FreeMathWorksheet
FreeMathWorksheet

Printable Worksheet

TN-MATH-SAT-34427 · v2.3

Substitution

SAT · Math · Algebra · National Curriculum (UK)

Grade

SAT

Subject

Math

Topic

Algebra

Subtopic

Substitution

Curriculum

National Curriculum (UK)

Difficulty

Core

Time

30 minutes

Total marks

54

Student name

Teacher name

Date

Learning objectives

  • Recognise substitution accurately in math contexts.
  • Explain the underlying rule of substitution in the student's own words.
  • Apply substitution to multi-step and unfamiliar problems.
  • Justify a chosen method and identify errors in another student's work.

Skills assessed

  • Fluency and recall
  • Method and setting out
  • Reasoning and justification
  • Problem solving in context
  • Self-assessment

Instructions

  1. Write your name, your teacher's name and the date in the header.
  2. Answer every question in the space provided. Continue on the back if needed.
  3. Show all working — method marks are awarded even when the final answer is wrong.
  4. Aim to finish in about 30 minutes.
  5. Complete the reflection box at the end before you hand the sheet in.

Warm-up

Bloom: Remember · 4 marks

Answer quickly. These check you are ready for the topic.

  1. 1.State one fact you already know about substitution.

    [1]
  2. 2.State one fact you already know about substitution.

    [1]
  3. 3.Write down one fact you already know about substitution.

    [1]
  4. 4.Circle one fact you already know about substitution.

    [1]

Recall

Bloom: Remember · 4 marks

Complete from memory. No calculator, no notes.

  1. 1.List the key term used in substitution described here: item 1.

    [1]
  2. 2.Label the key term used in substitution described here: item 2.

    [1]
  3. 3.Complete the key term used in substitution described here: item 3.

    [1]
  4. 4.Define the key term used in substitution described here: item 4.

    [1]

FreeMathWorksheet · TN-MATH-SAT-34427 · v2.3

© 2026 FreeMathWorksheet. Licensed for classroom and home use. Redistribution or resale is not permitted.

Page 1 of 4

FreeMathWorksheet · SAT Math

Substitution

Basic Practice

Bloom: Understand · 5 marks

Work through each item. Show the step you used.

  1. 1.Identify part 1 using the rule for substitution.

    [1]
  2. 2.Match part 2 using the rule for substitution.

    [1]
  3. 3.Work out part 3 using the rule for substitution.

    [1]
  4. 4.Match part 4 using the rule for substitution.

    [1]
  5. 5.Match part 5 using the rule for substitution.

    [1]

Guided Practice

Bloom: Understand · 8 marks

The first step is given. Finish the reasoning.

  1. 1.Using the first step given, finish part 1. Step 1 has been started for you.

    [2]
  2. 2.Using the first step given, finish part 2. Step 1 has been started for you.

    [2]
  3. 3.Using the first step given, finish part 3. Step 1 has been started for you.

    [2]
  4. 4.Continue the working for part 4. Step 1 has been started for you.

    [2]

FreeMathWorksheet · TN-MATH-SAT-34427 · v2.3

© 2026 FreeMathWorksheet. Licensed for classroom and home use. Redistribution or resale is not permitted.

Page 2 of 4

FreeMathWorksheet · SAT Math

Substitution

Independent Practice

Bloom: Apply · 10 marks

No scaffolding. Set out your full method.

  1. 1.Work out fully part 1 on substitution without help.

    [2]
  2. 2.Determine part 2 on substitution without help.

    [2]
  3. 3.Work out fully part 3 on substitution without help.

    [2]
  4. 4.Solve part 4 on substitution without help.

    [2]
  5. 5.Determine part 5 on substitution without help.

    [2]

Challenge Questions

Bloom: Analyse · 9 marks

Harder items. Attempt every one, even partially.

  1. 1.Deduce the statement in part 1 about substitution.

    [3]
  2. 2.Show that the statement in part 2 about substitution.

    [3]
  3. 3.Find and justify the statement in part 3 about substitution.

    [3]

FreeMathWorksheet · TN-MATH-SAT-34427 · v2.3

© 2026 FreeMathWorksheet. Licensed for classroom and home use. Redistribution or resale is not permitted.

Page 3 of 4

FreeMathWorksheet · SAT Math

Substitution

Real-life Application

Bloom: Apply · 6 marks

Use the skill in context. State units in your answer.

  1. 1.Apply a real math situation that depends on substitution.

    [3]
  2. 2.In context, work out a real math situation that depends on substitution.

    [3]

Critical Thinking

Bloom: Evaluate · 8 marks

Explain your reasoning in full sentences.

  1. 1.Explain why a student's method for substitution is or is not efficient.

    [4]
  2. 2.Evaluate whether a student's method for substitution is or is not efficient.

    [4]

Reflection

Bloom: Create · 0 marks

Not marked. Answer honestly — this guides your next worksheet.

  1. 1.Record how confident you feel with substitution and what you will practise next.

    [—]
  2. 2.Describe how confident you feel with substitution and what you will practise next.

    [—]

FreeMathWorksheet · TN-MATH-SAT-34427 · v2.3

© 2026 FreeMathWorksheet. Licensed for classroom and home use. Redistribution or resale is not permitted.

Page 4 of 4