GR 8 MATHEMATICS
EXAM QUESTION PAPERS & MEMOS
Exam Questions
Exam Memos
Paper 1
1
M1
Paper 2
3
M3
We trust that working through these
exam papers and following our detailed
answers and comments will help you prepare
thoroughly for your final exam.
The Answer Series Maths study guides offer
a key to exam success.
EXAM QUESTIONS
1
Q
1½ hours
100 marks
GR 8 MATHS PAPER 1
All necessary working must be shown in its
proper place with the answer.
No calculator may be used in this paper.
Diagrams are not necessarily drawn to scale.
Simplify:
3.1.2
11
5
÷ 2
1
12
16
(3)(3)
means the reciprocal of n.
?
1
= , for example.
5
Which of the following are true? Write down the
letter(s) that correspond to all the correct statements.
Imaginary
Real
Irrational
Rational
Integer
?
So, 5
Complete the table below.
Put ticks in the correct places to classify each number.
Natural
QUESTION 6
3.1 Simplify:
1
3.1.1 1 + 3 2
2
3
3.2 n
QUESTION 1
A 3
?
+6
?
= 9
?
B 6
?
-4
?
= 2
?
C 2
?
%6
?
= 12
?
= 2
?
D 10
?
÷5
?
6.1 -4x + 6x - x
(1)
6.2 -6x - (-x )
2
2
(1)
6.3 -4(x + 2y)
(2)
6.4
3
27x27
(2)
2
3
6.5 -3x y % 4xy
2 3
(2)[8]
(2)
4 x4
16 x16
(2)
(2)
6.7
QUESTION 4
6.8 3x - x (2x + 1)
4π
4.1 A pet shop sells only dogs, cats and mice in the
ratio 2 : 3 : 30. If there are 385 animals in total,
how many cats are there in the shop?
6.9
36
[4]
QUESTION 2
Remember:
2.1 Write down the lowest common multiple
of 10 and 12.
2.2 Which is bigger: 13,2 or
(Explain your answer.)
(1)
163 ?
2.3 How many whole numbers lie between
8 and 80 ?
QUESTION 5
2
2.5 Write down the factors of 18.
(2)
107
5 × 104
(2)
6 x3 × (- 4 x2 )
4
- (2 x)
- 12 x
(4)[18]
QUESTION 7
7.1 If a = - 2, which is the largest number in the set
{- 3a ; 4a ; 24a ; a ; 1 } ?
2
(3)
(3)[8]
(2)
7.2 Subtract: 3x - 4y - z
-x - 3y + z
2
3
(3)
3
7.3 Multiply:
-5xy (4x - xy )
(2)
7.4 Divide:
9 x3y 2 - 27 x y 4
- 9 xy 2
(2)[9]
3
Given: 3x - 4x + 2x - 1
2.7 and are natural numbers and % = 36.
What is the largest possible value of - ? (2)[10]
Copyright © The Answer
y
x
2
7
z
=
and
= find the value of x .
y
z
3
5
(1)
(1)
2.6 Simplify
When they finished, how many potatoes had
Charles peeled?
4.3 If
2.4 Consider the numbers: -7 ; -5 ; - 1 ; 1 ; 3
Using only two of the above numbers, what is
the smallest product one could make?
(2)
4.2 Matthew began peeling a pile of 44 potatoes at
a rate of 3 potatoes per minute. Four minutes
later Charles joined him and peeled at a rate of
5 potatoes per minute.
(1)
(2)
6.6 -(2x )
-3
-7
EXAM QUESTIONS: PAPER 1
QUESTION 3
5.1 What is the degree of the expression?
3
(1)
5.2 What is the coefficient of x ?
(1)
5.3 Write down the constant term.
(1)
Maths is easier than you thought !
5.4 What is the value of the expression if x = 1?
(1)
The Answer Series offers excellent material
for Maths (Gr 8 - 12).
(1)[5]
See our website www.theanswer.co.za
5.5 Rearrange the expression in descending
powers of x.
1
EXAM QUESTIONS
9.2 A 'stair-step' figure is made up
of alternating black and
white squares in each row.
8.1 Solve for x:
(first try and solve by inspection where possible)
12
= -3
x
(1)
2
8.1.2 x = 25
(2)
8.1.3 2 x - 3 = 5
(2)
8.1.4 -3(2x + 3) = 4x - 4
(3)
8.2.1
Solve for x: x - 5 + 2x = - 14
8.2.2
Hence solve for y:
3
(2)
th
How many black squares are in the 37 row?
(2)
9.3 Given the pattern 5 ; 11 ; 17 ; 23 ; 29 ; . . .
st
3
(4)
8.3 Jonathan can't quite read the board in his
Maths class. He writes down the equation
he reads on the board as 3x - 7 = 38.
He correctly solves the equation he wrote down,
but is surprised to hear the teacher say the
answer is 6 less than the answer he found.
When he asks the teacher to check his work,
the teacher says that Jonathan copied the
coefficient of x incorrectly (but copied everything
else correctly).
9
8
7
6
5
4
3
T 2
1
An island has treasure
buried on it at the
point T (-1; 2).
Three contestants
arrive at different
points on the island.
A arrives at (- 4; -1),
B arrives at (3; -5) and
C arrives at (4; 8).
- 8 - 7 - 6 - 5 - 4 - 3 - 2 -1-1
A
(2)[7]
Alan left school at 15h00. He walked home.
On the way home, he stopped to talk to a friend.
B
Here are the distance-time graphs for Alan's
and Barry's complete journeys.
QUESTION 9
3
C
9.1.1 11 ; 8 ; 5 ; 2 ; . . .
(1)
9.1.2 3 ; 6 ; 12 ; 24 ; . . .
9.1.3 4 ; 1 ; 6 ; 2 ; 8 ; 4 ; 10 ; 8 ; . . .
1 2 3 4 5 6 7 8
x
B
Instructions for C :
Start at (4; 8)
Enlarge by a scale factor
of
2
1
about the origin.
4
Reflect the new point in
the y-axis.
1
15h10
15h20
Time
15h30
Complete the table below to determine which person,
A, B or C reaches the treasure.
x
Start
10.1 How far did Alan walk during the first ten minutes
of his journey?
(1)
9.1 Write down the next term in the patterns below:
Q
Instructions for B :
Start at (3; - 5)
Rotate 90° clockwise about the origin.
Translate the new point
3 units right and 5 units up.
y
O
15h00
C
Instructions for A :
Start at (- 4; - 1)
Translate 5 units right and
2 units down.
Reflect the new point in the x-axis.
A
His brother, Barry, left the same school at 15h15.
He cycled home using the same route as Alan.
(5)[19]
-2
-3
-4
-5
-6
1
y
They each find a spade with a note attached to it.
Find the difference between the 201 term
and the first term.
QUESTION 10
2y + 1 - 5 + 2 2y + 1 = - 14
Showing some working, what should the
coefficient of x have been?
Rows 1 to 4 are shown.
All rows begin and end
with a white square.
Distance from school (km)
8.1.1 -
QUESTION 11
10.2 How long did Alan spend talking to his friend?
(1)
(1)
10.3 At what time did Barry pass Alan?
(1)
(1)
10.4 What was Barry's speed in kilometres per hour? (2)[5]
2
A
B
C
After first
transformation
After second
transformation
(- 4; - 1)
(3; - 5)
(4; 8)
Congratulations! _____ reaches the treasure!
(Fill in A, B or C).
[7]
TOTAL : 100
Copyright © The Answer
EXAM QUESTIONS: PAPER 1
QUESTION 8
EXAM QUESTIONS
1½ hours
100 marks
GR 8 MATHS PAPER 2
Q
All necessary working must be shown in its
proper place with the answer.
Calculators are allowed to be used.
Give answers to two decimal places, unless
instructed otherwise.
3.1 He wants to buy a VIP Limo Pass for $900 to get
dropped off at the red carpet. The exchange rate
is R10,93 to the US dollar ($). How much will he
pay for the ticket in South African rand?
(2)
Number of Gr 8 boys absent
7
6
Q3.2 below requires the knowledge and application
of the simple interest formula (using A, P, i and n)
and should therefore be treated as extension
beyond the Gr 8 Maths Curriculum.
5
4
3
2
0
x
Days of the week
3.2 Bolnick Travel Agency is offering a package deal
for South Africans who want to attend the VMAs
which includes your flight tickets with United Airlines
and 5 nights at the Double Tree Hilton Hotel for
only R18 500. How much money must Luke invest
at 17% per annum simple interest for 2,5 years
to get this amount?
(4)[6]
250
25
180
50
2.1.1 Determine the range.
(1)
190
45
2.1.2 Determine the mean.
(3)
220
38
2.1.3 Determine the median.
(2)
QUESTION 4
200
44
210
40
2.1.4 Determine the mode.
(1)
240
31
2.1.5 Which day of the week were the least
amount of Grade 8 boys absent?
(1)
4.1 'The Script' will be performing at the Grand Arena.
A Golden Ticket costs R520, inclusive of VAT.
Calculate the price of the ticket before VAT is
added.
(2)
1.1 Draw a scatter plot to represent this data.
Number of passengers
y
1
Price of ticket (Rand) Number of passengers
EXAM QUESTIONS: PAPER 2
Luke wants to attend the 2015 MTV's Video Music Awards
(VMAs) which will be held in Los Angeles, California.
Number of boys absent
The table below shows the price of a bus ticket against
the number of passengers:
(4)
y
50
45
40
35
30
25
180
2.1 Given below is a bar graph that displays the number
of days Grade 8 boys are absent from school during
the month of February.
8
A travel bureau found that the price of a bus ticket to
a certain town has an influence on the number of
passengers who make use of the service.
20
170
QUESTION 3
9
QUESTION 1
55
QUESTION 2
Mon
Tue
Wed
Thu
Fri
Mon
Tue
Wed
Thu
Fri
Mon
Tue
Wed
Thu
Fri
Mon
Tue
Wed
Thu
Fri
2
190
200 210 220 230
Price of ticket (Rand)
1.2 Draw a line of best fit.
240
250
x
(1)
1.3 Estimate the number of passengers if the price
of a ticket is R230.
(2)[7]
Copyright © The Answer
2.2 The pie chart alongside
Chocolate
shows the breakdown,
44°
in degrees, of the
English Toffee
different flavours
108°
Lemon Sorbet
of frozen yoghurt
80°
that Diego sold on
Vanilla
the first day
32°
Mixed Berry
in November.
96°
If Diego sold 180 units on
the first day of November, how many units of
the English Toffee flavour did he sell ?
3
(3)
[11]
4.2 Sony is offering a Triple Pack PS4 bundle which
includes three PS4 games with a standard
500GB black console for R5 170.
The Hire Purchase agreement is as follows:
you must pay a deposit of 10% and pay the balance
off at 9% per annum simple interest over 3 years.
4.2.1 Calculate the deposit you need to put down. (1)
4.2.2 Calculate the total amount paid for
the Triple Pack PS4, including interest,
after the deposit has been paid.
(4)
4.2.3 Calculate the amount of each monthly
instalment.
(2)[9]
EXAM QUESTIONS
QUESTION 5
QUESTION 7
5.1 Find the size of x in
the following triangle.
7.1 Find with reasons,
the value of
a, b and c in
alphabetical order.
20
(2)
21
M
5.2 State clearly what
kind of ΔKLM is,
be specific.
Show all working.
85
52
K
105
L
A
5.3 ABCD is a rhombus.
Given that AD = 10, BD = 2x and
AC is
(5)
10
4
times longer than BD.
3
Find the length of ED.
B
D
E
Show all working.
C
(7)[14]
7.2 Find with
reason(s),
the value
of x.
A
7.4 Find with
reasons,
the value
of x.
A
6.1.2 A quadrilateral with one pair of
opposite sides parallel is a _________ .
(1)
AD = 5 cm.
64°
2x - 10°
B
G
F
1m
(6)
8.3 The cross-section of a screw is given. It is made
up of rectangle STVW, semi-circle PQR and
a segment TUV.
B
If PW = VT = SR = 2 cm and it is given that the
area of the non-shaded shape VXUYT is 1
E
282
C
(6)[23]
of the area of the semi-circle, calculate the area
of the shaded part of the diagram.
Q
QUESTION 8
8.1 A tent in the form of a triangular prism
has an isosceles triangle
as one of the faces.
2,92 m
A
6.2 ABCD is a kite with
D̂ = y ;
D
(7)
6x
1
2
1,3 m
A 0,2 m H
C
B
(1)
Ĉ = 50° ;
C
y
4x + 30°
6.1.1 A quadrilateral with both pairs of
opposite sides parallel and a pair of
adjacent sides equal is a _________ .
Calculate the area of the shaded part of the diagram.
(4)
D
3x
D
6.1 Complete each of the following statements:
 = 85° ;
x + 30°
C
P
2 cm
2 cm
W
S
R
85°
2,5 m
B
Find with reasons, the:
4,2 m
y D
V
3m
6.2.1 length of AB.
(2)
6.2.2 the value of y.
(5)
50°
C
[9]
Q
D 0,2 m E
B
4x
2
EF = 1,3 m ; DE = AH = 0,2 m ; GF = 1 m and EA = HG.
D
(6)
A
7.3 Find with
reasons,
the value of
x and y.
QUESTION 6
b
C
B
X
8.1.1 Calculate the total surface area of
this prism.
(4)
8.1.2 Calculate the volume of this prism.
(3)
4
2 cm
U
T
Y
(8)[21]
TOTAL : 100
Copyright © The Answer
EXAM QUESTIONS: PAPER 2
x
c 105°
a
A
8.2 Wally wants to construct a ramp (EF) from the
top of the staircase (E) to the ground (F) at the
clock tower entrance of the school.
EXAM MEMOS
1
1½ hours
100 marks
GR 8 MATHS PAPER 1
M
2.4
The smallest product
= (-7) % 3 = -21 The number of cats =
Trial & error
The smallest will be the number
furthest left on the number line!
Remember: NO CALCULATOR
2.5
1.
Imaginary
Real
Irrational
Rational
Integer
Natural
2.6
-3
4π
⎡ 10 × 10 × 10 × 10 × 10 × 10 × 10 ⎤
107
= ⎢
⎥
5 × 10 × 10 × 10 × 10
5 × 104
⎣
⎦
103
=
5
1 000
=
5
= 200 2.7
36
F 18 = 1 ; 2 ; 3 ; 6 ; 9 ; 18 -7
36 - 1
Possibilities:
= 35 . . . 36 & 1 ; 18 & 2 ; 12 & 3 ; 9 & 4 ; 6 & 6
2.1
60 2
10 = 2 % 5 and 12 = 2 % 3
...
2
â LCM = 2 % 3 % 5
OR
2.2
10, 20, 30, 40, 50, 60, 70, . . .
12, 24, 36, 48, 60, 70, . . .
169 = 13
â
8 <
9 = 3 and
163 80 <
â The whole numbers between
3; 4; 5; 6; 7; 8
81 = 9
8 and
=
1
1
1
+ 1 = 2 + 1 = 3 =
≠
2
3
6
6
6
6
9
B:
2
3
1
1
1 1
=
= ≠
6 4
12 12
12
2
C:
1
1
1
?
%
=
= 12 2
12
6
D:
5
1
1
1
1
?
÷
=
%
=
= 2 1
2
10
5
10
C and D are true M1
385
3
%
1
35
1
=
3 × 11
1×1
11
Hint:
Draw a diagram!
44 potatoes to be peeled
Minutes
Potatoes
peeled by :
Matthew
Charles
Total peeled
st
1
2
nd
3
rd
4
3
3
3
3
3
6
9
th
th
5
th
6
th
7
8
th
9
th
10
11
3
5
3
5
3
5
3
3
3
3
5
5
5
5
th
th
12 20 28 36 44
Note: The total of 44 potatoes were
th
peeled by the 8 minute.
3
OR
Number of potatoes peeled
st
in the 1 4 minutes: 4 % 3 = 12
3×3
4×5
9
=
20
1
6
=
Number of potatoes which Charles peeled = 4 % 5 = 20 21
12
%
16 4
35 5
A:
80 are:
â The number of
Be sure to answer
whole numbers = 6 . . .
the question!
Copyright © The Answer
31
6
3.2
163 < 13
â 13,2 is bigger than
2.3
2
4.2
11
5
÷ 2
12
16
35
21
÷
=
12
16
3
3
of 385
2 + 3 + 30
= 33 1
=
=5
. . . 13 = 169
3.1.2
3
11
=
+
3
2
9 + 22
=
6
=
Note: No calculator allowed!
1
2
+ 3
2
3
1
3.1.1
EXAM MEMOS: PAPER 1
...
4.1
. . . Matthew
& thereafter:
3 + 5 = 8 per minute . . . Matthew & Charles
for the remaining
44 - 12 = 32 potatoes
â 4 minutes
...
32 potatoes
8 per min
â Number of potatoes Charles peeled = 4 % 5 = 20 4.3
y
x
%
z
y
â
=
2
7
%
3
5
x
14
=
z
15
15
z
â x =
14
. . . Note the possibility
of 'removing' y
by cancelling.
If fractions are equal then
their inverses are equal.
3
7.3
3x - 4x + 2x - 1
rd
5.4
If x = 1, the expr. = 3(1) - 4(1) + 2(1) - 1
= 3 - 4 + 2 - 1 The brackets are
= 0 very important!
3
2 5.3
-1 2
3
2x - 4x + 3x - 1 6.1
-4 x + 6x - x = x 2
2
2
-6x - (-x ) = -6x + x
6.2
-4(x + 2y)
3
6.4
27x
27
9
= 3x = -4x - 8y 6.5
=
3
-3x y % 4xy
2 3
6
6.6
-(2x ) = - 8 x 6.8
3x - x(2x + 1)
= -12x y 4 x4
1
=
16 x16
4x 12
2
8.1.1 -
8.1.2
8.1.3
6.9
- (2 x)
- 12 x
4
=
5
8.1.4
- 24 x
4
- (2x)
- 12 x
4
= 2x - 16 x
2
4x - y - 2z . . . -12 ÷ ? = -3
2
x = 25
2
Note:
5 = 25
2
But, also, (-5) = 25
...
2x - 3 = 5
â 2x - 3 + 3 = 5 + 3
â 2x = 8
2x
8
=
â
2
-3(2x + 3) = 4x - 4
-10
2
-4y - (- 3y) = -4y + 3y = -y
-z - (+ z) = -z - z = - 2z
-10
1
â x = - 2
a = (- 2) = 4
3x - (- x) = 3x + x = 4x
2
â y = -14 â -6x -- 4 x = 4x -- 4 x + 5
â -10x = 5
- 10x
5
=
â
8.2.1
7.2
2
12
= -3
x
â -6x = 4x + 5
-3a = -3(-2) = 6 ; 4a = 4(-2) = -8;
24
24
=
= - 12 ;
a
-2
M
â 2y = -28
2y
-28
â
=
. . . divide by 2 on both sides
â -6x - 9 + 9 = 4x - 4 + 9
4
= -14 x -3a 2
â -6x - 9 = 4x - 4
4
7.1
9x y
27 x y
- 9 x y2 - 9 x y2
1
8.3
If
3x - 7 = 38
then
3x = 45
then
x = 15,
Do this by inspection:
What number - 7 = 38?
3 times what number = 45?
â Jonathan's answer was 15, but the
teacher's answer is 6 less than this, i.e. 9
For x to be equal to 9, we must have 5 x = 45
â The coefficient of x is 5 â x = 4 2
6 x × (- 4 x2 )
Note: This equation has 3 2y + 1 in
the place of x, as in Q 8.2.1.
2y + 1 = -3 . . . the same solution as in Q 8.2.1
â 2y + 1 = -27 . . . raise both sides to
the power 3
â 2y + 1 -- 1 = -27 -- 1 . . . subtract 1 on both sides
Note: Each TERM in the
numerator must
...
be placed over
the denominator.
4
2
2
8.2.2
3
By inspection, x = 4 = 3x - 2x - x
= -2x + 2x 3
3 2
â x = ±5 3 4
6.7
. . . Distributive property:
a(b + c) = ab + ac
9 x3 y2 - 27 x y 4
- 9 x y2
7.4
2
2
2
2 5
EXAM MEMOS
= - x + 3y
= -5 x 6.3
-5xy (4x - x y )
2
5.5
3
= -20x y + 5x y
3
5.2
3
4 2
5.1
2
x - 5 + 2x = -14
â 3x - 5 + 5 = -14 + 5
â 3x = -9
3x
9
â
= 3
3
â x = -3 M2
9.1.1 11 ; 8 ; 5 ; 2 ; -- 1 . . . subtracting 3
9.1.2 3 ; 6 ; 12 ; 24 ; 48 . . . doubling, i.e. %2
9.1.3 4 ;
; 6;
1
; 8;
2
; 12 ; 10 ;
4
8
Note:
There are actually two separate patterns
4 ; 1 ; 6 ; 2 ; 8 ; 4 ; 10 ; 8 ; . . .
even numbers starting at 4: 4 ; 6 ; 8 ; 10 ; . . .
the powers of 2: 1 ; 2 ; 4 ; 8 ; . . .
0
1
2
3
(i.e. 2 ; 2 ; 2 ; 2 ; . . .) So, the NEXT term
would've been?
Copyright © The Answer
EXAM MEMOS: PAPER 1
5.
2
EXAM MEMOS
9.2
M
The number of black squares
st
in the 1 row : 0
nd
A pattern is seen here.
in the 2 row: 1
rd
The number of black
in the 3 row: 2
squares is always . . . ?
th
in the 4 row: 3
th
in the 37 row: 36 9.3
. . . 1 less than the
row number.
There is a constant difference of 6 between
the terms. So, compare the sequence to the
sequence of the multiples of 6:
6 : 12 ; 18 ; 24 ; 30 ; . . .
1½ hours
GR 8 MATHS PAPER 2 100 marks
55
50
10.1
1 km 10.2 5 minutes 10.4
3 km in 15 minutes
10.3 15h25 40
30
The formula: A = P(1 + in)
180
A = the final amount;
P = the initial amount;
25
190
200 210 220 230
Price of ticket (Rand)
approximately 34 passengers 240
250
x
i = the rate of interest per year;
n = the number of years
( )( )
â 18 500 = P ⎡⎢1 + 17 5 ⎤⎥
100 2 ⎦
⎣
. . . see graph
above
â 18 500 = P(1,425)
â
2.1.1 The range = 8 - 0
= 8 days 18 500
P(1,425)
=
1,425
1,425
â P = R12 982,46 2.1.2 The mean
61
=
20
20
After first
After second
transformation transformation
4.1
The price before VAT
= R520 ÷ 1,14
= 3,05 EXAM MEMOS: PAPER 2
3.2
where
i.e. Speed = 12 km/h = R456,14 2.1.3 Ranking the 20 scores:
A
(-4; -1)
(1; -3)
(1; 3)
B
(3; -5)
(-5; -3)
(-2; 2)
â The median = 3 C
(4; 8)
(1; 2)
(-1; 2)
. . . thethaveragethof the
10 and 11 terms.
. . . the score which
occurs most often.
2.1.4 The mode = 1 Congratulations! C reaches the treasure!
2.1.5 Thursday M3
VAT inclusive price
= original price x 1,14
4.2.1 The deposit = 10% of R5 170
0; 0; 1; 1; 1; 1; 1; 2; 2; 3; 3; 3; 3; ...
Copyright © The Answer
Cost of the ticket = 900 % 10,93 = R9 837 (Q 1.3)
= 2× 0 + 5×1 + 2× 2 + 4 × 3 + 2× 4 + 1× 5 + 2×6 + 1×7 + 1× 8
Start
. . . A revolution
is 360°
3.1
35
â 12 km in 1 hour
11.
108°
% 180
360°
45
st
â The difference between the 201 term and
the first term = 1 205 - 5 = 1 200 =
= 54 units â The 201 term = 201 % 6 - 1 = 1 205.
1.3
Number of units of English Toffee
y
20
170
Each term (in the given sequence) is 1 less.
st
2.2
1.1 & 1.2
Number of passengers
2
= R517 . . . 10% =
1
10
4.2.2 The balance = R5 170 - R517 = R4 653
â After the deposit, the total amount paid
= 4 653 + 3 % 9% % 4 653
= 4 653 + 1 256,31
= R5 909,31 OR
0,1
EXAM MEMOS
4.2.3 The monthly amount
ˆ = 90°
AED
5 909,31
=
36
2
. . . rounded off to the nearest cent
x2 = 202 + 212
. . . Theorem of
Pythagoras
= 841
â x = 841
= 29 x
20
2
2
â M̂ is an obtuse angle
2
2
2
... m > k + l
M
85
52
1
& AE = AC
2
1 4
=
× 2x
2 3
=
105
L
. . . diagonals bisect
one another
(
4
x
3
9
9
= 100 x 9
6.1.2
x is positive only
because it is a length
...
. . . AB = AD , adjacent sides of kite
â 2y = 225°
E
)
. . . sum of interior ø's
of a quadrilateral
â y = 112,5° a = 105° . . . vertically opposite angles
b = 180° - a
. . . co-interior ø's ;
AB || CD
= 75° c = b
= 75° OR :
A
c 105°
a
A
. . . corresponding ø's;
AB || CD
C
B
b
D
c = 180° - 105° . . . ø's on a straight line
= 75°
7.2
4 x = x + 30° . . . alternate ø's; AB || CD
â 4x -- x = x -- x + 30°
. . . by symmetry
â 2y + 85° + 50° = 360°
D
7.1
A quadrilateral with one pair of
opposite sides parallel is a trapezium. ˆ = y
6.2.2 ABC
10
B
M
25
A quadrilateral with both pairs of
opposite sides parallel and a pair of
adjacent sides equal is a rhombus. 6.2.1 AB = 5 cm A
)
= 112,5° 2
6.1.1
K
ED = x
9
i.e. The length of ED = 6 units â ΔKLM is a scalene,
obtuse-angled Δ ( 2
â In ΔACD: y = 180° - 42 1 ° + 25°
. . . 1 + 16 = 9 + 16 = 25
â x = 6
& 85 + 52 = 9 929, which is less than 105
5.3
= 100
= 100
the long
ˆ = 1 (50 °) . . . diagonal
ˆ = 1 (85°) & ACD
CAD
bisects the
2
2
1°
ø's of a kite
= 42
= 25°
2
2
2
105 = 11 025
2
( ) = 10
Join AC .
. . . Theorem of Pythagoras
â x = 36
21
5.2
2
2
â x + 4x
3
2
16 2
x
â x +
9
â 25 x 2
9
25 2
9
x
x
â
25
9
2
5.1
2
â ED + AE = AD
2
OR
â 3x = 30°
â
3x
3
=
30°
3
A
C
4x
x + 30°
B
D
â x = 10° 85°
y D
B
C
50°
M4
C
Copyright © The Answer
EXAM MEMOS: PAPER 2
l R164,15 . . . diagonals bisect
at right angles
EXAM MEMOS
2
ˆ = 3x
ACB
7.3
. . . ø's opposite equal sides
â The area of the shaded part
8.1.1
â In ΔACB:
M
3x + 3x + 6x = 180°
= 0,2 % 0,5 + 0,2 % 0,25
. . . sum of ø's in Δ
A
â 12x = 180°
C
y
3x
â x = 15° D
6x
0,1
+
0,05
2
= 0,15 m 4,2 m
3m
Q
8.3
The total surface area
& y = 6x + 3x . . . exterior ø of Δ
= sum of interior
= 9x
opposite ø's
= 9(15°)
s
= 2Δ + 3 rectangles
= 2 1 × 3 × 2,5 + (3 % 4,2) + 2(4,2 % 2,92)
2
=
7,5
+ 12,6 +
24,528
(
= 135° y = 180° - 3x
=
2,5 m
B
OR :
= Area of rectangle DCBE + area of rectangle ABGH
2,92 m
)
= 44,628 m
. . . ø's on a straight line
2
2
l 44,63 m = 180° - 3(15°)
...
= 135° P
2 cm
2 cm
W
Note:
instruction is
to round off to
2 decimal places
V
X
2 cm
S
2 cm
U
R
T
Y
The area of the shaded part
= Area of a semi-? PQR + Area of WXYS
8.1.2 The volume
r
Dˆ 1 = 4x + 30°
7.4
= area of the Δ base % the height of the prism
1
= (3 × 2,5) % 4,2
2
3
= 15,75 m (OR Ĉ = 2x - 10°)
. . . corresponding ø's; DE || BC
â In ΔADE (OR in ΔABC):
sum of
(4x + 30°) + (2x - 10°) + 64° = 180° . . . interior ø's
of triangle
â 6x + 84° = 180°
A
EXAM MEMOS: PAPER 2
1
2
D 0,2 m E
â 6x + 84° -- 84º = 180° -- 84º
64°
D
8.2
2x - 10°
E
4x + 30°
B
â
C
6x
6
=
â x = 16° Note: There is often more than one way!
= 6 cm
C
B
In ΔEBF:
G
2
1m
2
2
EB = EF - BF
2
2
= 1,3 - (0,2 + 1)
= 0,25
â EB = 0,5 m
& AB =
1
(0,5)
2
= 0,25 m
Copyright © The Answer
2
2
= 14,14 cm
2
= WX % WS . . . length % breadth
= 3 cm % 2 cm . . . WX = radius of ? = 3 cm
1,3 m
96°
6
Area of semi-?
π (3)2 . . . the radius = 1 % 6 = 3 cm
=
Area of WXYS
A 0,2 m H
â 6x = 96°
- Area of the non-shaded shape VXUYT
M5
. . . EA = HG
F
2
Area of the non-shaded shape VXUYT
=
1
of 14,14
282
= 0,05 cm
. . . area of semi-? in 2
â The area of the shaded part = 14,14 + 6 - 0,05
2
= 20,09 cm The challenge with this
question is to read it well!