Quadratic Inequalities (Grade 11) — Worksheet & Memo

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Grade 11 · Equations & Inequalities

Quadratic Inequalities (Grade 11)

EXAM-STYLE CLASS TEST

Marks

Duration

55 minutes

Questions

Name:

Class:

Date:

Mark

/ 34

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
Solve for x: x² − 4 > 0
(1)
A)x < −2 or x > 2
B)−2 < x < 2
C)x > 2 only
D)x > −2
1.2
Solve for x: x² − 4 < 0
(1)
A)−2 < x < 2
B)x < −2 or x > 2
C)x < 2
D)x < 4
1.3
Solve for x: x(x − 4) + 2(4 − x) ≤ 0
(1)
A)2 ≤ x ≤ 4
B)x ≤ 2 or x ≥ 4
C)−2 ≤ x ≤ −4
D)0 ≤ x ≤ 4
1.4
Solve for x: (x + 1)(x − 5) ≥ 0
(1)
A)x ≤ −1 or x ≥ 5
B)−1 ≤ x ≤ 5
C)x ≥ −1
D)x ≥ 5
1.5
Solve for x: x² ≥ 9
(1)
A)x ≤ −3 or x ≥ 3
B)x ≥ 3
C)−3 ≤ x ≤ 3
D)x ≥ −3
1.6
The FIRST step in solving a quadratic inequality is to …
(1)
A)move everything to one side so it is compared with 0, then factorise
B)divide both sides by x
C)take the square root of both sides
D)reverse the inequality sign
1.7
Solve for x: x² + x − 6 ≤ 0
(1)
A)−3 ≤ x ≤ 2
B)x ≤ −3 or x ≥ 2
C)−2 ≤ x ≤ 3
D)x ≤ 2
1.8
If a quadratic has NO real roots and a > 0, then ax² + bx + c > 0 for …
(1)
A)all real values of x
B)no values of x
C)x > 0 only
D)x < 0 only
1.9
Solve for x: x² < 0
(1)
A)there is no real value of x
B)x < 0
C)x = 0
D)all real x
1.10
Solve for x: (x − 3)² > 0
(1)
A)every real x except x = 3
B)x > 3
C)all real x
D)x = 3

Answer grid — circle your answers for Question 1

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[12 MARKS]

Solve for x. Show the critical values and give your answers in interval notation where asked.

2.1
2x² − 5x + 3 < 0
(4)
2.2
x² − x − 6 ≥ 0
(4)
2.3
−x² + 4 > 0
(4)

Question 3

[12 MARKS]

Answer the questions below.

3.1
Solve for x: x + 1x − 2 ≥ 0
(5)
3.2
Write your answer to the previous part in interval notation.
(2)
3.3
For which values of x is the graph of y = x² − x − 6 BELOW the graph of y = 2x − 6? Show all your working.
(5)

TOTAL: 34 marks

This question paper consists of 3 questions.