1 Sep/Oct

Question 1

Convert the following decimal into a fraction:

0.393939393939

Answer 1

0.39 recurring
r = 0.39

1) The number has two recurring digits so we multiply by 10² (10² =100):
100r = 39.3939393939

2) Subtract r from 100r:
100r = 39.393939
r = 0.393939
99r = 39.000000

3) Divide by the co-efficient of r:
39/99

4) Simplify where possible:
13/33

Question 2

Convert 0.21212121 into a fraction.

Answer 2

0.21 recurring, r = 0.21
Two recurring digits so 10² = 100
100r = 21.212121
100r - r = 99r  =  21.212121 - 0.212121 = 21
21/99
  = 7/33

Question 3

Convert 2.0666666666 into a fraction.

Answer 3

1) Ignore the 2, focus on the 0.066666.
2) 1000r - 100r = 900r
66.66 - 6.66 = 60
3) 60/900 = 6/90 = 1/15
4) Bring the 2 back:
= 2 1/15

Question 4

Convert 0.32828282828 into a fraction.

Answer 4

0.3 28 recurring
1000r - 10r = 990r = 328.2828 - 3.2828 = 325
325/990
= 65/198

Question 5

5(2x-1) 3(x+4)
_____ = _____
6 2

Answer 5

1) Multiply by the LCM of the denominators (6 for 6 and 2).
2) Cancel out the denominators:
5(2x-1) = 9(x+4)
3) Expand the brackets:
10x-5 = 9x+36
4) Solve:
x = 41

Question 6

4(2x-1) 5(2x-7)
_____ + x - 2 = ______
3 12

Answer 6

x = 5/34

Question 7

10(x+32) - 426 = 34

Answer 7

x = 14

Question 8

State the equation for arc length.

Answer 8

ϴ
___ x πd
360

Question 9

State the equation for sector area.

Answer 9

ϴ
___ x πr²
360

Question 10

State the equation for finding the surface area of a cone.

Answer 10

πr² + πrl

(l = slant height of cone)

Question 11

State the equation for finding the surface area of a cylinder.

Answer 11

2πr² + 2πrh

Question 12

State the equation for finding the surface area of a sphere.

Answer 12

4πr²

Question 13

State the equation for finding the area of a trapezium.

Answer 13

1/2 (a + b)h

Question 14

State the equation for finding the area of a parallelogram.

Answer 14

bh