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HKDSE Mathematics Exercise

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HKDSE Exercise MATHEMATICS (Core) By HENRY LEUNG

HKDSE Mathematics Exercise
Topic: Inequalities

1. Solve the inequalities 3 x−8>
18−5 x

3
or 5(x+2)>x+2 .

2. Solve {
3
4
(x−3)− x≤−5

2−
2
3
(3−x )>4

.

3. a) Solve {
2 x−1

3
≤4−

3 x
2

3 x+4> x−2
.

b) Furthermore, if x is a positive integer, list out all possible x .

4. Solve the inequality x
2
+2 x−15<0 .

5. Solve the inequality 2 x− x
2
≤0 .

6. Solve the inequality (x+2)(x+3)<2(x+2) .

7. Solve the inequality x
2
−4 x+4>0 .

8. a) Solve {x ( x+1)≤3(x+1)4 x2+4 x−3<0 .
b) If x is an integer, find the maximum value of x .

9. Find the range of k if x
2
+k x+k>0 for all real numbers x .

10. A ball is throw upwards, the height hm of the ball after t seconds can be modelled by
h=15 t−5t

2 . Find the range of t such that the height of the ball is higher than 10m .

11. Let sinθ=3 x−2 , where θ is any angle. Find the range of x .

12. If the base radius and the height of the cylinder are r cm and (r−2)cm respectively. If the
total surface area is less than 48π cm

2 , find the range of r .

13. How many integers of x satisfying the inequality (x−2)(1−x )≥3( x−2) ?

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