Factorising: The Complete Exam Guide (Every Type) — Worksheet & Memo

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Grade 9 · Algebra

Factorising: The Complete Exam Guide (Every Type)

EXAM-STYLE CLASS TEST

Marks

Duration

50 minutes

Questions

Name:

Class:

Date:

Mark

/ 33

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
Factorise: 5x + 15
(1)
A)5(x + 15)
B)5(x + 3)
C)x(5 + 15)
D)5x(1 + 3)
1.2
Factorise: x² − 49
(1)
A)(x − 7)²
B)(x + 7)(x − 7)
C)(x + 7)²
D)x(x − 49)
1.3
Factorise: x² + 9x + 20
(1)
A)(x + 4)(x + 5)
B)(x + 2)(x + 10)
C)(x − 4)(x − 5)
D)(x + 1)(x + 20)
1.4
Factorise: x² − 5x − 14
(1)
A)(x − 7)(x + 2)
B)(x + 7)(x − 2)
C)(x − 7)(x − 2)
D)(x + 7)(x + 2)
1.5
When factorising, the FIRST thing to look for is …
(1)
A)a difference of squares
B)a common factor
C)a trinomial
D)brackets
1.6
Factorise fully: 2x² − 18
(1)
A)2(x² − 9)
B)2(x + 3)(x − 3)
C)(2x + 3)(x − 6)
D)2(x − 3)²
1.7
Factorise by grouping: ax + ay + bx + by
(1)
A)(a + b)(x + y)
B)ab(x + y)
C)(a + x)(b + y)
D)abxy
1.8
Factorise: 4x² − 25y²
(1)
A)(4x + 5y)(4x − 5y)
B)(2x + 5y)(2x − 5y)
C)(2x − 5y)²
D)(4x − 25y)²
1.9
Which expression is NOT factorised completely?
(1)
A)3(x + 2)
B)2(x² − 16)
C)(x + 1)(x + 4)
D)5x(x − 3)
1.10
The factors of x² + 6x + 9 are …
(1)
A)(x + 3)(x − 3)
B)(x + 3)²
C)(x + 9)(x + 1)
D)(x + 6)(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]

Factorise the following COMPLETELY.

2.1
5x + 15, and hence factorise 5x + 15 + 2(x + 3) fully.
(3)
2.2
8a²b − 12ab
(3)
2.3
x² − 49, and hence factorise 4x² − 49.
(3)
2.4
3x² − 27
(3)

Question 3

[11 MARKS]

Factorise the following trinomials.

3.1
x² + 9x + 20, and hence factorise x² − 9x + 20.
(3)
3.2
x² − 8x + 15
(3)
3.3
x² + 2x − 15
(3)
3.4
State what you must ALWAYS check for first when factorising, and give a reason.
(2)

TOTAL: 33 marks

This question paper consists of 3 questions.