FreeMathWorksheet
FreeMathWorksheet

Practice Worksheet

TN-MATH-TOEFL-32200 · v1.-7

Tangent Ratio

TOEFL · Math · Trigonometry · Cambridge (CAIE)

Grade

TOEFL

Subject

Math

Topic

Trigonometry

Subtopic

Tangent Ratio

Curriculum

Cambridge (CAIE)

Difficulty

Core

Time

30 minutes

Total marks

54

Student name

Teacher name

Date

Learning objectives

  • Recognise tangent ratio accurately in math contexts.
  • Explain the underlying rule of tangent ratio in the student's own words.
  • Apply tangent ratio 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.Name one fact you already know about tangent ratio.

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

    [1]
  3. 3.State one fact you already know about tangent ratio.

    [1]
  4. 4.Write down one fact you already know about tangent ratio.

    [1]

Recall

Bloom: Remember · 4 marks

Complete from memory. No calculator, no notes.

  1. 1.Complete the key term used in tangent ratio described here: item 1.

    [1]
  2. 2.List the key term used in tangent ratio described here: item 2.

    [1]
  3. 3.Define the key term used in tangent ratio described here: item 3.

    [1]
  4. 4.List the key term used in tangent ratio described here: item 4.

    [1]

FreeMathWorksheet · TN-MATH-TOEFL-32200 · v1.-7

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

Page 1 of 4

FreeMathWorksheet · TOEFL Math

Tangent Ratio

Basic Practice

Bloom: Understand · 5 marks

Work through each item. Show the step you used.

  1. 1.Match part 1 using the rule for tangent ratio.

    [1]
  2. 2.Complete part 2 using the rule for tangent ratio.

    [1]
  3. 3.Identify part 3 using the rule for tangent ratio.

    [1]
  4. 4.Match part 4 using the rule for tangent ratio.

    [1]
  5. 5.Complete part 5 using the rule for tangent ratio.

    [1]

Guided Practice

Bloom: Understand · 8 marks

The first step is given. Finish the reasoning.

  1. 1.Continue the working for part 1. Step 1 has been started for you.

    [2]
  2. 2.Complete the method for 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.Using the first step given, finish part 4. Step 1 has been started for you.

    [2]

FreeMathWorksheet · TN-MATH-TOEFL-32200 · v1.-7

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

Page 2 of 4

FreeMathWorksheet · TOEFL Math

Tangent Ratio

Independent Practice

Bloom: Apply · 10 marks

No scaffolding. Set out your full method.

  1. 1.Determine part 1 on tangent ratio without help.

    [2]
  2. 2.Determine part 2 on tangent ratio without help.

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

    [2]
  4. 4.Determine part 4 on tangent ratio without help.

    [2]
  5. 5.Calculate part 5 on tangent ratio without help.

    [2]

Challenge Questions

Bloom: Analyse · 9 marks

Harder items. Attempt every one, even partially.

  1. 1.Find and justify the statement in part 1 about tangent ratio.

    [3]
  2. 2.Prove the statement in part 2 about tangent ratio.

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

    [3]

FreeMathWorksheet · TN-MATH-TOEFL-32200 · v1.-7

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

Page 3 of 4

FreeMathWorksheet · TOEFL Math

Tangent Ratio

Real-life Application

Bloom: Apply · 6 marks

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

  1. 1.In context, work out a real math situation that depends on tangent ratio.

    [3]
  2. 2.Apply a real math situation that depends on tangent ratio.

    [3]

Critical Thinking

Bloom: Evaluate · 8 marks

Explain your reasoning in full sentences.

  1. 1.Compare and justify a student's method for tangent ratio is or is not efficient.

    [4]
  2. 2.Explain why a student's method for tangent ratio is or is not efficient.

    [4]

Reflection

Bloom: Create · 0 marks

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

  1. 1.Describe how confident you feel with tangent ratio and what you will practise next.

    [—]
  2. 2.Record how confident you feel with tangent ratio and what you will practise next.

    [—]

FreeMathWorksheet · TN-MATH-TOEFL-32200 · v1.-7

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

Page 4 of 4