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.
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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)
?
1 = , for example. 5
A 3
?
+6
?
B 6
?
-4
?
C 2
?
%6
D 10
?
?
÷5
?
= 9
?
= 2
?
6.1 -4x + 6x - x 2
means the reciprocal of n.
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
(1)
6.2 -6x - (-x )
2
(1)
6.3 -4(x + 2y)
(2)
6.4
3
27x27
(2)
2
3
6.5 -3x y % 4xy
= 12
?
= 2
?
2 3
(2)[8]
(2)
4 x4 16 x16
(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)
(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 )
7.4 Divide:
9 x3y 2 - 27 x y 4 - 9 xy 2
(2)
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)
(2)[9]
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).
5.5 Rearrange the expression in descending powers of x.
1
(1)[5]
See our website www.theanswer.co.za
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 -3 -4 -5 -6
(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]
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
C y
64° 2x - 10°
6.1.2 A quadrilateral with one pair of opposite sides parallel is a _________ .
(1)
G
F
1m
(6)
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
B
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
B
(1)
D
(7)
6x
1 2
1,3 m
A 0,2 m H
C
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:
Aˆ = 85° ; Dˆ = y ;
x + 30°
C
P
2 cm
2 cm W
S
R
85°
Cˆ = 50° ;
2,5 m
AD = 5 cm.
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
2
â LCM = 2 % 3 % 5 OR
2.2
10, 20, 30, 40, 50, 60, 70, . . . 12, 24, 36, 48, 60, 70, . . .
â
2
3.2
163 < 13
8 <
9 = 3 and
163 80 <
â The whole numbers between 3; 4; 5; 6; 7; 8
81 = 9 8 and
â The number of Be sure to answer whole numbers = 6 . . . the question! Copyright © The Answer
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
=
3 × 11 1×1
11
Hint: Draw a diagram! st
Minutes
nd
2
1
Potatoes peeled by : Matthew Charles Total peeled
3
3
3
rd
3
3
6
9
th
4
3
th
5
th
6
th
7
th
8
3
3
3
3
5
5
5
5
th
9
th
th
10
11
3 5
3 5
3 5
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 1 1 + 1 = 2 + 1 = 3 = ≠ 2 3 6 6 6 6 9
385 3 % 1 35 1
44 potatoes to be peeled
=
1 6
=
Number of potatoes which Charles peeled = 4 % 5 = 20
21 12 % 16 4 35 5
A:
80 are:
4.2
11 5 ÷ 2 12 16 35 21 ÷ = 12 16 3
3 of 385 2 + 3 + 30
= 33
1
=
31 6
=5
. . . 13 = 169
â 13,2 is bigger than 2.3
=
Note: No calculator allowed! 169 = 13
3.1.2
3 11 = + 3 2 9 + 22 = 6
10 = 2 % 5 and 12 = 2 % 3
...
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!
2
5.3
-1
2
3
2x - 4x + 3x - 1
6.1
-4 x + 6x - x = x
3
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)
3 4
= -12x y 6.7
4 x4 1 = 16 x16 4x 12
=
2
8.1.1 -
8.1.2
8.1.3
6.9
6x
- (2 x)
- 12 x
4
=
5
8.1.4
4
2
4x - y - 2z
. . . -12 ÷ ? = -3
2
x = 25
2
Note: 5 = 25 2 But, also, (-5) = 25
â x = ±5
...
2x - 3 â 2x - 3 + 3 â 2x 2x â
= 5 = 5+3 = 8 8 = 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
Do this by inspection: What number - 7 = 38? 3 times what number = 45?
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 5 x = 45 â The coefficient of x is 5
â x = 4
- 24 x 4 - (2x) - 12 x
= 2x - 16 x
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
2
× (- 4 x2 )
3 2
8.2.2
3
By inspection, x = 4
= 3x - 2x - x = -2x + 2x
3
. . . 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 â 3x - 5 + 5 â 3x 3x â 3
= -14 = -14 + 5 = -9 9 = 3
â x = -3
M2
9.1.1 11 ; 8 ; 5 ; 2 ; -- 1
. . . subtracting 3
9.1.2 3 ; 6 ; 12 ; 24 ; 48 9.1.3 4 ;
; 6; 1
; 8; 2
. . . doubling, i.e. %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 ; . . .
GR 8 MATHS PAPER 2
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
. . . A revolution is 360°
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
108° % 180 360°
3.1
35
â 12 km in 1 hour
11.
=
45
st
1.3
Number of units of English Toffee
= 54 units
â The 201 term = 201 % 6 - 1 = 1 205. â The difference between the 201 term and the first term = 1 205 - 5 = 1 200
2.2
y
20 170
Each term (in the given sequence) is 1 less.
st
1½ hours 100 marks
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
2
â x + 2
5.1
â x +
x2 = 202 + 212
. . . Theorem of Pythagoras
= 841 â x = 841 = 29
â
x
â 9 x
20
25
2
2
ˆ is an obtuse angle â M 2 2 2 ... m > k + l
â ΔKLM is a scalene, obtuse-angled Δ
M 85
52
1 & AE = AC 2 1 4 = × 2x 2 3
=
105
L
. . . diagonals bisect one another
(
4 x 3
= 100 9
9
9
x is positive only because it is a length
...
6.1.2
. . . AB = AD , adjacent sides of kite
)
. . . 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.
â 2y = 225° E
2
M
25
A quadrilateral with both pairs of opposite sides parallel and a pair of adjacent sides equal is a rhombus.
ˆ = y 6.2.2 ABC 10
B
= 112,5°
= 100 x 9
2
6.2.1 AB = 5 cm
A
)
(
â In ΔACD: y = 180° - 42 1 ° + 25°
. . . 1 + 16 = 9 + 16 = 25
= 100
2
6.1.1
K
ED = x
= 10
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
i.e. The length of ED = 6 units
& 85 + 52 = 9 929, which is less than 105
5.3
( )
2
4 x 3 16 2 x 9 25 2 x 9 25 2 x 9
Join AC .
. . . Theorem of Pythagoras
â x = 6
105 = 11 025 2
2
â x = 36
21
5.2
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 Cˆ = 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!
