CXC MATHEMATICS CxcDirect Institute Solutions – May 2008

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** Please see the original past paper for the questions. Only the answers will be provided as per copyright obligations. **********************************************************

ii) iii)

6a b 12a b= 6a b b 2a 2m 9m – 5 let pq = ac ; p+q = b p+q = 9 pq = -10; p = 10, q = -1 2 2 2m 9m – 5 = 2m 10m – m− 5 2

2

3

4

2

2

2

a = 2, b = 9, c = -5

Q1a. s

3.90.27= 4.17

⇒

0.6724=0.82

so: 4.17 0.82= 4.99 b) simplifying the numerator : 17 1 4 5 4 2 − − = = 10 2 5 2 5 . Divide Numerator by denominator: 17 3 ⇒ ÷ 10 4 ⇒

⇒

⇒

= =

2m m 5−m 5 2m – 1 m 5

17 4 × = 10 3

34 = 15

2

4 15

**********************************************************

1.b

⇒

$1Can = J$72.50 $Can 250.00 = J $250 x 72.5 = J$18,125.00

Credit limit = $J 30,000 = $Can (30,000/72.5) = $Can 413.79 Credit card balance = $413.79 – $250.00 = $Can 163.79 **********************************************************

Question 2 a = 2, b = -1, c = 3 a(b+c) = 2(-1 +3) = 4

4b – 2ac ab c

2

=

4 −1 – 2× 2 ×3 2−1 3

2

=

4 – 12 = 4

− 2

b)

i) ii)

4 x5

ab 16

c) i) 15 – 4x = 6x +2

⇒

15− 2=10x 4x 13=10 x x=1.3

⇒

⇒

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Math club :

2

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Q3

Career Doctor Teacher Artist Lawyer Sales Total # 105 189 216 240 330 1080 Angle 35 63 72 80 110 360

Q4.

U M

N

16, 18, 20, 22, 24

17, 19, 23

't = 1080 - ( 240 + 189 + 216 + 330) = 105 Converting to a pie chart angle: ⇒

15,21,25

Doctor =

360 ×

0

105 1080

=

35

0

M = prime numbers = 17, 19, 23 N = Even numbers = 16, 18, 20, 22, 24 M ∪ N ' = 15, 21, 25

⇒

Teacher =

360 ×

0

189 = 1080

63

0

*********************************************************

b.

and so on... Pie Chart

D

C

7 cm

12.1 cm

Doctor ( 35 ) Sales ( 110 )

0 0

60 A

0

7 cm

B

Teacher ( 63 )

0

Construction details.

1. 2. 3. 4. 5.

Lawyer ( 80 )

0

Artist ( 72 )

0

Draw straight line AB = 7cm ∢ BAD using compass Construct 600 Measure AD = 7cm Set compass to a separation of 7cm and with centre D, construct an arc above B. Set compass to a separation of 7 cm and with centre B, construct a second arc to intersect the first arc. The intersection of the two arcs is the point C.

6. Measure AC = 12.1cm

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Q5.

The diagrams below highlight the main areas of Q5 (see past paper for original). R

RS = 6m

S

2m

10m 5m A

3m

B R 8m

x=4m RS = 6m

S

1.) 2.)

RS = 8 – 2 = 6m x = 10 – RS = 4m

Perimeter equal distance around the two objects. Since A and B are joined at RS, then RS is not taken into account so: Perimeter A Perimeter B = 2 ( 5 + 10 ) - RS = 30 – 6 = 24m = 2 ( 8 + 3 ) - RS = 22 – 6 = 16m

Perimeter (A+B) = 24 + 16 = 40m Area ( A + B ) = 10 x 5 + 8 x 3 = Area of floor board = 1m x 20cm = 1m x 0.2m ( 20cm = 0.2m) = 0.2m

2

74m

2

# floor boards needed to cover A = =

Area A area of floor board 10 ×5 = 250 0.2

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Q6 The diagrams below highlight the main areas of Q6

G

Question 6b – Transformation From the diagram given on the Past paper, we observe the following: 1. 2. 3. Size and Orientation of Object and Image are maintained P 4,2 Q...