No. 1(b) after evaluating, we'll get 29.853810... correcting to 1 SF, we get 30 (to 1 S.F.)

No. 2

Estimation:

538 x 0.053

≈ 500 x 0.05 (to 1 S.F.)

= 25

The value would be 28.514

No. 3

(a) The possible integers are 75, 76, 77, 78, 79, 81, 82, 83, 84

[Note that 80 is not included in the answer because it asked for integers that are rounded to... ]

(b) The prime numbers are 79, 83

No. 4

We will get 0.943309132... = 0.94 (to 2 decimal places)

No. 5

We will get 1.10845164... = 1.11 (correct to 3 S.F.)

No. 6

Answer: 7

`½`

No. 7

Given that the breadth is (2x - 1) m

Height is twice its length, Height = 2(2x - 1)

(a) Perimeter = 2 x Length + 2 x Breadth

= 2 x 2(2x - 1) + 2 x (2x - 1)

= 4(2x - 1) + 4x - 2

= 8x - 4 + 4x - 2

= 12x - 6 m (shown)

(b) Area = Length x Breadth {Note: This is beyond chapter 4}

= 2(2x - 1) x (2x - 1)

= 2 [(2x-1)(2x) - (2x-1)(1)]

= 2 [4x

`²`- 2x - 2x + 1]

= 2 [4x

`²`- 4x + 1]

= 8x

`²`- 8x + 2

No. 8

Note that the age given were "3 years ago"

(i) Given that, 3 years ago, Sam's age was x + 1

and Oreo's age was 1

`½`times as old as Sam

Oreo's age is therefore 1

`½`x (x + 1)

= 3/2 x (x + 1)

= 3x/2 + 3/2

alternatively, can be written as

= (3x + 3)/2

(ii) Oreo's present age

= 3x/2 + 3/2 + 3

= 3x/2 + 9/2

alternatively, can be written as

= (3x + 9)/2

(iii) Sum of Sam & Oreo's present age

= Sam's present age + Oreo's present age

= (x + 1 + 3) + 3x/2 + 9/2

= x + 4 + 3x/2 + 9/2

= 5x/2 + 17/2

alternatively, can be written as

= (5x + 17)/2

By the way, there's a piece of redundant information (i.e. the sum of their present ages is 86). This information only becomes useful if we need to find out the age of Oreo and Sam.