Factorising: Grouping in Pairs & the Cubes (Grade 10) — Worksheet & Memo

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Grade 10 · Algebraic Expressions

Factorising: Grouping in Pairs & the Cubes (Grade 10)

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
x² − z² + x + z factorises fully to …
(1)
A)(x + z)(x − z + 1)
B)(x − z)(x + z + 1)
C)(x + z)(x − z)
D)(x + z)²
1.2
x³ − 10x² + 21x factorises fully to …
(1)
A)x(x − 3)(x − 7)
B)x(x + 3)(x + 7)
C)(x − 3)(x − 7)
D)x(x − 21)(x + 1)
1.3
8x³ − 27 factorises to …
(1)
A)(2x − 3)(4x² + 6x + 9)
B)(2x − 3)(4x² − 6x + 9)
C)(2x − 3)(2x² + 6x + 9)
D)(2x − 3)³
1.4
3x + 3y + ax + ay factorises to …
(1)
A)(x + y)(3 + a)
B)(3 + x)(a + y)
C)3(x + y) + a(x + y)
D)(3x + a)(y + 1)
1.5
Which expression is FULLY factorised?
(1)
A)2(x − 2)(x + 2)
B)2(x² − 4)
C)(2x − 4)(x + 2)
D)(x − 2)(x + 2)
1.6
x³ + 64 factorises to …
(1)
A)(x + 4)(x² − 4x + 16)
B)(x + 4)(x² + 4x + 16)
C)(x − 4)(x² + 4x + 16)
D)(x + 4)³
1.7
2ax − 6a − x + 3 factorises to …
(1)
A)(x − 3)(2a − 1)
B)(x − 3)(2a + 1)
C)(x + 3)(2a − 1)
D)2a(x − 3) − (x − 3)
1.8
A rectangle has area x² − 9 and length x + 3. Its WIDTH is …
(1)
A)x − 3
B)x + 3
C)x² − 12
D)3 − x
1.9
Which method factorises x³ − 8?
(1)
A)the difference of two cubes
B)the difference of two squares
C)grouping in pairs
D)taking out a common factor
1.10
3x³ − 24 factorises fully to …
(1)
A)3(x − 2)(x² + 2x + 4)
B)3(x³ − 8)
C)(3x − 6)(x² + 2x + 4)
D)3(x − 2)(x² − 2x + 4)

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

[10 MARKS]

Factorise the following expressions FULLY.

2.1
x³ − 10x² + 21x
(3)
2.2
x² − z² + x + z
(4)
2.3
2x² + 7x + 3
(3)

Question 3

[13 MARKS]

Factorise the following FULLY.

3.1
x³ + 27
(3)
3.2
8x³ − 1
(3)
3.3
3x² − 27
(3)
3.4
Explain why x² + 9 cannot be factorised while x³ + 27 can, and state what you must ALWAYS check for first.
(4)

TOTAL: 33 marks

This question paper consists of 3 questions.