1. In each of the following, solve and find the greatest integer x that satisfies the inequality.

(a)

(b)

Ans: (a) x = [2]

(b) x = [3]

2. (a) Express 7.26 m2 in cm2.

(b) Express 34 860 000 cm3 in m3.

Ans: (a) _______________ cm2 [1]

(b) ________________ m3 [1]

3. (a) The length and breadth of a rectangle are 4x cm and 8 cm respectively.

(i) Express, in terms of x, the area of the rectangle.

(ii) Form an inequality in terms of x if the area of the rectangle is greater than

or equal to 88 cm2.

(iii) Solve the inequality.

(iv)Hence, find the minimum area of the rectangle if x is an integer.

(b) Solve the inequality and state the greatest value of x if x is a rational

number.

Ans: (a) (i) cm 2 [1]

(ii) [1]

(iii) [1]

(iv) cm 2 [2]

(b) x = [3]

4. (a) Solve the inequality 3( x−2 )≤x+4

(b) Find the largest prime number x such that 6 x<45

Ans: (a) [2]

(b) _____________________ [2]

5(a) Solve 5 x−2 x>−6 .

(b) Hence, find the smallest integer that satisfies the inequality.

Answer : (a) [1]

(b) [1]

6. Solve

35

x>−2

3

Ans: (a)_______________[2]

7. Find the greatest integer x which satisfies the inequality

56

x≤−74

Answer: (b) [2]

8. Find the range of values of x for which .

Answer …………………………… [2]

9. (a) Solve the inequality −2 + 5x ≤ −13.

(b) Find the largest integer that satisfies the inequality in (a).

Answer (a) ……………………………….. [2]

(b) ……………………………….. [1]

10. It is given that 1 ≤ x ≤ 9 and −2 ≤ y ≤ 2.

Find

(a) all the prime numbers within the range of x. [1]

(b) the greatest possible value of x − y, [1]

(c) the smallest possible value of x2 + y2. [2]

11. (a) Solve the inequality . [2]

(b) Hence, write down all the possible

(i) positive integers and [1]

(ii) prime numbers [1]

which satisfy the inequality.

(c) A number y, divided by 3 is less than 15.

Find the greatest possible integer value of y. [2]

12. (a) Solve the inequality 4 x+2>23+ x

.

(b) A container can hold a maximum of 1000 kilograms. A company has to load boxes of goods weighing 38 kilograms each. What is the maximum number of boxes that can be loaded into the container?

Answer (a) [1]

(b) boxes [2]

13. Solve 3+ 3 y

2≤8

, and hence find the largest possible value of y if(a) y is a rational number,(b) y is an integer.

Answer: (a) _______________ [2]

(b)_______ ________ [1]

14. (a) Solve the inequality 5( x−4 )>4 ( x−3 )(b) Hence, write down the smallest integer value of x that satisfies the inequality in

(a).

Answer: (a) ____________ [2]

(b) ____________ [1]

15. Given that 0 ≤ a < 6 and -4 < b ≤ 2,

(a) list all the integer values of a,

(b) list all the integer values of b,

(c) find the largest possible value of b – a.

Answer (a) ...................................... [1]

(b) ...................................... [1]

(c) ...................................... [1]

16. Solve the inequality, 11 x−5≤9 x+7

Answer: __________________ [2]

17. (a) Solve the following inequality and show the solution on the number line given below.

13

y − 4 < −12

(b) Hence, state the maximum integer value of y.

Ans: (a) [3]

Ans: (b) ___________________ [1]