FreeMathWorksheet
Worksheet · TN-MATH-GR12-62652 · v3.-1

Cosine Ratio — Homework Worksheet

A single-focus worksheet on cosine ratio for Grade 12 Math. Nothing else from trigonometry is mixed in — every question, from warm-up to reflection, assesses this one objective and builds towards mastery.

CoreAQA25 min44 marksNo answers on sheet

Sized for independent work at home with a parent note.

Grade

Grade 12

Subject

Math

Topic

Trigonometry

Subtopic

Cosine Ratio

Curriculum

AQA

Difficulty

Core

Time

25 min

Questions

25

Total marks

44

Worksheet ID

TN-MATH-GR12-62652

Version

v3.-1

Format

A4 · US Letter

Preview & download

Print-ready · high-resolution PDF · minimal ink
FreeMathWorksheet

Homework Worksheet

TN-MATH-GR12-62652 · v3.-1

Cosine Ratio

Grade 12 · Math · Trigonometry · AQA

Grade

Grade 12

Subject

Math

Topic

Trigonometry

Subtopic

Cosine Ratio

Curriculum

AQA

Difficulty

Core

Time

25 minutes

Total marks

44

Student name

Teacher name

Date

Learning objectives

  • Recognise cosine ratio accurately in math contexts.
  • Explain the underlying rule of cosine ratio in the student's own words.
  • Apply cosine 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 25 minutes.
  5. Complete the reflection box at the end before you hand the sheet in.

Warm-up

Bloom: Remember · 3 marks

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

  1. 1.Write down one fact you already know about cosine ratio.

    [1]
  2. 2.Circle one fact you already know about cosine ratio.

    [1]
  3. 3.Name one fact you already know about cosine ratio.

    [1]

Recall

Bloom: Remember · 3 marks

Complete from memory. No calculator, no notes.

  1. 1.Define the key term used in cosine ratio described here: item 1.

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

    [1]
  3. 3.Label the key term used in cosine ratio described here: item 3.

    [1]

FreeMathWorksheet · TN-MATH-GR12-62652 · v3.-1

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

Page 1 of 4

FreeMathWorksheet · Grade 12 Math

Cosine Ratio

Basic Practice

Bloom: Understand · 4 marks

Work through each item. Show the step you used.

  1. 1.Work out part 1 using the rule for cosine ratio.

    [1]
  2. 2.Work out part 2 using the rule for cosine ratio.

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

    [1]
  4. 4.Complete part 4 using the rule for cosine ratio.

    [1]

Guided Practice

Bloom: Understand · 6 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.Continue the working 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]

FreeMathWorksheet · TN-MATH-GR12-62652 · v3.-1

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

Page 2 of 4

FreeMathWorksheet · Grade 12 Math

Cosine Ratio

Independent Practice

Bloom: Apply · 8 marks

No scaffolding. Set out your full method.

  1. 1.Calculate part 1 on cosine ratio without help.

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

    [2]
  3. 3.Solve part 3 on cosine ratio without help.

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

    [2]

Challenge Questions

Bloom: Analyse · 6 marks

Harder items. Attempt every one, even partially.

  1. 1.Prove the statement in part 1 about cosine ratio.

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

    [3]

Real-life Application

Bloom: Apply · 6 marks

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

  1. 1.Use the information to decide a real math situation that depends on cosine ratio.

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

    [3]

FreeMathWorksheet · TN-MATH-GR12-62652 · v3.-1

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

Page 3 of 4

FreeMathWorksheet · Grade 12 Math

Cosine Ratio

Critical Thinking

Bloom: Evaluate · 8 marks

Explain your reasoning in full sentences.

  1. 1.Evaluate whether a student's method for cosine ratio is or is not efficient.

    [4]
  2. 2.Evaluate whether a student's method for cosine ratio 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 cosine ratio and what you will practise next.

    [—]
  2. 2.Reflect on how confident you feel with cosine ratio and what you will practise next.

    [—]

FreeMathWorksheet · TN-MATH-GR12-62652 · v3.-1

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

Page 4 of 4

Question progression

Recognition → understanding → application → reasoning → mastery. The ladder adapts to Grade 12, and every rung stays on cosine ratio only.

  1. 01Warm-up

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

    Remember3 questions3 marks
  2. 02Recall

    Complete from memory. No calculator, no notes.

    Remember3 questions3 marks
  3. 03Basic Practice

    Work through each item. Show the step you used.

    Understand4 questions4 marks
  4. 04Guided Practice

    The first step is given. Finish the reasoning.

    Understand3 questions6 marks
  5. 05Independent Practice

    No scaffolding. Set out your full method.

    Apply4 questions8 marks
  6. 06Challenge Questions

    Harder items. Attempt every one, even partially.

    Analyse2 questions6 marks
  7. 07Real-life Application

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

    Apply2 questions6 marks
  8. 08Critical Thinking

    Explain your reasoning in full sentences.

    Evaluate2 questions8 marks
  9. 09Reflection

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

    Create2 questions0 marks

Answer key & solutions

Every worksheet auto-generates a complete key with step-by-step solutions, the marking scheme and teacher notes. It prints as separate pages so the student copy stays clean.

Teacher notes

  • Set the warm-up as a five-minute starter; it diagnoses readiness for cosine ratio before you teach.
  • Guided practice is the pivot point — circulate here rather than during independent practice.
  • Mark the reasoning questions with the marking scheme bands, not raw totals, so progress is comparable across variants.
  • Students who band Emerging should repeat the Easy variant of this same subtopic before moving on within Trigonometry.

Common student mistakes

  • Confusing cosine ratio with a neighbouring idea in trigonometry.

Teaching tips

  • Model one worked example of cosine ratio under a visualiser before handing the sheet out.
  • Ask students to predict which question they will find hardest, then check the prediction afterwards.
  • Pair Developing students with Secure students for the guided practice block only.
  • Use the answer key as a self-marking station rather than collecting the sheets in.

Extension activities

  • Challenge worksheet on cosine ratio with justification-only questions.
  • Design your own cosine ratio question and write the mark scheme for it.
  • Link cosine ratio to the next subtopic in Trigonometry and explain the connection.
  • Ten-minute timed practice to convert accuracy into fluency.

Switch version

Same subtopic · same objectives · different job

Frequently asked

What exactly is in the download?
A 25-question, 44-mark sheet with branded header, objectives, skills, instructions, name and date fields, page numbering, footer branding, copyright, worksheet ID TN-MATH-GR12-62652, version v3.-1 and a QR code back to this page.
Does it print correctly on US Letter?
Yes. Switch paper size in the download panel — margins and typography are identical, so nothing reflows or clips.
Is the answer key included?
The student copy prints clean. Toggle answers on to append the answer key, marking scheme and teacher pack.

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