Solving Algebraic Equations (Grade 8) — Worksheet & Memo

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Grade 8 · Algebraic Equations

Solving Algebraic Equations (Grade 8)

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: x + 9 = 15
(1)
A)24
B)6
C)−6
D)135
1.2
Solve for x: 6x = 42
(1)
A)36
B)7
C)48
D)252
1.3
Solve for x: x ÷ 3 = 5
(1)
A)15
B)1,67
C)8
D)2
1.4
Solve for x: 2x + 5 = 17
(1)
A)11
B)6
C)6,5
D)−6
1.5
Solve for x: x² = 49
(1)
A)7 only
B)7 or −7
C)24,5
D)−7 only
1.6
Solve for x: 3(x − 2) = 12
(1)
A)2
B)6
C)4
D)14
1.7
Double a number and add 5 gives 17. The number is …
(1)
A)11
B)6
C)22
D)12
1.8
Which operation UNDOES "multiply by 4"?
(1)
A)add 4
B)divide by 4
C)subtract 4
D)multiply by −4
1.9
Solve for x: 5x − 3 = 2x + 9
(1)
A)2
B)4
C)12
D)1,7
1.10
A learner writes: 3x = 12, so x = 36. Their mistake is that they …
(1)
A)divided instead of multiplying
B)MULTIPLIED instead of dividing
C)added instead of dividing
D)made no mistake

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 ALL your steps.

2.1
x + 9 = 15, and check your answer by substituting it back into the equation.
(3)
2.2
6x = 42, and hence write down the solution of 6x = 84 without solving it again.
(3)
2.3
2x + 7 = 19
(3)
2.4
3(x − 2) = 12
(3)

Question 3

[12 MARKS]

Answer the questions below.

3.1
Solve for x: x² = 121, and explain why this equation has TWO solutions.
(3)
3.2
A number is doubled and 5 is added to the result, giving 17. Set up an equation and determine the number.
(4)
3.3
Check your answer to the previous question by substituting it back into the words of the problem.
(2)
3.4
Solve for x: x ÷ 4 = 6, and hence solve x ÷ 4 + 7 = 13.
(3)

TOTAL: 34 marks

This question paper consists of 3 questions.