Department of Education - Western Province

Department of Education - Western Province

Year End Evaluation - 2020 Grade 10 - Mathematics Answers

^01& 4 ? 6 days 12 2 days

^02& 6x2y

^03&

A

B

^04& 3 + 2 6y

5 6y

^05& a = 1200 b = 400

5

^06&

32 = 2

log 2 32 = 5

^07& between 25 and 36

^08&

1 = 3

a

1 a= 3

^09& x + 600 + 500 = 1800

x = 700

^10& 3 or 1

9

3

^11& 6 ? (5 ? 5)

150cm2

^12& (x + 2) (x - 7)

1800 - 1000 ^13& OAB =

2 = 400

^14& arc length = 36 - 14 = 22cm

1

^15& (i) ?

1

12

(ii) ?

12

22

^16& 126kg 3

22

42kg

^17& 60km

1

3h

20kmh-1

1 2 ^18&

1

^19& 12

x = 700

x = 800 y = 400

1 ^20& Gradient

12

4 =2

=2

1 12 1 12

22 1 12 1 12

2 2 ^21& Height of the cylinder =1540= 10cm 1 154

1

Height of the water column = 5cm

12

12 ^22& ADO D and BDO D ^RHS& 1+1 2

1

1 2 ^23& - 2x ? 12

1

x ? - 6

12

22

1

^24& Rs' 4200 ? 100 12

1

12

Rs' 35000

12

1+1 2 ^25&

1

P

12

1 12

- 01 -

drawing the angle bisector marking P

1 12

50

Grade 10 - Mathematics Answers - Western Province

Part - B (01) (i) 5

8

(ii) 2 of 5 58 1 4

(iii) 3 + 1 84

3 + 2

8

5

8

Remaining = 3

8

(iv) 3 of container 8

18l

capacity = 48l

11 1 12 1

(iii) 1 ? r2 4 1 ? 22 ? 7 ? 7 47 38.5 m2

(iv) 38.5 ? 7 5.5 m

1

(04) (i) 45

1

(ii) 3600 ? 45

14

80

(iii) 640, 800, 960, 1200 1

1

(iv) Drawing the pie chart

1

1

13 1 12

10

11 1 12 44 33

} Quantity of

water used for washing cloths

= 48 ? 1 4

(05) (a)

10

= 12l

1

(02)(a) (i) Rs' 1200 ? 4

1

Rs' 4800

1

(ii) 4800 ? 100%

1

120000

4 %

1

(iii) discount = Rs'4800? 10 1 100

= Rs'480

1

Amount paid = Rs' 4800-480

= Rs' 4320

1

(b)(i)Magnitude of work= 6? 8 md 1

Time

= 6? 8 days 1 4

= 12 days 1

(03) (i) 1 ? 2? r 4

1

1 ? 2 ? 22 ? 7

1

4

7

11m

1

(ii) 21 + 7 + 21 + 11 + 7

1

67m

1

3 (i) Second take

10

b2 ? ? ? ? ?

b1 ? ? ? ? ?

2

r3 ? ? ? ? ?

r2 ? ? ? ? ?

r1 ? ? ? ? ?

2

22

r1 r2 r3 b1 b2

First take

(ii) Circling

11

(iii) 13 25

22

3 (b) (i)

First take Second take

3 Red

5

3

3

5 Red 2

5 Blue

10

3

2 Blue 5

Red

5

2 5

Blue 3 3

3

(ii)

6 +

6

25 25

12

2

25

1 12

10

- 02 -

Grade 10 - Mathematics Answers - Western Province

Mathematics - II

(01) (a)

7 ? 5 of 8 34 5

2

=

7 3

? 5 ? 8 45

=

7 3

? 1 2

7 =6

1 = 16

(b) Rs' 2 500 000? 60 100

Rs' 1 500 000

Rs' 4 000 000 Rs' 4 000 000 ? 15

100

Rs' 600 000 Rs' 4 000 000 ? 600 000 Rs' 4 600 000

(02) (a) (i) y = 3 - x2 = 3 - 12 = 2

(iii)

1

-1

(x - 2) (x + 2) (x - 2) (x + 6)

1

(x + 6) - (x + 2)

=

1

(x - 2) (x + 2) (x + 6)

1

x + 6 - x - 2

= (x - 2) (x + 2) (x - 6)

1

1

1

=

4

(x - 2) (x + 2) (x - 6)

14

14

(04) (a) 15x - 6y = 30

3

1

4x - 6y = 46

4

1

19x = 76

1 1 1

16 10

x =4 4 ? 4 + 6y = 46

y = 5 (b)(i) 1 ? ( x + 5) ? x = 33

2 x2 + 5x = 66

x2 + 5x - 66 = 0

(ii) ( x - 6) (x + 11) = 0

x = 6 or x = - 11

10 1 1

1 14 1

12 2 1

Perpendicular height = 6cm 1 4

11

10

(ii) For the axes Marking the points Smooth curve

(b) (i) 3 (ii) x = 1.7 and x = -1.7

(iii) between -1.7 and 0 or

-1.7 < x < 0 (iv) y = 2 - x2

1 (05) (a) Writing the scale

1

1

Drawing the horizontal line 1

13

marking the 600 angle

1

11 1+1 2

Completing the diagram 1 Finding the height of the building 1 5

} (b) Distance travel in 12 seconds

60? 1000? 12

=

2 60? 60

1+1 2 11

= 200m Length of the train = 200 - 80

= 120m

1 1 15

10

10

(03) (i) (x - 2) (x + 6)

22

(ii) x2 - 4 = (x - 2) (x + 2)

2

x2 + 4x - 12 = (x - 2) (x + 6)

LCM = (x - 2) (x + 2) (x + 6) 2 4

- 03 -

Grade 10 - Mathematics Answers - Western Province

(06) (i) (30 - 40) (ii) x d

1 f f ? d

5 -30 2 -60

15 -20 5 -100

25 -10 9 -90

35 0 15

0

45 +10 10 +100

55 +20 6 +120

65 +30 3 +90

50 + 60

x column

1

d column

1

fd column

1

? fd

Mean age = A +

? f

(6 0

= 3 5 +

2

5 0

= 3 5 + 1 . 2 1

= 3 6 . 2

= 36 years

1

1 9

(b)

? 100%

1

5 0

38 %

1

(08) (i) Drawing the AB line

1

1

Constructing 900

1

Constructing BC line

1

Constructing ABC D 1 4

(ii)Constructing the bisector

of ACB

22

(iii)Constructing the perpendicular

bisector of AC line

11

(iv) Marking the center as O Drawing the circle

1 12

(v) Writing the radius

11

(09) (i) D

10

C P

Q A

2 B

7

AD = BC ^opposite sides&

1

DAQ = BCP ^alternate angles& 1

2

AQD = BPC ^perpendiculars& 1

10

\ ADQ D ? BCPD ^A.A.S.&

16

{

(

(07) (i) Tn = a + (n - 1) d

T12 = a + 11d 62 = 7 + 11d

1

(ii) DQP = BPQ ^perpendiculars& 1

DQ / / BP ^alternate ? & 1

1

DQ = BP ^corresponding elements& 1

55 = 11d

5 = d

1

T10 = a + 9d

1

= 7 + 9 ? 5

1

= 7 + 45

= 52

1

(ii) Sn=

n {2a + (n - 1) d} 2

1

{ 6

S6 = 2

2 ? 7 + 5 ? 5 1

= 3{14 + 25}

= 3 ? 39

1

= 117

1

\ BPDQ ^pair of opposite sides are equal and parallel) 14

10

} (10) (i) Angle subtended

6

at the center

= AOC 1

} Angle subtended = ABC 1 2

on the circle

(ii) ACB

1

ACB = 900

12

(iii) OB = OC ^radius&

1

OBC = OCB ^isosceles D & 1

4

AOC = 2 OBC

1

10

\ AOC = 2 OCB

14

or any other correct proof

- 04 -

Grade 10 - Mathematics Answers - Western Province

(iv) Writing a relevant proof

(12) (i) 22

10 girls

100 60 32

40 20 12

?

Those who came

(11)

(i)

Area

of

a

cross

section

=

1 2

? a ? 2a 1

= a2

1

Volume of the prism = a2 ? b

= a2b

13

(ii) p r2h = a2b

p a2h = a2b

1

28 by cars

Name theVenn diagram Writing the number of elements in each part

(ii) 12

1 45 11

(iii)

?

b h =

p

12

12 (iii) h =

3 . 1 4

log h = lg 12 - lg 3.14

1

(iv)

100

60

11

= 1.0792 - 0.4969 = 0.5823 h = antilog 0.5823

1+1

girls

1

by cars 32 28

40

h = 3.822

15

33

10 10

- 05 -

Grade 10 - Mathematics Answers - Western Province

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