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Gr 8 June 2017

BISHOPSGr 8 MATHEMATICS

MEMO

Time: 2 hours June 2017Total: 150 marks RJ/CSG

INSTRUCTIONS:

1. Answer ALL the questions on this question paper.2. All the necessary work and the answer must be shown in the proper place.3. The use of a calculator is not allowed in this question paper.

-------------------------

Name: ..................................................... Set: ....... Teacher’s Initials: ...............

Total Mark

Question 1

Number System 21

Question 2

Miscellaneous 11

Question 3

Basic Algebra 32

Question 4

Basic Algebra 17

Question 5

Substitution 6

Question 6

Equations and Word sums

15

Question 7

Pythagoras, Area and Perimeter

14

Question 8

Geometry 24

Question 9

Patterns 10

150

Gr 8 June 2017

Gr 8 June 2017

QUESTION 1

1.1 Study the numbers below and list the ones that fulfil the descriptions that follow:100 ; 162 ; 17 ; 90 ; 91; 4 ; 5 ; 22

Answer1.1.1

all the prime numbers 17 ; 5

1.1.2

all multiples of 5 100 ; 90 ; 5

1.1.3

the number that is divisible by both 6 and 9 162 or 90

1.1.4

the common multiple of 2, 3 and 5 90

1.1.5

all factors of 100 100 or 5 or 4

(6)

1.2 Which of the numbers isAnswer

1.2.1 Natural 4

1.2.2 an Integer 4 or

1.2.3 a rational number

1.2.4 an irrational number

1.2.5 non-real number

(6)1.3 Consider the number 784

1.3.1 Write 784 as a product of its prime factors. Show your working. (2)

2 7842 3922 1962 987 49

Gr 8 June 2017

7 71

1.3.2 Use your answer in Question 1.3.1 to find . (2)

1.4 Calculate each of the following. Show your steps.

1.4.1(2)

1.4.2(3)

[21]

QUESTION 2Indicate whether each of the statements are true or false. If false, correct the statements.

Statement True / False

Correct answer if false

2.1 T2.2 F

2.3

The fraction that lies

halfway between

and is

F

2.4 T

Gr 8 June 2017

2.5

The largest integer between and that is divisible by 2

is 4F 6

2.6 5200mm2 = 0,52cm2 F 52cm2

2.7

If the sides of a triangle are 3 cm,

cm and 2 cm, then the triangle is right-

angled.

T

[11]

Gr 8 June 2017

QUESTION 3Simplify the following:

Answer Mark

3.1 3 a − 5 a − 2a (1)3.2 c2 + c2 +c2 (1)3.3 (2)

3.4 (1)

3.5 6 b3 b 2 (1)

3.6 (4 q ) ( − 2 q ) (2)3.7 (2)

3.8 3 × a + 4 × a × b − 2 ×a (3)

3.9 (3)

3.10 2(a−2 b) (2)

3.11 5 a − 2a(3 a − 3) (3)

3.12

3 pq

÷ 6 qq2 (2)

3.13 3( x− y )−2(2 x− y )−3 x (4)

3.14 (3)

3.15

14 d2 − 7 d7 d

(2)

[32]

Gr 8 June 2017

Gr 8 June 2017

QUESTION 44.1 Given:

4.1.1 Rewrite the above expression in descending powers of .

(1)

4.1.2 Find the value of the expression if

(2)

4.1.3 What is the constant term?

(1)

4.1.4 What is the coefficient of ?7 (1)

4.1.5 Write down the degree of the expression.3 (1)

4.1.6 Add to the expression given above.

(3)

4.2 Answer the following questions:Answer Mark

4.2.1 How many legs do x dogs have? (1)

4.2.2 What is the odd number before if is also an odd number?

(1)

4.2.3What is your annual income if you earn a monthly salary of R ?

(2)

4.2.4What is the complement of

?(2)

4.2.5Jack is years old. Gary is 27 years younger than Jack. How old will Gary be in 5 years’ time?

(2)

[17]

Gr 8 June 2017

QUESTION 5If a = 3 , b = − 2 and c = 0 , calculate the value of:5.1 (2)

=

5.2 (2) =

5.3 (2)

[6] QUESTION 66.1 Solve for x in each of the following equations: 6.1.1 (1)

6.1.2 (3)

6.1.3 (3)6.1.4 (4)

6.2 A container is full of water. If 100 litres are tapped off, the tank is

full. Let x = the volume of the water in a full tank. Determine the volume of water in a full tank by setting up an equation. (4)

[15]

Gr 8 June 2017

Gr 8 June 2017

7.1.1

Determine the length of d. (2)

7.1.2

a) Determine the length of c(4)

b) Complete the statement for the area of by

writing down the name of the side and then the value of the side in the spaces provided. (2)

QUESTION 7

7.2 In the given diagram, ABCD is a kite. AE = EC = 4 cm. DE = 6 cm and EB = x cm.

The area of the kite is 64 cm2

7.2.1Calculate the area of

(2)

7.2.2Determine the length of EB (4)

Gr 8 June 2017

[14]

QUESTION 8:

8.1 Determine, stating reasons, the size of all

the angles marked a to d. (8)

8.2 In the given figure DE||BC, AD = AC, , and

8.2.1 Determine, without giving reasons, the value of x and y. Fill in the sizes of all angles calculated clearly on the given sketch. (4)

Statement Reason

a =

b =

c =

d =

Gr 8 June 2017

8.2.2 Now prove that AB||DC. (2)

Gr 8 June 2017

8.3 In the given sketch, AC|| DF.

and

8.3.1 Complete the statement and supply a reason for the statement

Statement Reason

(2)

8.3.2 Now determine the size of (2)

8.4 In the given sketch , ,

, and . BF is a straight line. Solve for x and y by setting up an equation.

Reasons must be given for all statements.

(6)

[24]

Gr 8 June 2017

Gr 8 June 2017

QUESTION 9

Case 1

1 2 3

Case 2

Use the given diagrams to complete the table below.

Case 1 Case 2

Number of layers Number of squares Number of layers Number of cans

Arrangement 1 1 1 2 3



Arrangement 4 4 16 5 15Arrangement 10 10 100 11 66

Arrangement n n n2 n + 1

[10]

TOTAL : 150

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