Linear equations (one variable) — KCSE Mathematics

KCSE Mathematics · 106 practice questions · 4 syllabus objectives

36 easy37 medium33 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Solve linear equations in one variable including those with brackets and fractions

Form and solve linear equations from word problems involving age, money, distance-time and mixture situations

Solve linear equations involving absolute values: |ax + b| = c

Linear equations (one variable)

Sample Questions

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1
easySHORT ANSWER4 marks

Identify the solutions to the equation |3x + 1| = 7. (4 marks)

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Part (a) — 1 mark
3x + 1 = 7 or 3x + 1 = -7 (1 mk)
Part (b) — 3 marks
3x = 6, so x = 2 (1 mk)
3x = -8, so x = -/3 (1 mk)
Both values x = 2 and x = -/3 identified (1 mk)
2
easySHORT ANSWER2 marks

A shop sells notebooks at Ksh 50 each. If a customer buys n notebooks, the total cost is Ksh 50n. If the customer pays Ksh 300, how many notebooks can they buy? (2 marks)

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Part (a) — 2 marks
Set up the equation: 50n = 300. (1 mk)
Solve for n: n = 300 / 50 = 6. (1 mk)
3
easySHORT ANSWER2 marks

Determine the value of y in the equation: (y - 5)/3 + 2 = 4. [2 marks]

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Part (a) — 2 marks
Subtract 2 from both sides to simplify to (y - 5)/3 = 2 (1 mk)
Multiply through by 3 to find y - 5 = 6 and solve to get y = 11 (1 mk)
4

Solve for x in the equation: 2(x + 3) = 4x - 8. [3 marks]

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