HighMarks

Number systems (natural numbers, integers, rational and irrational numbers, real numbers) — KCSE Mathematics

KCSE Mathematics · 110 practice questions · 4 syllabus objectives

37 easy37 medium36 hard

What You'll Learn

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

Classify numbers into natural numbers, whole numbers, integers, rational numbers, irrational numbers and real numbers with examples

Represent numbers on a number line and use the number line to compare and order integers and rational numbers

Apply the four operations on integers and state and use the properties of real numbers (commutative, associative, distributive)

Number systems (natural numbers, integers, rational and irrational numbers, real numbers)

Sample Questions

Try 3 questions free. Sign up to access all 110 questions with full marking schemes.

1
easySHORT ANSWER4 marks

Define the distributive property and illustrate it with an example involving integers. (4 marks)

View Marking Scheme
Part (a) — 1 mark
The distributive property states that a(b + c) = ab + ac for any numbers a, b, and c. (1 mk)
Part (b) — 3 marks
For example, 2(3 + 4) = 2×3 + 2×4. (1 mk)
Calculate: 2(3 + 4) = 2×7 = 14. (1 mk)
Calculate: 2×3 + 2×4 = 6 + 8 = 14. (1 mk)
2
easySHORT ANSWER2 marks

Define the commutative property of addition and provide an example using integers. (2 marks)

View Marking Scheme
Part (a) — 1 mark
The commutative property of addition states that changing the order of addends does not change the sum. (1 mk)
Part (b) — 1 mark
For example, 3 + 5 = 5 + 3 = 8. (1 mk)
3
easySHORT ANSWER4 marks

Identify and classify the numbers 4.75, -2, and √3 into natural numbers, integers, rational numbers, or irrational numbers. (4 marks)

View Marking Scheme
Part (a) — 4 marks
4.75 is classified as a rational number (1 mk)
-2 is classified as an integer (and rational) (1 mk)
√3 is classified as an irrational number (1 mk)
None of the numbers are natural numbers (1 mk)
4

List the following numbers in order from least to greatest on a number line: -3, 0.5, -1, and 2. (4 marks)

+107 More Questions

Sign up free to access all 110 questions with marking schemes, track your progress, and get personalised recommendations.

Why Practise Number systems (natural numbers, integers, rational and irrational numbers, real numbers)?

KNEC Aligned

Questions match the KCSE syllabus objectives and exam format exactly.

Detailed Marking Schemes

Every answer shows exactly what examiners award marks for.

Track Your Mastery

See your score improve as you practise and identify remaining gaps.

Master Number systems (natural numbers, integers, rational and irrational numbers, real numbers) for KCSE

Sign up free to unlock all 110 questions, track your progress, and get a personalised study plan for Mathematics.