Algebraic Fractions: Simplify, Add & Subtract (Grade 10)

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 10 · Algebraic Expressions

EXAM-STYLE CLASS TEST

Marks

Duration

55 minutes

Questions

Name:

Class:

Date:

Mark

/ 35

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 − 4x + 2 simplifies to …
(1)
A)x − 2
B)x + 2
C)x² − 2
D)−2
1.2
x3 + x4 = …
(1)
A)7x12
B)2x7
C)x12
D)2x12
1.3
3x + 6x² − 4 simplifies to …
(1)
A)3x − 2
B)3x + 2
C)3xx − 2
D)3(x + 2)x − 2
1.4
x2 ÷ x6 = …
(1)
A)3
B)13
C)x²12
D)x3
1.5
2x − 1x + 1 = …
(1)
A)x + 2x(x + 1)
B)1x(x + 1)
C)12x + 1
D)x + 22x + 1
1.6
For which value of x is x + 3x − 5 UNDEFINED?
(1)
A)x = 5
B)x = −3
C)x = −5
D)x = 3
1.7
x² + 5x + 6x² − 9 simplifies to …
(1)
A)x + 2x − 3
B)x + 2x + 3
C)x + 3x − 3
D)5x + 6−9
1.8
x + 1x − 2 × x − 2x + 3 = …
(1)
A)x + 1x + 3
B)x − 2x + 3
C)x + 1x − 2
D)(x + 1)(x − 2)(x − 2)(x + 3)
1.9
x³ − 8x − 2 simplifies to …
(1)
A)x² + 2x + 4
B)x² − 2x + 4
C)x² − 4
D)x² + 4
1.10
2x − 69 − x² simplifies to …
(1)
A)−23 + x
B)23 + x
C)23 − x
D)−23 − x

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

[11 MARKS]

Simplify the following FULLY.

2.1
x² − 16x + 4
(3)
2.2
x² − 1x ÷ x + 13x
(4)
2.3
2x + 1 + 3x − 1
(4)

Question 3

[14 MARKS]

Simplify the following FULLY, and answer the question that follows.

3.1
x − 2x³ − 8
(4)
3.2
x² + 5x + 6x² − 4
(4)
3.3
Write down the value(s) of x for which x + 3x − 2 is undefined, and explain why.
(3)
3.4
Explain why you may NOT cancel the x² terms in x² + 5x + 6x² − 4 before factorising.
(3)

TOTAL: 35 marks

This question paper consists of 3 questions.