DSE Pre-Training Mathematics (Compulsory Part) –– Section A
Important Knowledge and Formulas
Junior Secondary (involve knowledge in Non-foundation Part)
1.
2.
Estimation, Approximation and Errors
(a)
Absolute error  estimated value  exact value
(b)
Maximum absolute error  largest possible uncertainty of an estimation or a measurement
(c)
Relative error 
(d)
Percentage error  Relative error  100%
Maximum absolute error
or
Measured value

Absolute error
Exact valu e
Percentages
New value  Original value
 100%
Original value
(a)
Percentage change 
(b)
(i)
New value  Original value  (1  Percentage increase)
(ii)
New value  Original value  (1  Percentage decrease)
(c)
Profit and loss
Percentage change 
Selling price  Cost price
 100%
Cost price
If the percentage change  0, then there is a profit.
If the percentage change  0, then there is a loss.
(d)
Selling price  Cost price  (1  Profit percentage)
or
 Cost price  (1  Loss percentage)
Marked price  Selling price
 100%
Marked price
(e)
Discount percentage 
(f)
Selling price  Marked price  (1  Discount percentage)
(g)
Let P be the principal, r% be the interest rate per period, n be the number of periods,
I be the interest and A be the total amount.
(i)
Simple interest
(1)
(ii)
(2)
API
(2)
I  P  (1  r%) n  P
Compound interest
(1)
(h)
I  P  r%  n
A  P  (1  r%) n
Let n be the number of periods
(i)
Growth
New value  Original value  (1  Growth rate)n
(ii)
Depreciation
New value  Original value  (1  Depreciation rate)n
II
Useful Theorems and Definitions (Geometry)
Useful Theorems and Definitions (Geometry)
Junior Secondary (involve knowledge in Non-foundation Part)
A.
Angles and Parallel Lines
1.
Angles related to intersecting lines
AOB is a straight line.
a + b = 180°
a + b + c + d = 360°
(adj. ∠ s on st. line)
2.
a=b
(∠ s at a pt.)
(vert. opp. ∠ s)
a=b
b=c
(corr. ∠ s, AB // CD)
(alt. ∠ s, AB // CD)
c + d = 180°
Parallel lines
(a) If AB // CD, then
(int. ∠ s, AB // CD)
(b) (i) If a = b, then AB // CD.
(corr. ∠ s equal)
(ii) If b = c, then AB // CD.
(alt. ∠ s equal)
(iii) If c + d = 180°, then AB // CD.
(int. ∠ s supp.)
B.
Triangles
1.
Angles of a triangle
(a) a + b + c = 180°
(∠ sum of D )
(b) d = a + b
(ext. ∠ of D )
2.
Special triangles
(a) Isosceles triangle
(i) If AB = AC, then
b = c.
(ii) If b = c, then
AB = AC.
(base ∠ s, isos. D )
(sides opp. eq. ∠ s)
(iii) If AB = AC and any one of the following conditions is
satisfied, then the other two are also satisfied.
• AD ⊥ BC
• ∠BAD = ∠CAD
• BD = CD
(property of isos. D )
XI
Essential Calculator Programs
Essential Calculator Programs
We will introduce some useful built-in and user-defined programs for
fx-50FH II and fx-3650P II.
Command Keys
P1 (or P2, P3, P4) ..... 1 (or 2 , 3 , 4 )
A ............................... ALPHA
A
B ............................... ALPHA
B
C ............................... ALPHA
C
D ............................... ALPHA
D
X ............................... ALPHA
X
Y ............................... ALPHA
Y
M .............................. ALPHA
M
M+ ............................ M+
➞ .............................. SHIFT
P-CMD
2
: ................................ SHIFT
P-CMD
3
............................... SHIFT
P-CMD
4
➾............................... SHIFT
P-CMD
= ................................ SHIFT
P-CMD
≠ ................................ SHIFT
P-CMD
> ................................ SHIFT
P-CMD
< ................................ SHIFT
P-CMD
≥ ................................ SHIFT
P-CMD
≤ ................................ SHIFT
P-CMD
Goto.......................... SHIFT
P-CMD
Lbl............................. SHIFT
P-CMD
r
p ............................... SHIFT
EXP
SHIFT
1
2
3
1
2
3
4
1
▲ ▲
1
▲ ▲ ▲ ▲ ▲ ▲
P-CMD
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
? ................................ SHIFT
2
ANS
2
and
▲
• Press
▲
Special Command Keys
to move the cursor.
• Press DEL to delete the number, variable or function at the
position of the blinking cursor.
• Press
SHIFT
DEL
to insert number, variable or function. The
cursor becomes | . Press SHIFT
cursor back to a normal cursor.
DEL
to change the insert
XIX
DSE
E Pre-Training Mathematics
M
(Co
ompulsory Part)) –– Section A
Q
Questiion Dis
stribu
ution
Pa
aper 1 Mo
ock Practice
Thee following tab
ble shows the corresponding
c
topics of the questions
q
in Paaper 1 ‘Mock P
Practice (MP) 1  10’.
Junior Seco
ondary
Top
pic
Laaws of Indices
Seniorr Secondary
MP 1
MP
M 2
MP 3
MP 4
MP
M 5
1
1
1
1
1
5
4
Peercentages
5
Esstimation and Error
E
3
Foormulas and Po
olynomials
2, 4
5
MP 7
3
3
2
2
M 8
MP
MP 9
MP 10
3
6
4
2
3
1
1
1
5
2, 3
2, 3, 4
2, 3
2, 3
M
More about Poly
ynomials
Eqquations
MP 6
6
6
4
Fuunctions and Graphs
G
Raate, Ratio and Variations
6
Seequences
Innequalities
1
Syymmetry, Tran
nsformation of
Fiigures and 3-D
D Figures
Sttraight Lines an
nd Rectilinear
Fiigures
6
9
7
7
Baasic Propertiess of Circles
M
Mensuration
3
8
7, 8
Cooordinates and
d Equations of
8
5
Sttraight Lines
8
2
9
6
Loocus and Equaations of
Ciircles
4
5
5
5
5
5
1, 4
2
4
4
Trrigonometry
Prrobability
Sttatistics
XXIIV
4
7
7
8
DSE
E Pre-Training Mathematics
M
(Co
ompulsory Part)) –– Section A
Thee table below shows
s
the relatted topics and the correspond
ding questionss in Paper 1 ‘M
Mock Practice (MP)
(
1  5’ forr each Skill.
Topic
Skill
MP 1
MP 2
MP 3
MP 4
MP 5
Laws
L
of Indicess
1
Skill○
1
1
1
1
1
2
Skill○
2
2
3
2
2
Formulas and Polyno
omials
Estiimation and Errror
Equations
4
Skill○
4
5
Skill○
3
5
8
Skill○
5
Formulas and Polyno
omials
10
Skill○
5
12
Skill○
13
Skill○
6
14
Skill○
6
5
9
7
9
16
Skill○
9
7
7
8
8
8
8
9
8
19
Skill○
8
8
8
8
8
9
22
Skill○
6
23
Skill○
6
24
Skill○
6
5
25
Skill○
26
Skill○
4
27
Skill○
4
28
Skill○
7
8
29
Skill○
7
8
8
30
Skill○
31
Skill○
2
6
15
Skill○
21
Skill○
Statistics
4
7
20
Skill○
Probability
3
4
18
Skill○
C
Coordinates and
d Equations off Straight Lines
3
6
11
Skill○
17
Skill○
Mensuration
3
5
7
Skill○
9
Skill○
Straight Linees and Rectilin
near Figures
3
6
Skill○
Rate, Ratio
R
and Variaations
Percentages
2
3
Skill○
7
Pre-Training Course 1
Skill○
1 Use laws of indices to simplify expressions
Example
Instant Practice
Simplify the following expressions and express your
answer with positive indices.
(a) (x3y2)3
(b) (x2y4)5
x2
(c)
3 4
x y
Simplify the following expressions and express your answer with
positive indices.
(a) (a3b4)5
(b) (a4b2)3
a 3 b 5
(c)
b2
Solution:
(a)
33 23
(x3y2)3 = x y = x 9 y 6
(b)
(x2y4)5 = x10 y 20 =
(c)
y
y4
x2
=
=
3

2
x
x
x 3 y 4
x 10
y 20
4
2 Perform change of subject
Skill○
Example
(a)
(b)
(c)
(d)
(e)
Instant Practice
x  2y
Make x the subject of the formula
 4.
5
Make k the subject of the formula 7h + 3k = 2h.
2 3t  1
.
Make s the subject of the formula

s
t
Make m the subject of the formula 7m + pm = 5.
Make p the subject of the formula pq = 2(p + t).
Solution:
x  2y
(a)
4
5
(b)
x  2 y  20
x  20  2 y
(c)
(e)
2 3t  1

s
t
s
t

2 3t  1
2t
s
3t  1
(b)
(c)
(d)
(e)
g4
2.
3f
Make b the subject of the formula 2a  9b = 6a.
5
2S
Make R the subject of the formula
.

R 3S  1
Make x the subject of the formula 8 + kx  6x = 7.
Make r the subject of the formula 4(p  r) = p(q + r).
Make g the subject of the formula
7h + 3k = 2h
3k = –5h
k 
(d)
(a)
5h
3
7m + pm = 5
(7 + p)m = 5
m
5
7 p
pq = 2(p + t)
pq = 2p + 2t
pq– 2p = 2t
(q – 2)p = 2t
2t
p=
q2
3
Paper 1 Mock Practicee 1
Name: __
__________
_____
Class:
___
__________
____
Date:
__
__________
____
Marks: ______ /30
0
11 9
1.
Simpliify
a b
b5
ve indices.
and express your answerr with positiv
(3 markss)
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2.
Makee k the subjecct of the form
mula
4  5h  7k
2.
k
(3 markss)
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3.
(a) Round
R
down
n 9876. 54 to
o 1 significan
nt figure.
(b) Round
R
up 98
876. 54 to 1 decimal placce.
(c) Round
R
off 98
876. 54 to th
he nearest in
nteger.
(3 markss)
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15
DSE
E Pre-Training Mathematics
M
(Co
ompulsory Part)) –– Section A
Na
ame: _____
__________
__
Clas
ss:
______
__________
_
Datte:
_____
__________
Marks: ___
____ /19
nswer all qu
uestions (1 mark for ea
ach questio
on)
An
1.
2.
3.
4.
50
(x2 – 2x – 1)(x – 1) =
A. (x – 1)
1 3.
B. x3 – 3x
3 2 + x + 1.
C. x3 – x2 – 3x – 1.
D. x3 – 3x
3 2 – 3x – 1.
5.
Iff x + 2y = 100 and 7x + 5yy = 7, then x =
A.
A –7.
B.
B –4.
C.
C 4.
D.
D 7.
(3 x 5 ) 4
=
3x 6
A. 4x3.
B. 4x14.
C. 27x3.
D. 27x144.
6.
There
T
are 8440 audiences in a theatter. If the
nu
umber of m
male audiencces is 40% more
m
than
th
hat of femalle audiencess, then the number
n
of
male
m audiencces is
A.
A 250.
B.
B 350.
C.
C 490.
D.
D 590.
7.
Iff the volum
me of a balloon is decrreased by
60
0% and theen increasedd by 50%, find the
peercentage cchange in the volumee of the
baalloon.
A.
A –70%
B. –40%
C.
C –20%
D. –10%
8.
The
T width, tthe length and the heiight of a
reectangular block are meeasured as 5 cm, 4 cm
an
nd 7 cm correct too the neaarest cm
reespectively. Let v cm3 be
b the actuaal volume
off the block. Find the rannge of values of v.
A.
A 102.375  v  185.625
B.
B 102.375  v  185.625
C.
C 139.5  v  140.5
D.
D 139.5  v  140.5
9  (2s + t)
t 2=
A. (3  2s
2 + t)(3 + 2s
2  t).
B. (3  2s
2  t)(3 + 2s
2 + t).
C. (9  2s
2 + t)(9 + 2s
2  t).
D. (9  2s
2  t)(9 + 2s
2 + t).
Which off the follow
wing is an identity/ are
identities??
I.
9x2 – 16 = 0
II. 9x2 – 16 = (3x
( – 4)2
III. 9x2 – 16 = (3x
( + 4)(3x – 4)
A. II onlly
B. III on
nly
C. I and
d II only
D. I and
d III only
Paper 1 Mock Practicee 6
Name: __
__________
_____
Class:
___
__________
____
Date:
__
__________
____
Marks: ______ /23
3
1.
(a) Solve
S
the ineequality
8 x  23
 17  2 x .
5
(b) Find
F
all integ
gers satisfyin
ng both the inequalities
8 x  23
 177  2 x and 4x
4 + 12  0.
5
(4 markss)
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2.
It is given
g
that g((x) is the su
um of two parts,
p
one paart varies ass x2 and the other part is
i a constantt.
Suppo
ose that g(3)) = –20 and g(5)
g = –132. Find g(7).
(4 markss)
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773
DSE
E Pre-Training Mathematics
M
(Co
ompulsory Part)) –– Section A
Na
ame: _____
__________
__
Clas
ss:
______
__________
_
Datte:
_____
__________
Marks: ___
____ /11
nswer all qu
uestions (1 mark for ea
ach questio
on)
An
1.
Let a bee a constan
nt. Solve the
t
equation
n
2
2
(x + a) = 9a .
A. x = 4a
B. x = 2a
C. x = –2a
– or x = 4a
a
4.
D. x  –4a or x = 2a
a
2.
The figuree shows the graph of y = ax2 – x – b,
b
where a and
a b are constants.
c
Which
W
of the
following is true?
y = ax  x  b
2
A.
B.
C.
D.
3.
B.
B 8.
C.
C 12.
D.
D 20.
5.
[ssin (270  ) – 1][cos (180 + ) + 1] =
A.
A sin2 .
B.
B cos2 .
C.
C sin2 .
D.
D cos2 .
6.
In
n the figuree, ABCD iss a circle. BD is a
diiameter andd intersects AC
A at E. If AD
A // BC
an
nd CED = 108, then ABE

=
y
O
x
a > 0 and b > 0
a > 0 and b < 0
a < 0 and b > 0
a < 0 and b < 0
Itt is given thhat b partlyy varies direectly as a
an
nd partly vaaries inverselly as a2. Whhen a = 1,
b = 12; whenn a = 2, b = 15. Whenn a = –0.5,
b=
A.
A 4.
D
C
The solutiion of 3x  7 > 13 or 3 < 23 + 4x is
A. x < 5.

B. x > 5.

C. x < 2.

D. x > 2.

108
E
A
B
A.
A 36.
B.
B 42.
C.
C 48.
D.
D 54.
1000
DSE
E Pre-Training Mathematics
M
(Co
ompulsory Part)) –– Section A
uestions in DSE
D Exam (Section
(
A)
Crooss-Topic qu
Paper 1
Paperr 2
2017
7, 10, 11
22, 28
2
2016
7, 9

2015

22, 28
2
2014
13
22, 27
2
2013
6, 10
21
2012
13
22, 28
2
Practice Paaper

22
Sample Paaper


The table below
w shows thee strand(s) an
nd related to
opics of each
h of the folloowing crosss-topic questtions.
Noote that somee of them aree modified from
f
the DS
SE Exam queestions.
Q
Question
Strand
1
Geometry
2
Related Topics
T
Junior Seecondary:
Senior Seecondary:
Trigonomeetric Ratios
Basic Prop
perties of Cirrcles

Junior Seecondary:
Trigonomeetric Ratios
Mensuratio
on
Basic Prop
perties of Cirrcles

Geometry
Senior Seecondary:
3
Geometry
4
Geometry
5
Algebra
6
Junior Seecondary:
Coordinatee Geometry
Symmetry and Transfoormation
20016 I 7
Junior Seecondary:
Coordinatee Geometry
Symmetry and Transfoormation
Trigonomeetric Ratios
20013 I 6
Junior Seecondary:
Senior Seecondary:
Percentagees
Quadratic Equations
E
inn One Unknnown

Junior Seecondary:
Straight Liines and Recctilinear Figuures
Trigonomeetric Ratios
Equations of Straight L
Lines

Geometry
Senior Seecondary:
1100
DSE
E Exam
Reference
7
Data
Handling
Junior Seecondary:
Statistical Diagrams
D
Simple Ideea of Probabbility
8
Algebra /
Geometry
Junior Seecondary:
Senior Seecondary:
Coordinatee Geometry
Quadratic Equations
E
inn One Unknnown
20016 I 9

Cross-Topic Questions Pre-Training
7.
The frequency distribution table and the cumulative frequency distribution table below show the
distribution of the ages of the visitors to a theme park.
Age
Frequency
Age less than
Cumulative frequency
1 – 10
17
10.5
17
11 – 20
p
20.5
42
21 – 30
36
30.5
m
31 – 40
q
40.5
110
41 – 50
8
50.5
n
51 – 60
60.5
121
r
(a) Find p, q and r.
(b) A visitor with age less than 20.5 or greater than 50.5 can buy the ticket with half price. If a
visitor is randomly selected, find the probability that he / she CANNOT buy a ticket with half
price.
(5 marks)
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
115
Pre-DS
SE Assessmentt 1
Name: __________
_
______
Class:
__
__________
_____
Date:
__
__________
____
Marks: ______ /7
70
Unless oth
herwise spe
ecified, nume
erical answe
ers should be
b either exa
act or correcct to 3 signifiicant figuress.
Section A(1)
A
(35 marrks)
1.
Simp
plify
(m 8 n 3 ) 2
and ex
xpress your answer
a
with
h positive inddices.
( m 5 n ) 3
(3 markks)
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2.
1

Makee a the subjeect of the forrmula x  2 y   b .
a

(3 markks)
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1223
Pre-DS
SE Assessmentt 3
Name: __________
_
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Class:
__
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Date:
__
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Marks: ______ /3
30
Answer all
a question
ns (1 mark for
f each que
estion)
1.
2.
(a + a + a)(3b – b)
b =
A. 3a
3 + 2b.
B. 6ab.
6
C. 2a
2 2b.
D. 6a
6 2b.
4.
5.
If 3 < s < 5 and 5 < t < 7, thenn the range oof
s
values off
is
t
3 s
  1.
A.
5 t
3 s 3
  .
B.
5 t 7
7 s 5
  .
C.
5 t 3
3 s
  1.
D.
7 t
7.
Let k bbe a constaant. Solve the equatioon
(x + k)(x – k + 2) = (xx + k).
A. x = k – 2
B. x = k – 1
C. x = ––k or k – 1
D. x = ––k or k – 2
8.
The base of a parrallelogram is increaseed
from 166 cm to 244 cm but its height is
decreasedd by 50%
%. Find thee percentagge
4 2 x 16 x
=
8 x  23 x
A. 27x.
B. 22x.
C. 2x.
3
D.
.
2x
3.
6.
15x2z2  16xyz2  15y2z2 =
A. z2(5x  3y)(3
3x  5y).
2
B. z (5x  3y)(3
3x + 5y).
2
C. z (5x + 3y)(3
3x  5y).
2
D. z (5x + 3y)(5
5x  3y).
Let m and n be co
onstants. If
m(x2 – x) – n(x2 + x)  2x2 + 6x, then m =
A. –2.
–
B. 2.
C. –4.
–
D. 4.
Expreess
2400 as a decim
mal correct to
o5
change inn the area off the parallellogram.
A. An iincrease of 8.33%
8
B. 0%
C. A deecrease of 8.33%
D. A deecrease of 255%
signifficant figurees.
A. 48.989
4
B. 48.98979
4
C. 48.990
4
D. 48.999
4
1443