Solving Equations by Factorisation (Product = 0) — Worksheet & Memo

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Grade 9 · Algebraic Equations

Solving Equations by Factorisation (Product = 0)

EXAM-STYLE CLASS TEST

Marks

Duration

50 minutes

Questions

Name:

Class:

Date:

Mark

/ 31

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: x(x − 5) = 0
(1)
A)5 only
B)0 or 5
C)−5 only
D)0 only
1.2
Solve for x: (x + 3)(x − 2) = 0
(1)
A)3 or −2
B)−3 or 2
C)−3 or −2
D)3 or 2
1.3
Solve for x: x² − 9 = 0
(1)
A)3 only
B)3 or −3
C)9 or −9
D)0
1.4
Solve for x: x² + 5x + 6 = 0
(1)
A)2 or 3
B)−2 or −3
C)−2 or 3
D)2 or −3
1.5
Before factorising to solve, the equation must first be written with …
(1)
A)x on the left
B)ZERO on one side
C)no brackets
D)a positive x² term only
1.6
Solve for x: x² = 4x
(1)
A)4 only
B)0 or 4
C)2 only
D)−4 or 4
1.7
Solve for x: 2x² − 8 = 0
(1)
A)4 or −4
B)2 or −2
C)2 only
D)16
1.8
A rectangle has length (x + 2) and area 15. If the breadth is x, then …
(1)
A)x² + 2x = 15
B)x² + 2x − 15 = 0
C)x + 2 = 15
D)2x + 2 = 15
1.9
For that rectangle, the value of x is …
(1)
A)−5
B)3
C)5
D)−3
1.10
How many solutions does x² + 4x + 4 = 0 have?
(1)
A)two different ones
B)one (a repeated root)
C)none
D)three

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

[9 MARKS]

Solve for x.

2.1
(x − 2)(x + 6) = 0, and hence solve x(x − 2)(x + 6) = 0.
(3)
2.2
x² + 5x + 6 = 0
(3)
2.3
x² − 7x + 10 = 0
(3)

Question 3

[12 MARKS]

Answer the questions below.

3.1
Solve for x: x² − 3x = 0
(3)
3.2
Solve for x: x² − 25 = 0
(3)
3.3
Explain why you may NOT divide both sides of x² = 4x by x.
(3)
3.4
Simplify: (12x³ − 8x² + 4x) ÷ 4x
(3)

TOTAL: 31 marks

This question paper consists of 3 questions.