MATHEMATICS PAPER 1 MID YEAR EXAMINATION 2019 MEMORANDUM

GRADE 10

MATHEMATICS PAPER 1 MID YEAR EXAMINATION 2019 MEMORANDUM

MARKS: 75

This memorandum consists of 6 pages

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QUESTION 1[9]

1.1.1 1.1.2

v 2E m

2132 12

22

irrational

2 Grade 10

1.1.3

16 22 25 4 22 5 it lies between integers 4 and 5

1.2

0,52 0,5222222222..

let x 0,52

10x 5, 2 (1)

100x 52, 2 (2)

equation (2) - (1)

90x 47

x 47 92

QUESTION 2[18]

2.1.1 a 2 2a ax 2x a(a 2) x(a 2) (a 2)(a x)

2.1.2 2.2.1

x3 27 (x 3)(x2 3x 9)

x2 3x 9

x2 3x 9

x3

(2 y 3)(6 y 2 4 y 8) 2 y(6 y 2 4 y 8) 3(6 y 2 4 y 8) 12y3 8y2 16y 18y2 12y 24 12y3 10y2 28y 24

NW/June 2019

substitution answer

(2) answer

(1) 16 22 25 answer

(2)

equation 1 equation 2

90x 47 answer

(4)

a(a 2) x(a 2) answer

(3) factors answer

(3)

12y3 8y2 16y 18y2 12y 24 answer

(3)

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2.2.2

22n 4n 2 22n 22n.2

16n

24n

24n2 24n

2

3 Grade 10

2.2.3

3x3 7x 2 6x 3x 2 2x x(3x 2 7x 6) x(3x 2)

x2 9

3x 9 (x 3)(x 3) 3(x 3)

x(3x 2)(x 3) 3(x 3) (x 3)(x 3) x(3x 2)

3

NW/June 2019

changing 4 n to 2 2n changing 16n to 24n

answer (3)

x(3x 2 7x 6) (x 3)(x 3) x(3x 2) 3(x 3) (3x 2)(x 3) answer

(6)

QUESTION 3[17]

3.1.1

9x 4 5(2x 3) 9x 4 10x 15 9x 10x 4 15 18x 18 x 1

3.1.2 3.2

4x 1 256

22x 1 28

22x 28 2x 8 x 4

10 x 4 12 10 4 x 12 4 6 x8

6

removing brackets

adding like terms answer

(3)

expressing both 4 and 256 as the base of 2

answer (2)

transposing 4

critical values

notation

graphical

representation

8

(4)

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4 Grade 10

3.3

A R2 r2

A R 2 r 2

A R 2 r 2

3.4.1

r R2 A

x2 9y2 99

(x 3y)(x 3y) 99

x 3y 99 x 3y

3.4.2 x 3y 99 x 3y

x 3y 99 3

x 3y 33 equation1

x 3y 3 equation2

2x 36

x 18

18 3y 33

3y 15

y 5

QUESTION 4[10]

4.1.1 11; 16

4.1.2

4.1.3 4.1.3

Pattern is linear, Tn dn c To solve for c , substitute n 1and T1 4 4 5(1) c c 9 Tn 5n 9

Tn 5n 9 T27 5(27) 9

126 Tn 5n 9

71 5n 9 5n 80 n 16

4.2 111111X111111

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r 2 subj. of formula r subj. of formula NB: DO NOT PANELISE IF WRITE R2 A

(2)

factors answer

(2)

substituting 3

2x 36 value of x

value of y (4)

each term (2)

substitution value of c answer

(3) substitution answer

(2) substitution

answer (2)

answer (1)

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QUESTION 5[10] 5.1 y 1 5.2

5 Grade 10

NW/June 2019

answer (1)

Parabola x ? intercepts Turning point concave up Exponential intercepts at (0;0) asymptote increasing function

(6)

5.3 y 1 OR y (1; )

5.4 reflection about the x axis

answer (1)

reflection x axis

(2)

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