GR 8 MATHEMATICS
EXAM QUESTION PAPERS & MEMOS
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Paper 1 1 M1
Paper 2 3 M3
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EXAM QUESTIONS
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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.
QUESTION 1
Complete the table below.
Put ticks in the correct places to classify each number.
Na
tura
l
Inte
ge
r
Ra
tio
na
l
Irra
tio
na
l
Re
al
Ima
gin
ary
-3
4π
-7
36
[4]
QUESTION 2 Remember:
2.1 Write down the lowest common multiple
of 10 and 12. (1)
2.2 Which is bigger: 13,2 or 163 ?
(Explain your answer.) (1)
2.3 How many whole numbers lie between
8 and 80 ? (1)
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? (1)
2.5 Write down the factors of 18. (2)
2.6 Simplify
7
4
10
5 10×
(2)
2.7 � and � are natural numbers and � % � = 36.
What is the largest possible value of � - �? (2)[10]
QUESTION 3
3.1 Simplify :
3.1.1 1
12
+ 2
33
3.1.2 5
116
÷ 11
212
(3)(3)
3.2 n
? means the reciprocal of n.
So, 5? =
1
5, for example.
Which of the following are true? Write down the
letter(s) that correspond to all the correct statements.
A 3? + 6
? = 9
?
B 6? - 4
? = 2
?
C 2? % 6
? = 12
?
D 10? ÷ 5
? = 2
? (2)[8]
QUESTION 4
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? (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. When they finished, how many potatoes had
Charles peeled? (3)
4.3 If y
x =
2
3 and
y
z =
7
5 find the value of
z
x. (3)[8]
QUESTION 5
Given: 3x - 4x2 + 2x
3 - 1
5.1 What is the degree of the expression? (1)
5.2 What is the coefficient of x3
? (1) 5.3 Write down the constant term. (1) 5.4 What is the value of the expression if x = 1? (1)
5.5 Rearrange the expression in descending
powers of x. (1)[5]
QUESTION 6
Simplify :
6.1 -4x + 6x - x (1)
6.2 -6x2 - (-x
2) (1)
6.3 -4(x + 2y) (2)
6.4 3 2727x (2)
6.5 -3x2y % 4xy
3 (2)
6.6 - (2x2)3 (2)
6.7 4
16
4
16
x
x
(2)
6.8 3x - x (2x + 1) (2)
6.9 ( )
3 26 - 4
- 12
×x x
x
- (2x)4 (4)[18]
QUESTION 7
7.1 If a = -2, which is the largest number in the set
{ }
2
24- 3a ; 4a ; ; a ; 1
a ? (2)
7.2 Subtract : 3x - 4y - z
-x - 3y + z (3)
7.3 Multiply : -5xy2
(4x3 - xy
3) (2)
7.4 Divide:
3 2 4
2
9 y - 27 y
- 9 y
x x
x
(2)[9]
1½ hours
100 marks
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EXAM QUESTIONS
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QUESTION 8
8.1 Solve for x :
(first try and solve by inspection where possible)
8.1.1 -12
x = -3 (1)
8.1.2 x2 = 25 (2)
8.1.3 2x - 3 = 5 (2)
8.1.4 -3(2x + 3) = 4x - 4 (3)
8.2.1 Solve for x : x - 5 + 2x = -14 (2)
8.2.2 Hence solve for y :
3 3 2y + 1 - 5 + 2 2y + 1 = - 14
(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).
Showing some working, what should the
coefficient of x have been? (5)[19]
QUESTION 9
9.1 Write down the next term in the patterns below:
9.1.1 11 ; 8 ; 5 ; 2 ; . . . (1)
9.1.2 3 ; 6 ; 12 ; 24 ; . . . (1)
9.1.3 4 ; 1 ; 6 ; 2 ; 8 ; 4 ; 10 ; 8 ; . . . (1)
9.2 A 'stair-step' figure is made up
of alternating black and
white squares in each row. Rows 1 to 4 are shown.
All rows begin and end
with a white square.
How many black squares are in the 37th
row? (2)
9.3 Given the pattern 5 ; 11 ; 17 ; 23 ; 29 ; . . .
Find the difference between the 201st
term
and the first term. (2)[7]
QUESTION 10
Alan left school at 15h00. He walked home.
On the way home, he stopped to talk to a friend.
His brother, Barry, left the same school at 15h15.
He cycled home using the same route as Alan.
Here are the distance-time graphs for Alan's
and Barry's complete journeys.
10.1 How far did Alan walk during the first ten minutes
of his journey? (1)
10.2 How long did Alan spend talking to his friend? (1)
10.3 At what time did Barry pass Alan? (1)
10.4 What was Barry's speed in kilometres per hour? (2)[5]
QUESTION 11
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). They each find a spade with a note attached to it.
Complete the table below to determine which person,
A, B or C reaches the treasure.
Start After first
transformation
After second
transformation
A (-4; -1)
B (3; -5)
C (4; 8) Congratulations! _____ reaches the treasure!
(Fill in A, B or C). [7]
TOTAL: 100
x
T
C
A
B
y
9
8
7
6
5
4
3
2
1
-1
- 2
- 3
- 4
- 5
- 6
- 8 -1- 2- 3- 4- 5- 6- 7 1 2 3 4 5 6 7 8
Instructions for C :
� Start at (4; 8) � Enlarge by a scale factor
of 1
4about the origin.
� Reflect the new point in
the y-axis.
C
Instructions for B:
� Start at (3; -5) � Rotate 90° clockwise about the origin. � Translate the new point
3 units right and 5 units up.
B
Instructions for A:
� Start at (-4; -1) � Translate 5 units right and
2 units down. � Reflect the new point in the x-axis.
A
1
2
3
y
Dis
tan
ce f
rom
sch
oo
l (k
m)
15h00 15h10 15h20 15h30
Time
O x
EXAM QUESTIONS
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GR 8 MATHS PAPER 2
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.
QUESTION 1
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. The table below shows the price of a bus ticket against
the number of passengers:
Price of ticket (Rand) Number of passengers
250 25
180 50
190 45
220 38
200 44
210 40
240 31
1.1 Draw a scatter plot to represent this data. (4)
1.2 Draw a line of best fit. (1) 1.3 Estimate the number of passengers if the price
of a ticket is R230. (2)[7]
QUESTION 2
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.
2.1.1 Determine the range. (1) 2.1.2 Determine the mean. (3) 2.1.3 Determine the median. (2) 2.1.4 Determine the mode. (1) 2.1.5 Which day of the week were the least
amount of Grade 8 boys absent? (1)
2.2 The pie chart alongside
shows the breakdown,
in degrees, of the
different flavours
of frozen yoghurt
that Diego sold on
the first day
in November.
If Diego sold 180 units on
the first day of November, how many units of
the English Toffee flavour did he sell? (3)
[11]
QUESTION 3
Luke wants to attend the 2015 MTV's Video Music Awards
(VMAs) which will be held in Los Angeles, California. 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)
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]
QUESTION 4
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) 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]
Chocolate
44°
English Toffee
108°
Vanilla
32° Mixed Berry
96°
Lemon Sorbet
80°
Price of ticket (Rand)
x
y
170 180 190 200 210 220 230 240 250
50
55
Nu
mb
er
of
pa
sse
ng
ers
45
40
35
30
25
20
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.
1
8
9
Nu
mb
er
of
bo
ys
ab
sen
t
Days of the week
x
7
6
5
4
3
2
Number of Gr 8 boys absent
0
Tu
e
We
d
Th
u
Fri
Tu
e
We
d
Th
u
Fri
Mo
n
Tu
e
We
d
Th
u
Fri
Mo
n
Mo
n
Tu
e
We
d
Th
u
Fri
Mo
n
y
1½ hours
100 marks
EXAM QUESTIONS
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QUESTION 5
5.1 Find the size of x in
the following triangle.
(2)
5.2 State clearly what
kind of ΔKLM is,
be specific. Show all working. (5)
5.3 ABCD is a rhombus. Given that AD = 10, BD = 2x and
AC is 4
3 times longer than BD.
Find the length of ED. Show all working.
(7)[14]
QUESTION 6
6.1 Complete each of the following statements:
6.1.1 A quadrilateral with both pairs of
opposite sides parallel and a pair of
adjacent sides equal is a _________ . (1) 6.1.2 A quadrilateral with one pair of
opposite sides parallel is a _________ . (1)
6.2 ABCD is a kite with
ˆA = 85° ; ˆC = 50° ;
ˆD = y ; AD = 5 cm.
Find with reasons, the:
6.2.1 length of AB. (2)
6.2.2 the value of y. (5)
[9]
QUESTION 7
7.1 Find with reasons,
the value of
a, b and c in
alphabetical order.
(6)
7.2 Find with
reason(s),
the value
of x. (4)
7.3 Find with
reasons,
the value of
x and y. (7)
7.4 Find with
reasons,
the value
of x.
(6)[23]
QUESTION 8
8.1 A tent in the form of a triangular prism
has an isosceles triangle
as one of the faces.
8.1.1 Calculate the total surface area of
this prism. (4) 8.1.2 Calculate the volume of this prism. (3)
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. EF = 1,3 m ; DE = AH = 0,2 m ; GF = 1 m and EA = HG.
Calculate the area of the shaded part of the diagram.
(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.
If PW = VT = SR = 2 cm and it is given that the
area of the non-shaded shape VXUYT is 1
282
of the area of the semi-circle, calculate the area of the shaded part of the diagram.
(8)[21]
TOTAL: 100
M
K
52
105
85
L
A
10
B D
C
E
20
21
x B
C D
Ac
a
b
105°
C DA
y3x
6x
D E
F C B G
1,3 m
1 m
0,2 mA H
0,2 m
A
85°
B D
C
50°
y
BA
B C
D E 1
2
64°
2x - 10°
4x + 30°
B
C D
A4x
x + 30°
2,92 m
4,2 m
3 m
2,5 m
Q
P R
X YU
V
SW
2 cm 2 cm
T2 cm
EXAM MEMOS
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GR 8 MATHS PAPER 1
1.
Na
tura
l
Inte
ge
r
Ra
tio
na
l
Irra
tio
na
l
Re
al
Ima
gin
ary
-3 � � �
4π � �
-7
�
36 � � � �
2.1 60 � . . .
2.2 Note: No calculator allowed!
169 = 13 . . . 132 = 169
â 163 < 13
â 13,2 is bigger than 163 �
2.3 8 < 9 = 3 and 80 < 81 = 9
â The whole numbers between 8 and 80 are:
3 ; 4 ; 5 ; 6 ; 7 ; 8
â The number of
whole numbers = 6 � . . .
2.4 The smallest product
= (-7) % 3 = -21 � . . .
2.5 F18 = 1 ; 2 ; 3 ; 6 ; 9 ; 18 �
2.6
7
4
10
5 10×
= 10 10 10 10× × × 10× 10× 10×
5 10× 10× 10× 10×
⎡ ⎤⎢ ⎥⎣ ⎦
= 3
10
5
= 1 000
5
= 200 �
2.7 36 - 1
= 35 � . . .
3.1.1 1
21 +
2
33
= 3
2 +
11
3
= 9 + 22
6
= 31
6
= 1
65 �
3.2
C and D are true �
4.1 The number of cats = 3
2 + 3 + 30 of 385
=
1
3
35
% 385
11
1
= 3 11
1 1
×
×
= 33 �
4.2
44 potatoes to be peeled
Minutes 1st
2nd
3rd
4th
5th
6th
7th
8th
9th
10th
11th
Potatoes peeled by:
Matthew 3 3 3 3 3 3 3 3 3 3 3
Charles 5 5 5 5 5 5 5
Total peeled 3 6 9 12 20 28 36 44
Number of potatoes which Charles peeled = 4 % 5 = 20 �
OR Number of potatoes peeled � in the 1
st 4 minutes: 4 % 3 = 12 . . . Matthew
� & thereafter :
3 + 5 = 8 per minute . . . Matthew & Charles
for the remaining
44 - 12 = 32 potatoes â 4 minutes . . .
â Number of potatoes Charles peeled = 4 % 5 = 20 �
4.3 y
x %
y
z =
2
3 %
7
5 . . .
â x
z =
14
15
â z
x =
15
14 � Be sure to answer
the question!
A: 1
3 +
1
6 =
2
6 +
1
6 =
3
6 =
1
2 ≠
1
9
B: 1
6 -
1
4 =
2
12 -
3
12 = -
1
12 ≠
1
2
C: 1
2 %
1
6 =
1
12 = 12
? �
D: 1
10 ÷
1
5 =
1
10 %
5
1 =
1
2 = 2
? �
Note the possibility
of ' removing' y
by cancelling.
3.1.2 5
161 ÷
11
122
= 21
16 ÷
35
12
= 3
21
164
% 12
3
355
= 3 3
4 5
×
×
= 9
20 �
Possibilities:
36 & 1 ; 18 & 2 ; 12 & 3 ; 9 & 4 ; 6 & 6
Trial & error
Note: The total of 44 potatoes were
peeled by the 8th
minute.
32 potatoes
8 per min
The smallest will be the number
furthest left on the number line!
Hint:
Draw a diagram!
If fractions are equal then
their inverses are equal.
Remember: NO CALCULATOR
10 = 2 % 5 and 12 = 22 % 3
â LCM = 22 % 3 % 5
OR 10, 20, 30, 40, 50, 60, 70, . . .
12, 24, 36, 48, 60, 70, . . .
1½ hours
100 marks
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5. 3x - 4x2 + 2x
3 - 1
5.1 3rd
� 5.2 2 � 5.3 -1 �
5.4 If x = 1, the expr. = 3(1) - 4(1)2 + 2(1)
3 - 1
= 3 - 4 + 2 - 1
= 0 �
5.5 2x3 - 4x
2 + 3x - 1 �
6.1 -4x + 6x - x = x � 6.2 -6x2 - (-x
2) = -6x
2 + x
2
= -5x2 �
6.3 -4(x + 2y) 6.4 3 2727x = 3x
9 �
= -4x - 8y �
6.5 -3x2y % 4xy
3 6.6 - (2x
2)3 = -8x
6 �
= -12x3y
4 �
6.7 4
16
4
16
x
x
= 12
1
4x
� 6.8 3x - x (2x + 1)
= 3x - 2x2 - x
= -2x2 + 2x �
6.9 ( )
3 26 - 4
- 12
×x x
x
- (2x)4 =
5- 24
- 12
x
x
- (2x)4
= 2x4 - 16x
4
= -14x4 �
7.1 -3a �
7.2 4x - y - 2z �
7.3 -5xy2
(4x3 - xy
3)
= -20x4
y2
+ 5x2
y5 �
7.4
3 2 4
2
9 y - 27 y
- 9 y
x x
x
=
3 2
2
9 y
- 9 y
x
x
-
4
2
27 y
- 9 y
x
x
= - x2 + 3y
2
8.1.1 -12
x = -3
By inspection, x = 4 � . . . -12 ÷ ? = -3
8.1.2 x2 = 25
â x = ±5 �
8.1.3 2x - 3 = 5
â 2x - 3 + 3 = 5 + 3
â 2x = 8
â 2x
2 =
8
2
â x = 4 �
8.1.4 -3(2x + 3) = 4x - 4
â -6x - 9 = 4x - 4
â -6x - 9 + 9 = 4x - 4 + 9
â -6x = 4x + 5
â -6x -- 4x = 4x -- 4x + 5
â -10x = 5
â -10x
-10 =
5
-10
â x = -1
2 �
8.2.1 x - 5 + 2x = -14
â 3x - 5 + 5 = -14 + 5
â 3x = -9
â 3x
3 = -
9
3
â x = -3 �
8.2.2
3
2y + 1 = -3 . . . the same solution as in Q 8.2.1
â 2y + 1 = -27 . . .
â 2y + 1 -- 1 = -27 -- 1 . . . subtract 1 on both sides
â 2y = -28
â 2y
2 =
-28
2 . . . divide by 2 on both sides
â y = -14 �
8.3 If 3x - 7 = 38
then 3x = 45
then x = 15, 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 5x = 45 â The coefficient of x is 5 �
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 ; ; 8 ; ; 10 ; ; 12 �
1 2 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 ; . . .
( i.e. 20 ; 2
1 ; 2
2 ; 2
3 ; . . . )
The brackets arevery important!
-3a = -3(-2) = 6 ; 4a = 4(-2) = -8;
24
a =
24
- 2 = -12 ; a
2 = (-2)
2 = 4
3x - (- x) = 3x + x = 4x
-4y - (-3y) = -4y + 3y = -y
-z - (+ z) = -z - z = -2z
Do this by inspection:
What number - 7 = 38? 3 times what number = 45?
raise both sides tothe power 3 . . .
Note: Each TERM in the
numerator must
be placed over
the denominator.
Note: This equation has 3 2y + 1 in
the place of x, as in Q 8.2.1.
So, the NEXT term would've been?
. . .Note: 5
2 = 25
But, also, (-5)2 = 25
Distributive property:
a(b + c) = ab + ac. . .
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9.2 The number of black squares
in the 1st
row: 0
in the 2nd
row: 1
in the 3rd
row: 2
in the 4th
row: 3
in the 37th
row: 36 �
9.3
â The difference between the 201st
term and
the first term = 1 205 - 5 = 1 200 �
10.1 1 km � 10.2 5 minutes � 10.3 15h25 �
10.4 3 km in 15 minutes
â 12 km in 1 hour
i.e. Speed = 12 km/h �
11. Start After first
transformation
After second
transformation
A (-4; -1) (1; -3) (1; 3)
B (3; -5) (-5; -3) (-2; 2)
C (4; 8) (1; 2) (-1; 2)
Congratulations! C reaches the treasure!
GR 8 MATHS PAPER 2
1.1 & 1.2
1.3 approximately 34 passengers � . . .
2.1.1 The range = 8 - 0
= 8 days �
2.1.2 The mean
= 2 0 + 5 1 + 2 2 + 4 3 + 2 4 + 1 5 + 2 6 + 1 7 + 1 8
20
× × × × × × × × ×
= 61
20
= 3,05 �
2.1.3 Ranking the 20 scores: 0 ; 0 ; 1 ; 1 ; 1 ; 1 ; 1 ; 2 ; 2 ; 3 ; 3 ; 3 ; 3 ; . . .
â The median = 3 � . . .
2.1.4 The mode = 1 � . . .
2.1.5 Thursday �
2.2 Number of units of English Toffee
= 108°
360° % 180 . . .
= 54 units �
3.1 Cost of the ticket = 900 % 10,93 = R9 837 �
3.2 The formula: A = P(1 + in)
where A = the final amount;
P = the initial amount;
i = the rate of interest per year;
n = the number of years
â 18 500 = ( )( )⎡ ⎤⎢ ⎥⎣ ⎦
17 5
100 2P 1 +
â 18 500 = P(1,425)
â 18 500
1,425 =
P(1,425)
1,425
â P = R12 982,46 �
4.1 The price before VAT
= R520 ÷ 1,14
= R456,14 �
4.2.1 The deposit = 10% of R5 170
= R517 � . . . 10% = 1
10 OR 0,1
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 �
A revolution
is 360°
see graph
above
the average of the
10th
and 11th
terms.
the score which
occurs most often.
VAT inclusive price
= original price x 1,14
Price of ticket (Rand)
x
y
170 180 190 200 210 220 230 240 250
50
55
Nu
mb
er
of
pa
sse
ng
ers
45
40
35
30
25
20
(Q 1.3)
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 ; . . .
Each term (in the given sequence) is 1 less.
â The 201st
term = 201 % 6 - 1 = 1 205.
. . . 1 less than the
row number.
A pattern is seen here. The number of black squares is always . . . ?
1½ hours
100 marks
EXAM MEMOS
M4 Copyright © The Answer
2
EX
AM
ME
MO
S:
PA
PE
R 2
M
4.2.3 The monthly amount
= 5 909,31
36
l R164,15 � . . . rounded off to the nearest cent
5.1 x2 = 20
2 + 21
2 . . .
= 841
â x = 841
= 29 �
5.2 1052 = 11 025
& 852 + 52
2 = 9 929, which is less than 105
2
â ˆM is an obtuse angle
. . . m2 > k
2 + l
2
â ΔKLM is a scalene,
obtuse-angled Δ �
5.3 ED = x . . .
& AE = 1
2AC
= ( )x×1 4
22 3
= x4
3
ˆAED = 90° . . .
â ED2 + AE
2 = AD
2 . . . Theorem of Pythagoras
â x2 + ( )x
24
3 = 10
2
â x2 + x
216
9 = 100
â x225
9 = 100 . . . 1 +
16
9 =
9 + 16
9 =
25
9
â 9
25 x x
225
9 = 100 x
9
25
â x2 = 36
â x = 6 . . .
i.e. The length of ED = 6 units �
6.1.1 A quadrilateral with both pairs of
opposite sides parallel and a pair of
adjacent sides equal is a rhombus. �
6.1.2 A quadrilateral with one pair of
opposite sides parallel is a trapezium. �
6.2.1 AB = 5 cm � . . . AB = AD, adjacent sides of kite
6.2.2 ˆABC = y . . . by symmetry
â 2y + 85° + 50° = 360° . . .
â 2y = 225°
â y = 112,5° �
OR
Join AC.
ˆCAD = °
1(85 )
2 & ˆACD = °
1(50 )
2 . . .
= °1
422
= 25°
â In ΔACD: y = 180° - ( )°
°
142 + 25
2
= 112,5° �
7.1 a = 105° � . . . vertically opposite angles
b = 180° - a . . .
= 75° �
c = b . . .
= 75° �
OR : c = 180° - 105° . . . ø's on a straight line
= 75°
7.2 4x = x + 30° . . . alternate ø's ; AB || CD
â 4x -- x = x -- x + 30°
â 3x = 30°
â x
3
3 =
°
3
30
â x = 10° �
the long
diagonal
bisects the
ø's of a kite
Theorem of
Pythagoras
diagonals bisect
one another
diagonals bisect
at right angles
sum of interior ø's of a quadrilateral
co-interior ø's ;
AB || CD
corresponding ø's;
AB || CD
A
85°
B D
C
50°
y
20
21
x
M
K
52
105
85
L
A
10
B D
C
E
B
C D
Ac
a
b
105°
x is positive only because it is a length
B
C D
A4x
x + 30°
EXAM MEMOS
Copyright © The Answer M5
M
EX
AM
ME
MO
S:
PA
PE
R 2
2
7.3 ˆACB = 3x . . . ø's opposite equal sides
â In ΔACB:
3x + 3x + 6x = 180° . . . sum of ø's in Δ
â 12x = 180°
â x = 15° �
& y = 6x + 3x . . .
= 9x
= 9(15°)
= 135° �
OR : y = 180° - 3x . . . ø's on a straight line
= 180° - 3(15°)
= 135° �
7.4 ˆ
1D = 4x + 30° (OR ˆC = 2x - 10°)
. . . corresponding ø's ; DE || BC
â In ΔADE (OR in ΔABC):
(4x + 30°) + (2x - 10°) + 64° = 180° . . .
â 6x + 84° = 180°
â 6x + 84° -- 84º = 180° -- 84º
â 6x = 96°
â x
6
6 =
°
6
96
â x = 16° �
8.1.1
The total surface area
= 2Δs + 3 rectangles
= 2 ( )× ×
13 2,5
2 + (3 % 4,2) + 2(4,2 % 2,92)
= 7,5 + 12,6 + 24,528
= 44,628 m2
l 44,63 m2 � . . .
8.1.2 The volume
= area of the Δr base % the height of the prism
= ×
1(3 2,5)
2 % 4,2
= 15,75 m3 �
8.2
In ΔEBF: EB2
= EF2 - BF
2
= 1,32 - (0,2 + 1)
2
= 0,25
â EB = 0,5 m
& AB = 1(0,5)
2 . . . EA = HG
= 0,25 m
â The area of the shaded part
= Area of rectangle DCBE + area of rectangle ABGH
= 0,2 % 0,5 + 0,2 % 0,25
= 0,1 + 0,05
= 0,15 m2 �
8.3
The area of the shaded part
= � Area of a semi-? PQR + � Area of WXYS
- � Area of the non-shaded shape VXUYT
� Area of semi-?
= π
2(3)
2 . . . the radius =
1
2 % 6 = 3 cm
= 14,14 cm2
� Area of WXYS
= WX % WS . . . length % breadth
= 3 cm % 2 cm . . . WX = radius of ? = 3 cm
= 6 cm2
� Area of the non-shaded shape VXUYT
= 1
282 of 14,14 . . . area of semi-? in �
= 0,05 cm2
â The area of the shaded part = 14,14 + 6 - 0,05
= 20,09 cm2 �
exterior ø of Δ = sum of interior opposite ø's
sum of
interior ø's
of triangle A
B C
D E1
2
64°
2x - 10°
4x + 30°
Note: There is often more than one way!
Note:
instruction is
to round off to
2 decimal places
D E
FC B G
1,3 m
1 m
0,2 mA H
0,2 m
The challenge with this
question is to read it well !
B
C DA
y3x
6x
2,92 m
4,2 m
3 m
2,5 m
Q
P R
X YU
V
SW
2 cm 2 cm
T2 cm
2 cm
