MATHEMATICS GRADE 8 NOVEMBER 2018
PAPER 2
Examiner
Date:
November 2018
Moderator
Time:
1½ hours
Marks
80
MEMO
Name
Educator's
name
INSTRUCTIONS:
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY:
1
This question paper consists of 13 pages. Please check that your paper is complete.
2
Read the questions carefully and answer all the questions on this question paper.
3
Unless stated otherwise, all diagrams are not drawn according to scale.
4
You may draw and make notes on all the diagrams.
5
You may use an approved, non-programmable and non-graphical calculator, unless
otherwise stated.
6
Round off your answers to two decimal digits where necessary.
7
All the necessary working details must be clearly shown.
8
It is in your own interest to write legibly and to present your work neatly.
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
4
7
4
14
4
7
4
12
13
Q10 Q11 Q12 TOTAL
4
4
3
80
-2QUESTION 1
Study the diagram below and choose the correct type of angle from the column on the right
SKETCH
TYPE OF ANGLES
complementary
co-interior
alternate
vertically opposite
right
corresponding
(a)
𝐴̂4 and 𝐵̂3 are ________ corresponding _________ angles.
✓
(1)
(b)
𝐵̂2 and 𝐵̂4 are _________ vertically opposite _____ angles.
✓
(1)
(c)
𝐴̂3 and 𝐵̂3 are ______ co-interior _____________ angles.
✓
(1)
(d)
𝐴̂3 and 𝐵̂4 are _______ alternate ____________ angles.
✓
(1)
[4]
QUESTION 2
(a)
Use the diagram below to determine the size of the angles. Given: 𝐶̂5 = 35°.
̂2 = 35°. ✓
𝐷
(1)
̂4 = 35°. ✓
𝐷
(1)
̂1 = 180°. ✓
𝐶̂5 + 𝐷
(1)
𝐶̂4 = 65°. ✓
(1)
𝐶̂1 + 𝐶̂2 + 𝐶̂3 + 𝐶̂4 + 𝐶̂5 = 360°. ✓
(1)
(b)
-3Use the diagram below to answers the questions that follow: (1 mark per reason ONLY)
Is AB parallel to CD? Give a reason for your answer:
No
Corresponding angles not the same (40° and 50°) ✓
Or Alternating angles not the same
Or Co-int angles are not supplementary
Or any other valid reason.
(1)
Is EF parallel to GH? Give a reason for your answer:
Yes
Co-int angles are supplementary (130° and 50°)
Or any other valid reason
(1)
[7]
QUESTION 3
Choose the quadrilateral(s) for which the given property is applicable. Make a ✓ the appropriate
column(s). (1 mark per row, allow halves)
Properties
All adjacent sides are equal
Rhombus
Trapezium
Parallelogram
✓
Only 1 pair of opposite sides are parallel
✓
✓
Diagonal intersect perpendicular
✓
Diagonal bisect the opposite angles
✓
✓
[4]
QUESTION 4
(a)
The polygon below is a regular pentagon. Calculate the value of 𝑥.
Sum of interior angles = 180 x 3 = 540 ✓
540
So 𝑥 = 5 = 108 ✓
(2)
(b)
-4The triangle below is an isosceles triangle. Calculate the value of 𝑥.
(2)
Size of bottom left angle is (180 – 50)/2 = 65o ✓
So 𝑥 = 180 − 65 = 115✓
Or 𝑥 = 50 + 65 = 115
(c)
̂ 𝐶 = 70𝑜 .
In parallelogram ABCD, 𝐵𝐴̂𝐶 = 20𝑜 and 𝐴𝐷
Determine the value of 𝑥 and 𝑦.
(2)
𝑥 = 70 ✓
𝑦 = 180 − 20 − 70 = 90 ✓
(d)
In trapezium QRST, 𝑄𝑆̂𝑅 is a right angle.
𝑇𝑄̂ 𝑆 is equal to _____90____ °. ✓
(1)
The sum of the four interior angles is equal
to _______360_________ °. ✓
(1)
Solve for 𝑥. Hint: Make use of an equation.
90 + 90 + 2𝑥 + 𝑥 = 360 ✓
180 + 3𝑥 = 360
3𝑥 = 180
𝑥 = 60 ✓
(2)
-5(e)
ABDC is a rectangle. AC = AF =FE.
(4)
𝐶𝐴̂𝐵 is equal to ____90_____ degrees. ✓
∆AFC is an isosceles triangle.
∴ 𝑥 = 45 ✓
CE is a straight line.
∴ 𝑦 = 180 − 45 = 135 ✓
∴𝑧=
180−135
2
= 22,5 ✓
[14]
QUESTION 5
In the diagram below, two identical small circles and one large circle are sketched inside a grey
rectangle.
(a)
Calculate the area of one of the small circle with radius r = 2m.
(1)
𝐴 = 𝜋𝑟 2 = 4𝜋𝑚2 ✓
𝑂𝑟 𝐴 = 12,57𝑚2
(b)
Calculate the area of the large circle with radius r = 5m.
(1)
-6𝐴 = 𝜋𝑟 2 = 25𝜋𝑚2 ✓
𝑂𝑟 𝐴 = 78,54𝑚2
(c)
Calculate the area of the rectangle.
(1)
𝐴 = 18 × 10 = 180𝑚2 ✓
(d)
Use your answers in (a), (b) and (c) to calculate the area of the shaded part.
(1)
𝐴 = 180 − 4𝜋 − 4𝜋 − 25𝜋 = 76,33𝑚2 ✓
Allow continuous assessment
Allow rounding off differences due to previous answers
[4]
QUESTION 6
Calculate the area of the shaded parts in the figures below.
Divided into a rectangle and a triangle:
Area of the rectangle = 11 × 10 = 110𝑚2 ✓
1
Area of the triangle = 2 × 10 × 4 = 20𝑚2 ✓
Total Area = 130 𝑚2 (trivial, so not for marks)
Also accept other logical calculations and steps
(2)
-7-
Calculate area of large rectangle and subtract the 2
small rectangles OR break up into smaller
rectangles
Area of the large rectangle = 7 × 10 = 70𝑚2 ✓
Area of a small rectangle = 1,5 × 5 = 7,5𝑚2 ✓
Shaded area = 70 − 7,5 − 7,5 = 55𝑚2 ✓
(3)
1
Area of semi-circle = 2 × 64𝜋 = 32𝜋𝑚2 ✓
Area of square = 100𝑚2 (trivial, not for marks)
Total area = 32𝜋 + 100
=200,53 𝑚2 ✓
(2)
[7]
QUESTION 7
(a)
Calculate the area of a circle with circumference 20𝜋cm.
(2)
Since C = 20𝜋cm, r = 10 cm ✓
Thus area = 100𝜋𝑐𝑚2 ✓ OR 314,16𝑐𝑚2
(b)
A piece of string was used to form a circle with radius r = 9cm. If the same string is used to
form an equilateral triangle, calculate the length of one side of the triangle.
(2)
Total length of string = circumference = 18 𝜋𝑐𝑚 ✓
Length of one side of the triangle =
18𝜋𝑐𝑚
3
= 6𝜋𝑐𝑚 ✓
OR 18,85cm
[4]
-8QUESTION 8
(a)
Underline the equation that represents the theorem of Pythagoras.
(1)
• 𝑟2 + 𝑠2 = 𝑡 2
• 𝑟2 + 𝑡 2 = 𝑠2
• 𝑡 2 + 𝑠2 = 𝑟2 ✓
(b)
In the diagram in (a), side r is called the _____hypotenuse ✓___________
(c)
Calculate the value of 𝑥.
(1)
122 + 92 = 𝑥 2 ✓
𝑥
9m
𝑥 = 15𝑚 ✓
(2)
12m
Firstly, find BC:
512 + 𝐵𝐶 2 = 852 ✓
𝑠𝑜 𝐵𝐶 = 68𝑚 ✓
𝑥
Second, since BE = CE, BE = 34m ✓
Lastly, 342 + 342 = 𝑥 2
𝑠𝑜 𝑥 = 48,08𝑚 ✓
(4)
(d)
Underline the option that best describes the unidentified sides of the triangle below.
•
XY = 76m and XZ = 95m ✓
•
XY = 72m and XZ = 94m
•
XY = 70m and XZ = 92m
(1)
(e)
-9A school has a rectangular field. John takes 350
Tuck shop
steps to walk across the field from the tuck shop to
the library and 210 steps to walk from the tuck
shop to the bathroom. John claims that he can walk
Field
from the bathroom to the library in only 260 steps.
Calculate whether his statement is true.
Bathroom
Library
𝑥 2 + 2102 = 3502 ✓✓
𝑥 = 280 𝑠𝑡𝑒𝑝𝑠 ✓ (allow for continuous assessment)
Therefore his claim is false. (trivial conclusion, not for marks)
(3)
[12]
QUESTION 9
(a)
The area of the shaded kite is 24cm². Calculate the volume and the surface area of
this prism.
Volume:
Volume = area of base x height of prism
= 24 x 6
= 144𝑐𝑚3 ✓
(1)
Surface Area:
A = 24m²
There are 6 areas to sum:
Surface area = 24 + 24 + 4x6 + 4x6 + 5x6 + 5x6
✓
✓
= 156𝑚2 ✓
(3)
(b)
- 10 Calculate the volume of the following structure:
Volume = 15x28x3 – 4x18x3
= 1260 – 216
✓
✓
= 1044𝑚3 ✓
(3)
(c)
Two prisms are combined to form a larger object: (SA – surface area)
State whether the following statements are True or False. If false, give a reason (without any
calculation):
(4)
Statement
True or False (with a reason)
True✓✓
The combined object has a
volume of 105m3.
False. ✓Did not subtract the 2 faces that are pressed together
The combined object has a
surface area of 134cm2.
(d)
OR any other logical answer✓
A classroom has a volume of 528m3. If the floor is 11m wide and 12m long, what is the
height of the classroom’s ceiling?
528 = 11 × 12 × 𝑥 ✓
So 𝑥 = 4𝑚, the ceiling is 4m high. ✓
(2)
- 11 -
[13]
QUESTION 10
In a study about social media platforms, people were asked if they prefer Twitter, Instagram or
Snapchat. The data collected is presented in the pie chart below.
FAVOURITE SOCIAL MEDIA PLATFORM
None
?%
Twitter
25%
Snapchat
30%
Instagram
35%
(a)
If 30 people prefer Twitter, determine how many people took part in this survey.
(1)
30 x 4 = 120 people ✓
(b)
How many people prefer to use Instagram?
(1)
35% of 120 = 42 people ✓ (allow continuous assessment)
(c)
How many people do not use any of these platforms?
(1)
10% of 120 = 12 people ✓
(d)
Create a short and quick survey that can be used for this investigation.
(1)
Any logical survey. ✓
For example: “Which social media platform do you prefer the most between Instagram,
Snapchat, Twitter or none of those?”
[4]
- 12 QUESTION 11
The time taken by athletes to complete a marathon is shown in the histogram below.
Time taken to complete a marathon
50
Frequency
40
30
20
10
0
1 to 1,5
1,5 to 2
2 to 2,5
2,5 to 3
3 to 3,5
3,5 to 4
4 to 4,5
4,5 to 5
Time (hours)
(a)
(b)
Use the data in the histogram to complete the following frequency table:
Time taken (hours)
Frequency
1 to 2
45 ✓ half
2 to 3
90 ✓ half
3 to 4
60 ✓ half
4 to 5
25 ✓ half
Total
220
How many athletes took longer than 4½ hours to complete the marathon?
(2)
(1)
10 people ✓
(c)
Which percentage of the athletes completed the marathon within 2 hours?
(1)
45
× 100 = 20,45% ✓
220
[4]
- 13 QUESTION 12
The number of subscribers for a certain YouTube channel was recorded over a period of
6 months.
Number of subscribers (millions)
4.2
3.9
3.4
3.1
2.7
2.3
MARCH
(a)
APRIL
MAY
JUNE
JULY
AUGUST
What is the range of the number of subscribers over this period?
(1)
4,2 – 2,3 = 1,9 million subscribers ✓ (or 1 900 000 subscribers)
(b)
What is the mean number of subscribers per month over this period?
(1)
19,6 / 6 = 3,27 million subscribers ✓ (or 3 266 667 subscribers)
(c)
During which month did this channel have the most number of subscribers?
(1)
In June (half a million growth) ✓
[3]
Total: 80