​get​ ​a​ ​black​ ​hairpin?
____________________________________
(c) What​ ​is​ ​the​ ​probability​ ​that​ ​the​ ​models​ ​get​ ​the​ ​same​ ​colour​ ​hairpin​ ​as
each​ ​other?
____________________________________
____________________________________
(d) Prove​ ​(showing​ ​calculations)​ ​that​ ​it​ ​is​ ​more​ ​likely​ ​to​ ​get​ ​two​ ​different
colours​ ​than​ ​two​ ​colours​ ​the​ ​same.
MHJC
Page​ ​51
____________________________________
2014​ ​EOY​ ​Year​ ​10​ ​(104)
____________________________________
(c) Calculate​ ​the​ ​probability​ ​that​ ​a​ ​randomly​ ​chosen​ ​person​ ​is
right-handed.
____________________________________
____________________________________
(d) If​ ​three​ ​people​ ​are​ ​selected​ ​at​ ​random​ ​from​ ​the​ ​general​ ​population,
what​ ​is​ ​the​ ​probability​ ​that​ ​all​ ​of​ ​them​ ​are​ ​left-handed​ ​males?
____________________________________
QUESTION​ ​FOUR
Jeremy​ ​has​ ​a​ ​theory​ ​that​ ​toast​ ​is​ ​more​ ​likely​ ​to​ ​land​ ​with​ ​the​ ​butter​ ​side
down.​ ​ ​He​ ​tests​ ​this​ ​theory​ ​by​ ​dropping​ ​a​ ​piece​ ​of​ ​toast​ ​50​ ​times.
____________________________________
____________________________________
(e) In​ ​a​ ​co-ed​ ​school​ ​(both​ ​genders​ ​attend)​ ​with​ ​700​ ​students,​ ​how​ ​many
left-handers​ ​would​ ​we​ ​expect​ ​to​ ​have?
____________________________________
____________________________________
(f) Identify​ ​at​ ​least​ ​one​ ​assumption​ ​we​ ​would​ ​have​ ​to​ ​make​ ​in​ ​order​ ​to
calculate​ ​the​ ​answer​ ​to​ ​the​ ​previous​ ​question.
(a) The​ ​toast​ ​lands​ ​butter​ ​side​ ​down​ ​28​ ​times.​ ​ ​Use​ ​this​ ​to​ ​give​ ​an​ ​estimate
(as​ ​a​ ​fraction​ ​in​ ​its​ ​simplest​ ​form)​ ​for​ ​the​ ​probability​ ​of​ ​toast​ ​landing
butter​ ​side​ ​down.
____________________________________
(b) A​ ​group​ ​of​ ​schools​ ​got​ ​together​ ​to​ ​carry​ ​out​ ​10​ ​000​ ​trials​ ​of​ ​this
experiment.​ ​ ​They​ ​found​ ​that​ ​the​ ​toast​ ​landed​ ​butter​ ​side​ ​down​ ​6​ ​248
times​ ​in​ ​their​ ​experiment.
(i) Give​ ​an​ ​estimate​ ​for​ ​the​ ​probability​ ​of​ ​toast
landing​ ​butter​ ​side​ ​down​ ​based​ ​on​ ​this
experiment.
____________________________________
____________________________________
____________________________________
____________________________________
MHJC
Page​ ​52
2014​ ​EOY​ ​Year​ ​10​ ​(104)
____________________________________
(ii) Another​ ​group​ ​of​ ​schools​ ​decide​ ​to​ ​carry​ ​out​ ​10​ ​000​ ​trials​ ​of
buttered​ ​toast​ ​drops.​ ​ ​Will​ ​they​ ​find​ ​that​ ​the​ ​toast​ ​lands​ ​butter​ ​side
down​ ​6248​ ​times?​ ​ ​Explain.
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
(c) Which​ ​estimate​ ​(the​ ​one​ ​from​ ​Jeremy’s​ ​experiment​ ​or​ ​the​ ​one​ ​from​ ​the
group​ ​of​ ​schools)​ ​is​ ​likely​ ​to​ ​be​ ​more​ ​accurate?​ ​ ​Why?
____________________________________
____________________________________
QUESTION​ ​FIVE
An​ ​English​ ​teacher​ ​made​ ​a​ ​game​ ​involving​ ​two​ ​spinners.​ ​ ​Students​ ​have​ ​to
spin​ ​both​ ​spinners​ ​and​ ​put​ ​the​ ​parts​ ​together​ ​to​ ​make​ ​a​ ​“word”.​ ​ ​Some
“words”​ ​are​ ​not​ ​proper​ ​English.​ ​ ​Each​ ​spinner​ ​has​ ​even-sized​ ​sections.
(a) If​ ​you​ ​play​ ​the​ ​game,​ ​what​ ​is​ ​the​ ​probability​ ​of​ ​getting​ ​a​ ​word​ ​that
ends​ ​in​ ​“ing”?
____________________________________
(b) How​ ​many​ ​“words”​ ​are​ ​possible?
____________________________________
(c) If​ ​you​ ​play​ ​the​ ​game​ ​and​ ​get​ ​a​ ​word​ ​ending​ ​in​ ​“ing”,​ ​what​ ​is​ ​the
probability​ ​that​ ​it​ ​is​ ​a​ ​real​ ​word?
____________________________________
(d) Sarah​ ​gets​ ​hooked​ ​on​ ​the​ ​game​ ​and​ ​plays​ ​it​ ​a​ ​lot.​ ​ ​If​ ​she​ ​has​ ​5​ ​turns,
what​ ​is​ ​the​ ​probability​ ​that​ ​every​ ​“word”​ ​she​ ​makes​ ​begins​ ​with​ ​the
letter​ ​b?
____________________________________
____________________________________
____________________________________
____________________________________
MHJC
Page​ ​53
2014​ ​EOY​ ​Year​ ​10​ ​(104)
(e) ​ ​Sarah​ ​then​ ​plays​ ​100​ ​games​ ​and​ ​gets​ ​either​ ​“coldest”​ ​or​ ​“colder”​ ​25
times.​ ​ ​ ​ ​Comment​ ​on​ ​whether​ ​this​ ​result​ ​seems​ ​unusual.
____________________________________
____________________________________
MHJC
Page​ ​54
2014​ ​EOY​ ​Year​ ​10​ ​(104)
Year​ ​10​ ​Mathematics
2014​ ​Examination​ ​Schedules
Topics
MHJC
Number
Page​ ​1
Algebra
Page​ ​2
Patterns​ ​and​ ​Graphs
Page​ ​3
Measurement
Page​ ​4
Trigonometry
Page​ ​5
Page​ ​55
2014​ ​EOY​ ​Year​ ​10​ ​(104)
MHJC
Geometry
Page​ ​6
Angles
Page​ ​7
Statistics
Page​ ​9
Probability
Page​ ​10
Page​ ​56
2014​ ​EOY​ ​Year​ ​10​ ​(104)
Section​ ​1:​ ​NUMBER
Level​ ​3
Level​ ​4
Level​ ​6
count​ ​towards​ ​Level​ ​4​ ​if​ ​needed.
Level​ ​5
4​ ​=​ ​5B,​ ​7​ ​=​ ​5P,​ ​10​ ​=​ ​5A.​ ​ ​Work​ ​at​ ​Level
6​ ​can​ ​count​ ​towards​ ​Level​ ​5​ ​if​ ​needed.
1a​ ​ ​25%
1c​​ ​Rate​ ​of​ ​125mB/day,​ ​so​ ​3750​ ​mB​ ​for​ ​a​ ​month
3​​ ​110.08,​ ​110.309,​ ​110.7,​ ​111.3,​ ​112.0
1b​ ​ ​\$225​ ​&divide;​ ​8​ ​=​ ​28.125​ ​(i.e.​ ​29​ ​hours)
8
4b​​ ​e.g.​ ​ ​convert​ ​to​ ​ 20
+
1d​​ ​ ​Answer​ ​is​ ​consistent​ ​with​ ​1c​ ​but​ ​without
clear​ ​reasoning​ ​for​ ​why​ ​it​ ​is​ ​the​ ​best​ ​solution.
1d​​ ​ ​Need​ ​some​ ​reasoning​ ​given​ ​e.g.
3​ ​Gb​ ​is​ ​cheaper​ ​than​ ​3​ ​1gB​ ​packs.​ ​ ​Similarly,
need​ ​to​ ​use​ ​large​ ​data​ ​packs​ ​if​ ​possible.
Buy​ ​a​ ​3Gb​ ​pack​ ​and​ ​a​ ​1Gb​ ​pack​.​ ​ ​While​ ​this​ ​is
more​ ​data​ ​than​ ​needed,​ ​it​ ​is​ ​cheaper​ ​than​ ​buying
a​ ​3Gb,​ ​a​ ​500​ ​mB​ ​and​ ​4​ ​50​ ​mB​ ​packs.​ ​ ​ ​Cost
will​ ​be​ ​\$70​ ​per​ ​month.
1​ ​=​ ​4B,​ ​3​ ​=​ ​4P,​ ​5​ ​=​ ​4A.​​ ​ ​Work​ ​at​ ​Level​ ​5​ ​can
1b​​ ​ ​She​ ​needs​ ​to​ ​raise​ ​\$225
4a​​ ​ ​e.g.​ ​10%​ ​is​ ​80,​ ​20%​ ​is
160
4c​ ​ ​e.g.​ ​76​ ​–​ ​62​ ​=​ ​14
5​​ ​ ​Nearest​ ​hundred​ ​column:
any​ ​correct
(4800,​ ​5200,​ ​100)
2a​​ ​ ​\$681.85
15
20
=
23
20
3
or 1 20
5​​ ​ ​ ​ ​2​ ​d.p.​ ​column,​ ​at​ ​least​ ​2​ ​correct
(4768.21,​ ​5211.37,​ ​59.01)
6a​​ ​ ​One​ ​percentage​ ​correctly​ ​calculated.​ ​ ​e.g.​ ​72%​ ​of
\$530​ ​ ​=​ ​\$381.60
2b​ ​ ​\$734.30
4d​​ ​ ​e.g.​ ​8​ ​–​ ​6​ ​+​ ​4​ ​=​ ​6
4e​​ ​ ​e.g.​ ​listing​ ​multiples,​ ​selects​ ​24.
4f​​ ​ ​e.g.​ ​5.2​ ​&times;​ ​4​ ​&times;​ ​10​8​​ ​=​ ​2​ ​080​ ​000​ ​000
5​ ​ ​ ​3​ ​s.f.​ ​column,​ ​at​ ​least​ ​2​ ​correct
(4770,​ ​5210,​ ​59.0)
6a​​ ​ ​Correctly​ ​increases​ ​by​ ​72%​ ​(\$911.60)​ ​but
does​ ​not​ ​add​ ​GST​ ​on​ ​top​ ​of​ ​this.
6b​​ ​ ​Consistent​ ​with​ ​6a.​ ​ ​Correct​ ​answer​ ​is
\$733.84​ ​to​ ​the​ ​nearest​ ​cent.
6d​ ​ ​\$756.52
NCEA​ ​STYLE​ ​QUESTION
Correctly​ ​calculates​ ​discounted​ ​cost​ ​of​ ​iPad​ ​or
amount​ ​Tina​ ​earns​ ​per​ ​week.
MHJC
Page​ ​57
2014​ ​EOY​ ​Year​ ​10​ ​(104)
2​ ​=​ ​6B,​ ​ ​4​ ​=​ ​6P,​ ​6​ ​=​ ​6A.
2c​​ ​ ​\$977.50
6a​​ ​ ​\$1048.34
6c​​ ​ ​ 911.60−733.84
&times;100 = 19.5% (1 d.p.)
911.60
NCEA​ ​STYLE​ ​QUESTION​ ​(fully​ ​solved
gives​ ​2​ ​x​ ​ ​evidence​ ​for​ ​L6.​ ​ ​One​ ​mistake​ ​=​ ​1​ ​x
evidence​ ​for​ ​L6)
\$​ ​earned​ ​per​ ​week:​ ​ ​430​ ​&times;​ ​2​ ​&times;​ ​0.05​ ​=​ ​\$43
Discounted​ ​cost​ ​of​ ​iPad:​ ​ ​724​ ​&times;​ ​0.85​ ​=​ ​\$615.40
Amount​ ​Tina​ ​needs​ ​to​ ​save:​ ​ ​5/7​ ​of​ ​615.40​ ​=
\$439.57
Time​ ​taken​ ​for​ ​Tina​ ​to​ ​save:​ ​439.57/43
=​ ​10.22​ ​weeks
–​ ​therefore​ ​11​ ​weeks,​ ​as​ ​10​ ​will​ ​not​ ​be
enough.
Section​ ​2:​ ​ALGEBRA
Level​ ​3
Level​ ​4
4​ ​=​ ​4B,​ ​8​ ​=​ ​4P,​ ​12​ ​=​ ​4A.​​ ​ ​Work​ ​at​ ​Level​ ​5​ ​can
Level​ ​5
3​ ​=​ ​5B,​ ​6​ ​=​ ​5P,​ ​9​ ​=​ ​5A.​ ​ ​Work​ ​at​ ​Level​ ​6
can​ ​count​ ​towards​ ​Level​ ​5​ ​if​ ​needed.
Level​ ​6
2d​ ​ ​4
2f​​ ​ ​4​ ​or​ ​-3​ ​(need​ ​both)
2e​​ ​10
3f​ ​ ​
1a​​ ​ ​5
count​ ​towards​ ​Level​ ​4​ ​if​ ​needed.
1b​​ ​4​ ​diamonds
2a​​ ​18
2c​ ​ ​12
2b​​ ​12
3a​​ ​p4​
3e​​ ​9n​
3b​​ ​3n
3c​​ ​2n​ ​+​ ​5p
3g​​ ​partially​ ​simplified
5a​​ ​5b​ ​+​ ​5c
3d​​ ​ ​56n​2
4aiii​​ ​ ​55
4ai​​ ​b​ ​=​ ​number​ ​of​ ​biscuits,​ ​n​ ​=​ ​number​ ​of​ ​people
4bii​​ ​ ​9.375%
4aii​ ​70
5d​​ ​ ​6n​ ​–​ ​n2​​ ​ ​+​ ​2n​ ​+​ ​6​ ​=​ ​-n​2​​ ​+​ ​8n​ ​+​ ​6
4bi​ ​ ​\$3600
5i​​ ​6(7n​ ​–​ ​2)
5b​​ ​12n​ ​+​ ​48
5c​​ ​5p​2​​ ​+​ ​p
6b​​ ​(Writes​ ​and​​ ​solves​ ​equation).
If​ ​t​ ​=​ ​time​ ​in​ ​weeks,
15t​ ​+​ ​100​ ​=​ ​520,​ ​t​ ​=​ ​28​ ​weeks
5d​​ ​ ​Either​ ​bracket​ ​set​ ​correctly​ ​expanded
6c​​ ​solved,​ ​some​ ​working​ ​shown.
5e​ ​Either​ ​bracket​ ​set​ ​correctly​ ​expanded
6d​​ ​solved​ ​for​ ​x,​ ​some​ ​working
MHJC
8
3​ ​=​ ​6B,​ ​5​ ​=​ ​6P,​ ​7​ ​=​ ​6A.
11y
15
3
3g​​ ​ ​ 2n5
5e​​ ​ ​4y​ ​+​ ​12​ ​–​ ​3y​ ​+​ ​3​ ​=​ ​y​ ​+​ ​15
5f​ ​ ​x2​​ ​ ​+​ ​2x​ ​–​ ​8
5g​​ ​ ​p2​​ ​ ​–​ ​12p​ ​+​ ​36​ ​+​ ​6p​ ​=​ ​ ​p2​​ ​ ​–​ ​6p​ ​+​ ​36
5j​​ ​(x​ ​–​ ​4)(x​ ​–​ ​2)
6c​​ ​(Must​ ​have​ ​a​ ​correct​ ​equation​ ​as
well​ ​as​ ​solution)
If​ ​j​ ​=​ ​James’​ ​age
(j​ ​+​ ​2)(j​ ​–​ ​1)​ ​=​ ​154
j​2​​ ​+​ ​j​ ​–​ ​2​ ​=​ ​154
j​2​​ ​–​ ​j​ ​–​ ​156​ ​=​ ​0
(j​ ​+​ ​13)(j​ ​–​ ​12)​ ​=​ ​0
As​ ​James’​ ​age​ ​can’t​ ​be​ ​negative,
James​ ​is​ ​12.
5h​​ ​5(p​ ​+​ ​2)
6d​​ ​5x​ ​–​ ​20​ ​=​ ​180
6a​​ ​12x​ ​=​ ​180,​ ​x​ ​=​ ​15​ ​ ​(accept​ ​correct​ ​answer​ ​only)
x​ ​=​ ​40​o
Page​ ​58
y​ ​=​ ​180​ ​–​ ​(2​x​40​ ​+​ ​38)​ ​=​ ​62​o
2014​ ​EOY​ ​Year​ ​10​ ​(104)
6b​​ ​Correct​ ​answer​ ​without​ ​equation​ ​formed.
MHJC
Page​ ​59
2014​ ​EOY​ ​Year​ ​10​ ​(104)
Section​ ​3:​ ​GRAPHS
Level​ ​3
Level​ ​4
2​ ​=​ ​4B,​ ​4​ ​=​ ​4P,​ ​6​ ​=​ ​4A.​​ ​ ​Work​ ​at​ ​Level​ ​5
can​ ​count​ ​towards​ ​Level​ ​4​ ​if​ ​needed.
2a​​ ​ ​22,​ ​26
1​​ ​ ​Correctly​ ​plotted,​ ​may​ ​have​ ​one​ ​or​ ​two
errors.
2b​​ ​ ​75,​ ​90
3a
Pattern​ ​(P)
1
2
3
4
5
Matches​ ​(M)
4
7
10
13
16
Level​ ​5
5​ ​=​ ​5B,​ ​8​ ​=​ ​5P,​ ​10​ ​=​ ​5A.​ ​ ​Work​ ​at
Level​ ​6​ ​can​ ​count​ ​towards​ ​Level​ ​5​ ​if
needed.
2d​​ ​ ​34,​ ​46
Level​ ​6
2e​​ ​ ​5n​ ​–​ ​8,​ ​6n​ ​–​ ​11
4c​​ ​ ​S​ ​=​ ​P​2​​ ​+​ ​3P​ ​+​ ​2​ ​ ​ ​(or​ ​equivalent)
3b​​ ​ ​M​ ​=​ ​3P​ ​+​ ​1
6b​​ ​ ​Draws​ ​inverted​ ​parabola​ ​with​ ​y
intercept​ ​of​ ​-2
3c​​ ​70
4b​​ ​(complete)
Pattern​ ​(P)
1
2
3
4
5
4b​​ ​ ​(first​ ​two​ ​correct)
7b​​ ​ ​4​ ​km/h
Squares​ ​(S)
6
12
20
30
42
5b​​ ​ ​-1/3
6a​​ ​ ​Redraws​ ​parabola​ ​3​ ​units​ ​higher
7a​ ​ ​(3​ ​pieces​ ​of​ ​evidence)
Petra:​ ​ ​y​ ​=​ ​-4x​ ​+​ ​12
Anna:​ ​y​ ​=​ ​2x
Kelly:​ ​ ​y​ ​=​ ​6
5a​​ ​ ​2
5c​​ ​ ​0
7c​ ​ ​Kelly’s​ ​house​ ​is​ ​6km​ ​from​ ​Anna’s
MHJC
Page​ ​60
3d​​ ​ ​Pattern​ ​81
6c​ ​ ​y​ ​=​ ​(x-1)​2​​ ​or​ ​equivalent
3e​​ ​1​ ​or​ ​(0,​ ​1)
​​
2c​ ​ ​-1,​ ​-4
4a
Gain​ ​at​ ​least​ ​5P​ ​plus
2​ ​=​ ​6B,​ ​4​ ​=​ ​6P,​ ​6​ ​=​ ​6A.
2014​ ​EOY​ ​Year​ ​10​ ​(104)
7c​​ ​ ​6​ ​km​ ​–​ ​shown​ ​by​ ​the​ ​y​ ​intercept​ ​of​ ​6
and​ ​because​ ​we​ ​know​ ​Kelly​ ​is​ ​at​ ​home.
7d​​ ​ ​2​ ​km/h
7e​​ ​ ​At​ ​4pm​ ​they​ ​are​ ​the​ ​same​ ​distance​ ​as
each​ ​other​ ​from​ ​Anna’s​ ​house,​ ​but​ ​not
necessarily​ ​in​ ​the​ ​same​ ​direction.
Section​ ​4:​ ​MEASUREMENT
Level​ ​3
Level​ ​4
count​ ​towards​ ​Level​ ​4​ ​if​ ​needed.
Level​ ​5
2​ ​=​ ​5B,​ ​4​ ​=​ ​5P,​ ​6​ ​=​ ​5A.​ ​ ​Work​ ​at​ ​Level​ ​6
can​ ​count​ ​towards​ ​Level​ ​5​ ​if​ ​needed.
5a​​ ​ ​0.49​ ​m
2b​ ​2271​ ​cm​3​​ ​(nearest​ ​whole)
5b​​ ​ ​1020​ ​g
4a​​ ​ ​10500​ ​(rectangle​ ​section)
+​ ​3848​ ​(two​ ​semicircles)​ ​=​ ​14348​ ​ ​cm​2
(nearest​ ​whole)
3​ ​=​ ​4B,​ ​6​ ​=​ ​4P,​ ​9​ ​=​ ​4A.​​ ​ ​Work​ ​at​ ​Level​ ​5​ ​can
1a​​ ​ ​6000​ ​cm​2
(or​ ​equivalent)
2a​​ ​ ​288​ ​cm​3
3​​ ​ ​First​ ​thermometer​ ​60​o
(+/-​ ​2)
3​​ ​ ​Second​ ​thermometer​ ​42​o​​ ​ ​(+/-​ ​1)
5c​​ ​ ​15.4​ ​cm
5d​​ ​ ​0.024​ ​L
1b​​ ​ ​0.6​ ​&times;​ ​500g​ ​=​ ​300​ ​g
4b​​ ​14348​ ​&times;​ ​22​ ​=​ ​315​ ​656​ ​ ​cm​3​​ ​(nearest
whole.​ ​ ​Mark​ ​for​ ​consistency​ ​with​ ​4a).
6a​ ​ ​47​ ​cm
6b​ ​ ​90​ ​g
6c​ ​ ​190​ ​cm
6d​ ​ ​625​ ​cm​
2
7a​​ ​ ​8330​ ​mm
Level​ ​6
At​ ​least​ ​5P,​ ​plus…
1​ ​=​ ​6B,​ ​3​ ​=​ ​6P,​ ​5​ ​=​ ​6A.
4c​​ ​ ​14348​ ​&times;​ ​28​ ​=​ ​401​ ​744​ ​ ​cm​3
=​ ​401.744​ ​L
Time​ ​taken​ ​at​ ​0.8​ ​L/second:
8​ ​and​ ​a​ ​half​ ​minutes).
7c​​ ​ ​Vinyl:​ ​ ​2.345m​ ​&times;​ ​\$90​ ​+​ ​\$120
=​ ​\$331.05
Laminate:​ ​ ​2.002​ ​&times;​ ​\$180​ ​=​ ​\$360.36
7b​​ ​ ​e.g.​ ​1000​ ​&times;​ ​2345​ ​+​ ​70​ ​&times;​ ​1700
-​ ​(1100​ ​&times;​ ​420)​ ​=​ ​2002​ ​000​ ​mm​2
(or​ ​20020​ ​cm​2​​ ​or​ ​2.002​ ​m2​​ )
Therefore​ ​vinyl​ ​is​ ​cheaper.
8a​​ ​ ​11π(5​2​ ​-​ ​22​​ )​ ​=​ ​725.7​ ​cm​3
9bi​​ ​ ​ 13 ​ ​&times;​ ​9.2​2​​ ​&times;​ ​16.1​ ​=​ ​454.2​ ​cm​3
9ai​​ ​ ​48​ ​cm​2
9​bii​​ ​Cube​ ​root​ ​of​ ​previous​ ​answer
(7.7​ ​cm​ ​to​ ​nearest​ ​1​ ​d.p.)​ ​for
length,​ ​width,​ ​height.
9aii​​ ​ ​48​ ​&times;​ ​2.5​ ​=​ ​120​ ​cm​3​​ ​(mark​ ​for
consistency​ ​with​ ​9ai)
8b​​ ​ ​200​ ​&times;​ ​12​ ​&times;​ ​11​ ​=​ ​26​ ​400​ ​ ​cm​2
9ci​​ ​179.6​ ​cm​3​​ ​(1​ ​d.p.)
9cii​​ ​6177.6​ ​cm​3​​ ​of​ ​bath​ ​bomb​ ​mix.
This​ ​will​ ​make​ ​34​ ​whole​ ​bath
bombs.
MHJC
Page​ ​61
2014​ ​EOY​ ​Year​ ​10​ ​(104)
MHJC
Page​ ​62
2014​ ​EOY​ ​Year​ ​10​ ​(104)
Section​ ​5:​ ​TRIGONOMETRY
Level​ ​3
Students​ ​working​ ​at​ ​Level
3​ ​are​ ​not​ ​expected​ ​to​ ​be
able​ ​to​ ​access
Trigonometry​ ​questions.
Level​ ​4
2​ ​=​ ​4B,​ ​4​ ​=​ ​4P,​ ​6​ ​=​ ​4A.​ ​ ​Work​ ​at​ ​Level​ ​5​ ​can
count​ ​towards​ ​Level​ ​4​ ​if​ ​needed.
1a​ ​ ​n2​​ ​ ​=​ ​65,​ ​ ​n​ ​=​ ​8.06​ ​(2​ ​d.p.)
2​
1b​​ ​ ​n​ ​ ​=​ ​80,​ ​ ​n​ ​=​ ​8.94​ ​(2​ ​d.p.)
1c​​ ​ ​4.59​ ​(2​ ​d.p.)
Level​ ​5
3​ ​=​ ​5B,​ ​5​ ​=​ ​5P,​ ​7​ ​=​ ​5A
Accept​ ​alternative​ ​rounding
2
2
3a​ ​ ​ √18 − 10 ​ ​=​ ​14.97​ ​km​ ​(2​ ​d.p.)
10
) = ​ ​56.3​o​​ ​(1​ ​d.p.)
3b​​ ​ ​ cos−1 ( 18
4​​ ​ ​(Two​ ​pieces​ ​of​ ​evidence)
1d​​ ​ ​0.07​ ​(2​ ​d.p.)
35
x
y
35
o​
1e​​ ​ ​29.7​ ​ ​(1​ ​d.p.)
= cos 72, x = 113.3 m
= tan 72, y = 107.7 m
5​ ​ ​ √32 − 0.92 ​ ​=​ ​2.86​ ​m​ ​(2​ ​d.p.)
2
2
2
6a​​ ​ ​x​ ​=​ ​ √22 − 8 ​ ​=​ 2​ 0.49​ ​m​ ​(2​ ​d.p.)
8
6b​​ ​ ​A​ ​=​ ​ sin−1 ( 22
) = ​ ​21.3​o​​ ​(1​ ​d.p.)
6c​ ​ ​ 12
y = cos 50, y = 18.7 m ​ ​ ​(1​ ​d.p.)
1.6
7a​ ​ ​ AB
= sin 48,
AB = 2.15 m ​ ​ ​(2​ ​d.p.)
7b​ ​ ​(Calculates​ ​AC)
1.6
e.g.​ ​ ​ AC
= tan 48,
AC = 1.44 m ​ ​ ​(2​ ​d.p.)
(Accept​ ​consistent​ ​Pythagoras​ ​working​ ​that
Completes​ ​diagram​ ​(units​ ​not​ ​required)​ ​and/or
uses​ ​an​ ​incorrectly​ ​calculated​ ​length​ ​AB.)
gives​ ​solution​ ​x​ ​=​ ​ √39 ​ ​=​ ​6.24​ ​(2​ ​d.p.)
Level​ ​6
At​ ​least​ ​5P,​ ​plus
1​ ​=​ ​6B,​ ​2​ ​=​ ​6P,​ ​3​ ​=​ ​6A.
3c​​ ​ ​Third​ ​angle​ ​in​ ​triangle​ ​is​ ​33.7​o​.​ ​ ​This
angle​ ​is​ ​supplementary​ ​to​ ​the​ ​bearing.​ ​ ​180
–​ ​33.7​ ​=​ ​143.6
Bearing​ ​of​ ​144​ ​to​ ​nearest​ ​whole​ ​degree.
7b​​ ​ ​First​ ​calculates​ ​AC​ ​(see​ ​Level​ ​5
column).​ ​ ​CD​ ​=​ ​4.2​ ​–​ ​1.44​ ​=​ ​2.76​ ​m
1.6
BDC​ ​=​ ​ tan−1 ( 2.76
) = ​ ​30.1​o​​ ​(1​ ​d.p.)
8​​ ​ ​&frac12;​ ​bh​ ​=​ ​area
0.5​ ​&times;​ ​2.39​ ​&times;​ ​BD​ ​=​ ​1.61
BD​ ​=​ ​1.35​ ​(2​ ​d.p.)
1.35
sin 20
= AB, AB = 3.95 m (1 d.p.)
(Calculating​ ​AB​ ​is​ ​evidence​ ​of​ ​L6​ ​alone)
Therefore​ ​BC​ ​=​ ​8.2​ ​–​ ​2.39​ ​–​ ​3.95​ ​=​ ​1.86​ ​m
9​​ ​ ​Horizontal​ ​distance​ ​from​ ​boat​ ​to​ ​plane
=​ ​ √122 + 322 ​ ​=​ 3​ 4.18​ ​km​ ​(2​ ​d.p.)
Height​ ​of​ ​plane​ ​=​ ​tan​ ​29​ ​&times;​ ​34.18
=​ ​18.94​ ​km​ ​(2​ ​d.p.)
(Need​ ​height​ ​of​ ​plane​ ​for​ ​L6​ ​evidence).
MHJC
Page​ ​63
2014​ ​EOY​ ​Year​ ​10​ ​(104)
MHJC
Page​ ​64
2014​ ​EOY​ ​Year​ ​10​ ​(104)
Section​ ​6:​ ​GEOMETRY
Level​ ​3
1a​​ ​ ​Octomino,​ ​one
line​ ​of​ ​symmetry
Level​ ​4
3​ ​=​ ​4B,​ ​6​ ​=​ ​4P,​ ​9​ ​=​ ​4A.​ ​ ​Work​ ​at​ ​Level​ ​5​ ​can
count​ ​towards​ ​Level​ ​4​ ​if​ ​needed.
Level​ ​5
1ci​ ​ ​(see​ ​below)
1cii​ ​(see​ ​below)
1ciii
2d​​ ​ ​Thessaloniki
2a​​ ​ ​Circle​ ​centred​ ​at​ ​Irakleions,
3​ ​=​ ​5B,​ ​5​ ​=​ ​5P,​ ​7​ ​=​ ​5A
1b​​ ​ ​ ​Octomino,​ ​two
lines​ ​of​ ​symmetry
Level​ ​6
At​ ​least​ ​5P​ ​plus
1​ ​=​ ​6B,​ ​2​ ​=​ ​6P,​ ​3​ ​=​ ​6A.
6​​ ​ ​Identifies​ ​the​ ​danger​ ​zones​ ​AND​ ​indicates
clearly​ ​where​ ​there​ ​are​ ​double​ ​dangers
(overlapping​ ​loci,​ ​shaded​ ​below).​ ​ ​Compass
marks​ ​must​ ​be​ ​shown.
8a​​ ​ ​4
8b​​ ​ ​Octomino​ ​with
rotational​ ​symmetry
drawn,
2e​​ ​ ​Canakkale
3​​ ​(Up​ ​to​ ​three​ ​pieces​ ​of​ ​evidence)
A​ ​could​ ​be​ ​square,​ ​rectangle
B​ ​could​ ​be​ ​rhombus,​ ​parallelogram
C​ ​could​ ​be​ ​kite
D​ ​could​ ​be​ ​trapezium
2b​​ ​ ​Perpendicular​ ​bisector
construction
2c​​ ​ ​Angle​ ​Bisector​ ​construction.
5
4a​​ ​ ​5
​ ​ ​(Both)
4b​​ ​
MHJC
Page​ ​65
2014​ ​EOY​ ​Year​ ​10​ ​(104)
9​​ ​ ​One​ ​piece​ ​of​ ​evidence​ ​if​ ​3
well-described​ ​steps.​ ​ ​Two​ ​pieces​ ​if​ ​fully
described.
8b​​ ​ ​Octomino​ ​with​ ​rotational​ ​symmetry​ ​drawn
AND​ ​order​ ​of​ ​rotational​ ​symmetry​ ​stated.
6​​ ​ ​A​ ​loci​ ​from​ ​this​ ​diagram​ ​can
contribute​ ​ONE​ ​piece​ ​of​ ​evidence​ ​if
not​ ​already​ ​gained​ ​from​ ​Question​ ​2.
7​​ ​ ​Valid​ ​triangular​ ​prism​ ​net.
9​​ ​ ​Detailed​ ​description​ ​for​ ​one​ ​step,
well-labelled​ ​=​ ​one​ ​piece​ ​of
evidence.
e.g.​ ​Reflect​ ​original​ ​in​ ​mirror​ ​m​ ​(1)
Rotate​ ​original​ ​90​ ​degrees​ ​about​ ​point​ ​P
(2)
Reflect​ ​2​ ​in​ ​mirror​ ​n​ ​(3)
Rotate​ ​3​ ​270​ ​degrees​ ​about​ ​R​ ​(4)
Enlarge​ ​4​ ​by​ ​scale​ ​factor​ ​2​ ​centre​ ​Q​ ​AND
then​ ​translate​ ​3​ ​squares​ ​right​ ​and​ ​2​ ​up.
Section​ ​7:​ ​ANGLES
Level​ ​3
Level​ ​4
8​ ​opportunities.
3​ ​=​ ​4B,​ ​5​ ​=​ ​4P,​ ​7​ ​=​ ​4A.
1a​​ ​ ​Puts​ ​a​ ​cross
inside​ ​any​ ​angle
other​ ​than​ ​ACB​ ​or
the​ ​right​ ​angle.
o
1b​​ ​90​
MHJC
Work​ ​at​ ​Level​ ​5​ ​can​ ​count
towards​ ​Level​ ​4​ ​if​ ​needed.
1c​ ​ ​CBA
1e​​ ​ ​360​o
2b​​ ​ ​155​o
Level​ ​5
3​ ​=​ ​5B,​ ​7​ ​=​ ​5P,​ ​11​ ​=​ ​5A.​ ​ ​Work​ ​at​ ​Level​ ​6​ ​can​ ​count
towards​ ​Level​ ​5​ ​if​ ​needed.
Level​ ​6
3a​​ ​ ​A​ ​=​ ​135​o​​ ​(exterior​ ​angle​ ​of​ ​triangle​ ​=​ ​sum​ ​of​ ​other​ ​interior
angles​ ​or​ ​angles​ ​on​ ​a​ ​straight​ ​line​ ​add​ ​to​ ​180​​ ​o​)
4​​ ​ ​Full​ ​working​ ​leading​ ​to​ ​calculation​ ​of​ ​angle
E,​ ​giving​ ​geometric​ ​reasons​ ​for​ ​each​ ​step​ ​(see
Level​ ​5​ ​for​ ​an​ ​example)
3b​​ ​ ​A​ ​=​ ​38​o​ ​(co-interior​ ​angles​ ​on​ ​parallel​ ​lines​ ​add​ ​to​ ​180​​ ​o​)
B​ ​=​ ​142​o​ ​(vertically​ ​opposite​ ​angles​ ​are​ ​equal)
Page​ ​66
2014​ ​EOY​ ​Year​ ​10​ ​(104)
2​ ​=​ ​6B,​ ​3​ ​=​ ​6P,​ ​4​ ​=​ ​6A.
1d​ ​ ​Puts​ ​a​ ​tick​ ​inside
ACB
2a​​ ​ ​65​o​​ ​ ​ ​(+/-​ ​2)
2c​​ ​ ​40​o
2d​​ ​ ​115​o
3a​​ ​ ​A​ ​=​ ​135​o
3b​​ ​ ​A​ ​=​ ​38​o
​​​​​​​​​​
B​ ​=​ ​142​o
4​​ ​ ​Accept​ ​angles​ ​with​ ​reasons​ ​for​ ​up​ ​to​ ​4​ ​pieces​ ​of​ ​evidence
towards​ ​Level​ ​5
e.g.
a​ ​=​ ​46​o​​ ​(angles​ ​on​ ​a​ ​straight​ ​line​ ​add​ ​to​ ​180​o​)
b​ ​=​ ​46​o​​ ​(base​ ​angles​ ​of​ ​isosceles​ ​triangle​ ​are​ ​equal)
c​ ​=​ ​88​o​​ ​(angle​ ​sum​ ​of​ ​triangle​ ​is​ ​180​o​)
d​ ​=​ ​46​o​​ ​(co-interior​ ​angles​ ​on​ ​parallel​ ​lines​ ​add​ ​to​ ​180​o​)
E​ ​=​ ​46​o​​ ​(angles​ ​on​ ​a​ ​straight​ ​line​ ​add​ ​to​ ​180​o​)​ ​OR​ ​because​ ​b
and​ ​E​ ​are​ ​corresponding​ ​angles​ ​on​ ​parallel​ ​lines.
on​ ​parallel​ ​lines​ ​add​ ​to​ ​180​o​)
r​ ​=​ ​95​o​​ ​(angle​ ​sum​ ​of​ ​triangle)
5​ ​Accept​ ​angles​ ​with
reasons​ ​for​ ​up​ ​to​ ​3​ ​pieces
of​ ​evidence​ ​towards​ ​Level
5
e.g.
p​ ​=​ ​40​o​​ ​(angles​ ​on​ ​a​ ​straight
q​ ​=​ ​45​o​​ ​(co-interior​ ​angles
A​ ​=​ ​85​o​​ ​(angles​ ​on​ ​a​ ​straight​ ​line)
6​​ ​ ​One​ ​angle​ ​calculated​ ​with​ ​geometric​ ​reason.
7​​ ​ ​Any​ ​angles​ ​calculated​ ​with​ ​geometric​ ​reasons​ ​(allow​ ​ ​up​ ​to
4​ ​pieces​ ​of​ ​evidence​ ​towards​ ​Level​ ​5).​ ​ ​See​ ​Level​ ​6​ ​column​ ​for
reasoning​ ​example.
MHJC
Page​ ​67
2014​ ​EOY​ ​Year​ ​10​ ​(104)
5​​ ​ ​Full​ ​working​ ​leading​ ​to​ ​calculation​ ​of​ ​angle
A,​ ​giving​ ​geometric​ ​reasons​ ​for​ ​each​ ​step.​ ​ ​(see
Level​ ​5​ ​for​ ​an​ ​example)
6​​ ​ ​Completed​ ​proof.
Angles​ ​ABC​ ​and​ ​ADE​ ​are​ ​equal​ ​because:
they​ ​are​ ​corresponding​ ​angles​ ​on​ ​parallel​ ​lines
Angles​ ​ACB​ ​and​ ​AED​ ​are​ ​equal​ ​because:
they​ ​are​ ​corresponding​ ​angles​ ​on​ ​parallel​ ​lines
Angles​ ​BAC​ ​is​ ​also​ ​Angle​ ​DAE
Because​ ​triangles​ ​ABC​ ​and​ ​ADE​ ​have
all​ ​angles​ ​the​ ​same,​ ​they​ ​are​ ​similar​ ​triangles.
7
a​ ​=​ ​22​o​​ ​(base​ ​angles​ ​of​ ​isosceles​ ​triangle​ ​are​ ​equal)
b​ ​=​ 1​ 36​o​​ ​(angle​ ​sum​ ​of​ ​triangle)
c​ ​=​ 3​ 1​o​​ ​(base​ ​angles​ ​of​ ​isosceles​ ​triangle​ ​are​ ​equal)
d​ ​=​ 1​ 18​o​​ ​(angle​ ​sum​ ​of​ ​triangle)
e​ ​=​ 1​ 06​o​​ ​(angles​ ​about​ ​a​ ​point)
Conclusion​:​ ​Angle​ ​ACB​ ​=​ ​31​ ​+​ ​22​ ​=​ ​53.
Angle​ ​e​ ​is​ ​double​ ​angle​ ​ACB​ ​ ​ ​(must​ ​have
conclusion)
8​​ ​ ​Angle​ ​all​ ​found​ ​in​ ​terms​ ​of​ ​x​ ​(see​ ​below)
MHJC
Page​ ​68
2014​ ​EOY​ ​Year​ ​10​ ​(104)
Section​ ​8:​ ​STATISTICS
Level​ ​3
Level​ ​4
6​ ​opportunities.
2​ ​=​ ​4B,​ ​4​ ​=​ ​4P,​ ​6​ ​=​ ​4A.
2a​​ ​ ​Continuous
3a
Work​ ​at​ ​Level​ ​5​ ​can​ ​count
towards​ ​Level​ ​4​ ​if​ ​needed.
1a​​ ​ ​General​ ​description​ ​e.g.
that​ ​the​ ​percentage​ ​is
generally​ ​falling​ ​over​ ​time.
1b​​ ​ ​A​ ​scatterplot
1e​​ ​ ​Estimate​ ​in​ ​the​ ​range
15-25%.
3b​​ ​ ​Calculates​ ​mode​ ​or
range
2d​​ ​ ​No​ ​–​ ​it​ ​does​ ​not​ ​look​ ​like
half​ ​the​ ​data​ ​is​ ​below​ ​50.
3b​​ ​ ​Calculates​ ​median​ ​or
mean
4a​​ ​ ​Cars​ ​travelling​ ​faster​ ​past
Sam​ ​tended​ ​to​ ​be​ ​travelling
faster​ ​past​ ​Katrina​ ​(or​ ​other
valid​ ​description​ ​of
correlation).
Level​ ​5
2​ ​=​ ​5B,​ ​4​ ​=​ ​5P,​ ​6​ ​=​ ​5A.​ ​ ​Work​ ​at​ ​Level​ ​6​ ​can​ ​count​ ​towards
Level​ ​5​ ​if​ ​needed.
Level​ ​6
1a​​ ​ ​More​ ​detailed​ ​description​ ​e.g.​ ​that​ ​in​ ​1996​ ​it​ ​was​ ​over​ ​80%,
gradually​ ​dropping,​ ​then​ ​dropped​ ​quickly​ ​ ​between​ ​2001-2005,
slowing​ ​again​ ​after​ ​that​ ​and​ ​finishing​ ​with​ ​a​ ​short​ ​rise.
1c​​ ​ ​ONE​ ​OF​ ​reason​ ​for​ ​sampling,​ ​suggested​ ​collection​ ​method
e.g.​ ​It​ ​is​ ​not​ ​realistic​ ​to​ ​have​ ​found​ ​the​ ​speed​ ​of​ ​every​ ​single​ ​car.
1d​​ ​ ​We​ ​only​ ​have​ ​percentages.​ ​ ​We​ ​need​ ​to​ ​know​ ​how​ ​many
cars​ ​are​ ​on​ ​the​ ​road​ ​to​ ​calculate​ ​numbers​ ​that​ ​were​ ​speeding.
2b​​ ​ ​There​ ​are​ ​gaps​ ​between​ ​bars​ ​–​ ​usually​ ​a​ ​histogram​ ​would​ ​be
used.​ ​ ​Nearest​ ​1​ ​km/h.
2c​​ ​ ​Up​ ​to​ ​2​ ​pieces​ ​of​ ​evidence​ ​for​ ​comments​ ​on​ ​at​ ​least​ ​2
features​ ​e.g.​ ​ ​peaks​ ​around​ ​60,​ ​slightly​ ​asymmetrical,​ ​a​ ​few
outlier​ ​values​ ​in​ ​both​ ​tails,​ ​range​ ​of​ ​about​ ​50.
3b​​ ​ ​Calculates​ ​median​ ​and​ ​quartiles​ ​(other​ ​statistics​ ​given
below).
Range
11
Median
53
Mean
51.16
Mode
53
Lower​ ​quartile
50.5
Upper​ ​quartile
55.5
3c​ ​or​ ​consistent​ ​with
​ ​ ​ ​ ​ ​table.
1c​ ​ ​Reason​ ​for​ ​sampling​ ​AND​ ​suggested
collection​ ​method​ ​e.g.​ ​It​ ​is​ ​not​ ​realistic​ ​to
find​ ​the​ ​speed​ ​of​ ​every​ ​single​ ​car.​ ​ ​Data
could​ ​be​ ​gathered​ ​from​ ​speed​ ​cameras
and​ ​police​ ​scans​ ​on​ ​car​ ​speeds.
2c​​ ​ ​One​ ​piece​ ​of​ ​evidence​ ​if​ ​3​ ​features​ ​are
commented​ ​on​ ​clearly.
3d​​ ​ ​At​ ​least​ ​two​ ​comments​ ​e.g.​ ​Sam​ ​is
only​ ​there​ ​at​ ​one​ ​time​ ​of​ ​day​ ​(not
representative​ ​of​ ​other​ ​times).​ ​ ​Cars​ ​may
tend​ ​to​ ​travel​ ​more​ ​slowly​ ​at​ ​certain​ ​times
e.g.​ ​at​ ​3pm​ ​when​ ​a​ ​lot​ ​of​ ​students​ ​are
crossing.​ ​Sam’s​ ​visible​ ​presence​ ​may
change​ ​the​ ​behaviours​ ​of​ ​drivers.
4c​​ ​ ​Answer​ ​with​ ​justification​ ​e.g.​ ​yes,
Katrina​ ​is​ ​correct.​ ​ ​If​ ​I​ ​draw​ ​a​ ​line​ ​to
show​ ​y​ ​=​ ​x,​ ​most​ ​of​ ​the​ ​points​ ​fall
beneath​ ​it​ ​(or​ ​most​ ​points​ ​have​ ​a​ ​smaller
x​ ​value​ ​than​ ​y​ ​value).
5​​ ​(gives​ ​at​ ​least​ ​2​ ​comments,​ ​e.g.)
● Biased​ ​sample
● Not​ ​all​ ​may​ ​have​ ​cars
● Not​ ​all​ ​may​ ​drive​ ​past​ ​the​ ​school
● Q3​ ​makes​ ​the​ ​assumption​ ​that​ ​they
break​ ​the​ ​limit​ ​–​ ​they​ ​may​ ​not.
● Q2​ ​people​ ​may​ ​be​ ​unwilling​ ​to​ ​admit
they​ ​break​ ​the​ ​limit
4b​ ​ ​Reasonable​ ​position​ ​for​ ​line​ ​of​ ​best​ ​fit.
MHJC
Page​ ​69
2014​ ​EOY​ ​Year​ ​10​ ​(104)
At​ ​least​ ​5P,​ ​plus
2​ ​=​ ​6B,​ ​3​ ​=​ ​6P,​ ​4​ ​=​ ​6A.
●
MHJC
Page​ ​70
2014​ ​EOY​ ​Year​ ​10​ ​(104)
Q1​ ​people​ ​may​ ​not​ ​be​ ​able​ ​to​ ​answer
accurately.
Section​ ​9:​ ​PROBABILITY
Level​ ​3
1a​​ ​ ​Impossible
Level​ ​4
2​ ​=​ ​4B,​ ​4​ ​=​ ​4P,​ ​6​ ​=​ ​4A.​ ​ ​Work​ ​at​ ​Level​ ​5
can​ ​count​ ​towards​ ​Level​ ​4​ ​if​ ​needed.
1c​​ ​ ​Placed​ ​over​ ​&frac12;
2a​​ ​ ​Black/Black,​ ​Black/Brown,
Black/Silver,​ ​Brown/Black,
Brown/Brown,​ ​Brown/Silver,
Silver/Black,​ ​Silver/Brown,​ ​Silver/Silver.
1d​​ ​ ​Place​ ​under​ ​&frac12;
2b​​ ​ ​&frac14;
1b​​ ​ ​&frac12;
28
4a​​ ​ ​ 50
=
14
25
4bi​​ ​ ​e.g.​ ​
6248
10 000
5a​ ​ ​
Level​ ​5
2​ ​=​ ​4B,​ ​4​ ​=​ ​4P,​ ​5​ ​=​ ​4A.​ ​ ​Work​ ​at​ ​Level​ ​6
can​ ​count​ ​towards​ ​Level​ ​5​ ​if​ ​needed.
3a
Level​ ​6
2​ ​=​ ​6B,​ ​4​ ​=​ ​6P,​ ​6​ ​=​ ​6A.
1 1
2c​​ ​ ​ 2 &times; 2 +
1 1
3&times;3
+
1 1
6&times;6
=
14
36
or 187
2d​​ ​ ​e.g.​ ​calculates​ ​2c​​ ​and​ ​comments​ ​that​ ​it​ ​is
below​ ​50%,​ ​therefore​ ​different​ ​colours​ ​are
more​ ​likely.
3c​ ​ ​0.5​ ​&times;​ ​0.88​ ​+​ ​0.5​ ​&times;​ ​0.91​ ​=​ ​0.895
​ ​=​ ​
781
1250
​ ​or​ ​equivalent
1
3
3b​​ ​ ​0.5​ ​&times;​ ​0.09​ ​=​ ​0.045
4bii​​ ​ ​No​ ​–​ ​because​ ​(e.g.)​ ​every​ ​time​ ​you
run​ ​a​ ​probability​ ​experiment,​ ​the​ ​results
can​ ​be​ ​different.​ ​ ​Each​ ​set​ ​of​ ​trials​ ​just
gives​ ​one​ ​estimate.
5b​​ ​ ​12
5c​​ ​ ​&frac12;
1
5d​ ​ ​(&frac12;)​5​​ ​=​ ​ 32
​ ​or​ ​equivalent​ ​(e.g.
0.03125)
3d​​ ​ ​(0.5​ ​&times;​ ​0.12)​3​​ ​=​ ​0.000216
3e​ ​700​ ​&times;​ ​0.105​ ​=​ ​73.5
(accept​ ​73​ ​or​ ​74)
3f​​ ​ ​Answers​ ​will​ ​vary​ ​e.g.​ ​assume​ ​the​ ​school
has​ ​equal​ ​numbers​ ​of​ ​males​ ​and​ ​females.
4c​​ ​ ​The​ ​10​ ​000​ ​trials​ ​will​ ​give​ ​a​ ​better
estimate,​ ​as​ ​long-run​ ​experiments​ ​give​ ​more
reliable​ ​results​ ​than​ ​smaller​ ​numbers​ ​of​ ​trials.
5e​​ ​ ​Probability​ ​of​ ​one​ ​of​ ​these​ ​two​ ​words​ ​is
1
.​​ ​ ​From​ ​100​ ​trials,​ ​we​ ​would​ ​expect​ ​to​ ​get
6
them​ ​16​ ​or​ ​17​ ​times.
(Based​ ​on​ ​this,​ ​either​ ​say​ ​it​ ​is​ ​more​ ​than​ ​what
we​ ​would​ ​expect​ ​or​​ ​not​ ​too​ ​far​ ​off​ ​to​ ​be​ ​truly
unusual).
MHJC
Page​ ​71
2014​ ​EOY​ ​Year​ ​10​ ​(104)
MHJC
Page​ ​72
2014​ ​EOY​ ​Year​ ​10​ ​(104)
```