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Number line representation of inequalities — KCSE Mathematics

KCSE Mathematics · 109 practice questions · 3 syllabus objectives · 3 revision lessons

37 easy37 medium35 hard

Last updated · Aligned to the KNEC KCSE syllabus

What You'll Learn

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

Represent the solution set of a linear inequality on a number line using open and closed circles

Read and interpret number line diagrams and write the corresponding inequality or solution set

Number line representation of inequalities

Revision Notes

Concise lesson notes for Number line representation of inequalities, written to the KCSE Mathematics marking standard. Read the first lesson free below.

Number Line Representation of Inequalities

To represent a linear inequality on a number line, you must first identify whether the inequality is strict (using < or >) or non-strict (using ≤ or ≥). Open circles are used for strict inequalities, indicating that the endpoint is not included in the solution set. Closed circles are used for non-strict inequalities, showing that the endpoint is included.

Steps to represent inequalities:

  1. Identify the inequality type: strict or non-strict.
  2. Draw a horizontal line to represent the number line.
  3. Place an open or closed circle at the endpoint based on the inequality.
  4. Shade the appropriate direction to indicate the solution set.

For example, to represent the inequality x < 3:

  • Draw a number line.
  • Place an open circle at 3 (not included).
  • Shade to the left of 3 to show all numbers less than 3.

For x ≥ 2:

  • Draw a number line.
  • Place a closed circle at 2 (included).
  • Shade to the right of 2 to show all numbers greater than or equal to 2.

Key points to remember

  • Use open circles for strict inequalities ( <, > ).
  • Use closed circles for non-strict inequalities ( ≤, ≥ ).
  • Shade left for less than and right for greater than.
  • Clearly indicate included or excluded endpoints.

Worked example

Represent the solution set for x > 4 on a number line.

  • Draw a number line.
  • Place an open circle at 4.
  • Shade to the right of 4.

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Lesson 2: Interpreting Number Line Inequalities

Objective: Read and interpret number line diagrams and write the corresponding inequality or solution set

In mathematics, a number line is a visual representation of numbers, which can also illustrate inequalities. To read a number line diagram, observe the following:

  • Open Circles indicate that the endpoint is not included in the solution set (e.g., x < 3).
  • Closed Circles indicate that the endpoint is included (e.g., x ≤ 5).
  • The arrow indicates the direction of the inequality.

For example, if a number line shows an open circle at 2 and an arrow extending to the left, this represents the inequality: x < 2. Conversely, if there is a closed circle at 4 and an arrow extending to the right, it represents: x ≥ 4.

When writing the corresponding inequality, ensure to use the correct symbols (<, ≤, >, ≥) based on the type of circle and direction of the arrow. This will help you express the solution set accurately.

  • Open circles indicate values not included in the solution set.
  • Closed circles show values included in the solution set.
  • Arrows indicate the direction of the inequality.
  • Use correct inequality symbols based on circles and arrows.
  • Read diagrams carefully to write accurate inequalities.

Given a number line with an open circle at -1 and an arrow to the left, the corresponding inequality is: x < -1.

Lesson 3: Understanding Inequalities on a Number Line

Objective: Number line representation of inequalities

To represent inequalities on a number line, follow these steps:

  1. Identify the inequality: Determine whether it is strict (e.g., <, >) or inclusive (e.g., ≤, ≥).
  2. Draw the number line: Create a horizontal line with evenly spaced intervals.
  3. Mark the critical point: Locate the number that the inequality refers to.
  4. Use open or closed circles:
    • Use an open circle for strict inequalities (e.g., x < 3).
    • Use a closed circle for inclusive inequalities (e.g., x ≤ 3).
  5. Shade the appropriate region:
    • Shade to the left for less than (<, ≤).
    • Shade to the right for greater than (>, ≥).

For example, to represent the inequality x > 2:

  • Draw a number line.
  • Mark an open circle at 2.
  • Shade the region to the right of 2.

If representing x ≤ 4:

  • Mark a closed circle at 4.
  • Shade the region to the left of 4.

This visual representation helps in understanding the solution set of inequalities.

  • Identify if the inequality is strict or inclusive.
  • Use open circles for strict inequalities.
  • Use closed circles for inclusive inequalities.
  • Shade the correct region based on the inequality.
  • Number lines visually represent solution sets.

Represent the inequality x < -1 on a number line:

  • Draw a number line.
  • Use an open circle at -1.
  • Shade to the left of -1.

Sample Questions

Read 3 questions and answers free. Sign up to access all 109 questions with full KNEC-style marking schemes and a personalised study plan.

1
easySHORT ANSWER3 marks

State the inequality represented by the solution set where x is greater than -5 but less than or equal to 3. (3 marks)

Answer & marking scheme

Part (a) — 3 marks
Correctly identify the inequality as -5 < x ≤ 3 (1 mk)
Explain that -5 is represented by an open circle (1 mk)
Explain that 3 is represented by a closed circle (1 mk)
2
easySHORT ANSWER3 marks

Identify the inequality represented by the statement 'x is less than 5 but greater than or equal to 2'. (3 marks)

Answer & marking scheme

Part (a) — 3 marks
Correctly identifies the lower bound as x ≥ 2 (1 mk)
Correctly identifies the upper bound as x < 5 (1 mk)
Combines both bounds in the inequality: 2 ≤ x < 5 (1 mk)
3
easySHORT ANSWER2 marks

State the solution set for the inequality x > 2. (2 marks)

Answer & marking scheme

Part (a) — 2 marks
x ∈ (2, ∞) (2 mks)
4

Name the inequality represented by the solution set where x is less than or equal to -3. (2 marks)

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Frequently asked questions

What does the KCSE Mathematics topic "Number line representation of inequalities" cover?

Number line representation of inequalities covers Represent the solution set of a linear inequality on a number line using open and closed circles; Read and interpret number line diagrams and write the corresponding inequality or solution set; Number line representation of inequalities, all aligned to the official KNEC KCSE Mathematics syllabus.

How many practice questions are available for Number line representation of inequalities?

HighMarks has 109 Number line representation of inequalities practice questions for KCSE Mathematics, each with a full marking scheme. The first 3 are free; sign up to access the rest, plus all KCSE mock exams and past papers.

Are these aligned with the KNEC KCSE syllabus?

Yes. Every objective on this page is taken directly from the official KNEC KCSE Mathematics syllabus. Practice questions match the KCSE exam format and are graded against the standard KNEC marking scheme.

How should I revise Number line representation of inequalities for the KCSE exam?

Start with the revision notes on this page to refresh the core concepts, then work through the practice questions in increasing difficulty. Sign up for HighMarks to get a personalised study plan that adapts to the topics you keep getting wrong, plus mock exams, subject-wide practice, and detailed performance tracking. See pricing.

Why Practise Number line representation of inequalities?

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