Exercises for Question Type 2: Finding solutions to quadratic inequalities by converting into ax^2+bx+c > or < 0 and checking intervals

Question 1

Skill question

Find the set of $x$ satisfying $4 x^{2} - 12 x + 9 \leq 0$ .

[3]

Question 2

Skill question

Determine the solution set of $4 x^{2} + 6 x - 10 > 0$ .

[4]

Question 3

Skill question

Solve the inequality $2 x^{2} - 3 x - 2 > 0$ . [4 marks]

[4]

Question 4

Skill question

Solve $x^{2} + 2 x + 5 < 4 x + 1$ .

[6]

Question 5

Skill question

Solve $- 2 x^{2} + 8 x + 6 \geq 0$ .

[4]

Question 6

Skill question

Find the set of values of $x$ for which $- 3 x^{2} + 12 x - 9 \geq 0$ .

[4]

Question 7

Skill question

Find all $x$ such that $x^{2} + 4 x + 3 \geq 0$ .

[4]

Question 8

Skill question

Solve the inequality $x^{2} - 2 x > 3 x - 6$ .

[3]

Question 9

Skill question

Solve the inequality $x^{2} - 5 x + 6 < 0$ .

[3]

Question 10

Skill question

Solve the inequality $5 - 6 x - x^{2} < 0$ .

[5]

Question 11

Skill question

Find all real $x$ such that $6 x^{2} - 5 x + 1 > 2 x^{2} + 7 x - 3$ .

[4]

Question 12

Skill question

Find the set of values of $x$ for which $3 x^{2} + x < 4$ .

[4]

IB Mathematics Analysis and Approaches Question Type 2: Finding Solutions to Quadratic Inequalities by Converting Into Ax^2+bx+c > or < 0 and Checking Intervals Exercises