A Level Year 12 / Mathematics / Curriculum
Applied option: Mechanics: structured theory, worked examples, answered practice, and a mastery checklist for A Level Year 12.
CHAPTER PLAN
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Estimated active study time
209 minutes
Objectives, key ideas, and structured theory.
Open →Worked examples that explain every step.
Open →Graded tasks with hints and answer guidance.
Open →Assignments from core work to challenge.
Open →A timed, marked test with solution guidance.
Open →Progress is stored only in this browser and does not require AI credits.
Unit
The essential chapter ideas in a clear sequence before practice.
Write the number in a useful form, check sign and place value, and only then choose the operation. A clear representation reduces mechanical errors.
Fractions, decimals, percentages, ratios, and powers can describe the same quantity. Changing form is a solving tool, not a separate trick.
Estimate before and after the exact calculation. The sign, order of magnitude, and unit must agree with the problem context.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Mathematics
Follow the method step by step and check why every step is valid.
Calculate and simplify 5/30 + 6/30.
11/30
Before calculating, explain the key idea from “Forces and equilibrium” and which conditions must be checked.
The answer should show not only which rule is used for “Forces and equilibrium”, but also why it is valid here.
Applied option: Mechanics
Eight graded tasks from core fluency to exam-style application. Work independently before opening a hint or answer.
Calculate 3 + 5 × 8 and justify the order of operations.
Multiplication precedes addition.
3 + 5 · 8 = 43.
Find 6/12 of 24.
Multiply by the fraction and simplify first.
6/12 · 24 = 12.
Increase 360 by 45%.
Use multiplier 1 + 45/100.
360 · 1.45 = 522.0.
Divide 132 in the ratio 5:6.
There are 11 ratio parts.
132 : 11 = 12; 60 and 72.
Compare 8/11 and 3/24 using a common denominator or decimals.
Use cross-products.
8 · 24 = 192, 3 · 11 = 33; 8/11 > 3/24.
Write 2000000 in standard form.
The first factor must be at least 1 and less than 10.
2000000 = 2.0 × 10^6.
Estimate 686 ÷ 19.8, then calculate to one decimal place.
Round to compatible numbers before calculating exactly.
Estimate ≈ 700 ÷ 20 = 35.0. Exact ≈ 34.6.
Test the claim 3² + 4² = 7² and explain.
Calculate both sides separately.
9 + 16 = 25, while 7² = 49; false.
Applied option: Mechanics
Six distinct assignments from core fluency to challenge, each with an estimated time, hint, and answer guide.
Homework 1: Calculate 6 + 6 × 12 and justify the order of operations.
Multiplication precedes addition.
6 + 6 · 12 = 78.
Homework 2: Find 9/27 of 81.
Multiply by the fraction and simplify first.
9/27 · 81 = 27.
Homework 3: Increase 250 by 25%.
Use multiplier 1 + 25/100.
250 · 1.25 = 312.5.
Homework 4: Divide 120 in the ratio 8:2.
There are 10 ratio parts.
120 : 10 = 12; 96 and 24.
Homework 5: Compare 4/8 and 4/16 using a common denominator or decimals.
Use cross-products.
4 · 16 = 64, 4 · 8 = 32; 4/8 > 4/16.
Homework 6: Write 4200000 in standard form.
The first factor must be at least 1 and less than 10.
4200000 = 4.2 × 10^6.
50 minutes / 40 marks
A timed, full-mark self-assessment with model-answer guidance.
Start the timer when ready, work without notes, show every step, and open model answers only after finishing.
1. Calculate 4 + 6 × 10 and justify the order of operations.
2 marks4 + 6 · 10 = 64.
2. Find 7/21 of 63.
3 marks7/21 · 63 = 21.
3. Increase 150 by 15%.
3 marks150 · 1.15 = 172.5.
4. Divide 96 in the ratio 6:2.
4 marks96 : 8 = 12; 72 and 24.
5. Compare 9/13 and 4/36 using a common denominator or decimals.
4 marks9 · 36 = 324, 4 · 13 = 52; 9/13 > 4/36.
6. Write 3000000 in standard form.
4 marks3000000 = 3.0 × 10^6.
7. Estimate 784 ÷ 29.700000000000003, then calculate to one decimal place.
5 marksEstimate ≈ 800 ÷ 30 = 26.7. Exact ≈ 26.4.
8. Test the claim 4² + 5² = 9² and explain.
5 marks16 + 25 = 41, while 9² = 81; false.
9. Create and solve a two-step exam-style problem about “Work, energy and power” using 7, 2, and 14.
5 marksA valid response uses the data in two justified steps and includes an independent check; for example 7 × 2 = 14, then 14 + 9 = 23.
10. Write a revision rule for “Momentum”, one example, and one counterexample.
5 marksFull response: an accurate rule for “Momentum”, a numerical example that satisfies it, and an explained counterexample.
Unit
Curriculum reference sources. Always confirm the teaching sequence with the school and tutor.
Mathematics
Start from the board specification and work topic by topic before full papers.
The structure follows the official textbook layout and is used to organise study.
The areas that usually create mistakes or need extra revision.
Where to start: textbook, daily material, PDFs, videos, and worked examples.
Targeted practice before full tests so coverage is clear.
How to measure progress in this chapter and when it enters a cumulative mock.
What to do after finishing the chapter and how it connects to the next unit.
Note: for the official examinable syllabus of each school year, always confirm with the school, tutor, and current Ministry/IEP announcements.
