A-Level Maths · Year 13 · Pure
Numerical Methods worksheets with answers
Free worksheets for the 7 lessons in A-Level Maths Numerical Methods, written by qualified teachers. Each lesson has a worksheet, full answers to the worksheet and a homework sheet, as PDFs to print or share. No sign-up needed.
7 lessonsAQA 7357 · Edexcel 9MA0
We don't publish answers to the homework, so teachers can set it as independent work.
Lesson 1 of 7
Locating Roots
Shows that a root lies in an interval by a change of sign, and explains when this fails, for example at repeated roots or asymptotes. Students also count roots by sketching two graphs, and show that a root is correct to a given number of decimal places.
- AQA 7357
- I1
- Edexcel 9MA0
- 9.1
Lesson 2 of 7
Iteration
Rearranges f(x) = 0 into the form x = g(x) and uses the iteration xₙ₊₁ = g(xₙ) to approach a root. Students recognise convergence and divergence, see that different rearrangements can find different roots, and check the accuracy of a root with a change of sign.
- AQA 7357
- I2
- Edexcel 9MA0
- 9.2
Lesson 3 of 7
Staircase and Cobweb Diagrams
Shows iterations on a graph as staircase and cobweb diagrams. Students draw the diagrams, tell convergence from divergence, and use them to explain which root an iteration finds or why it cannot find one.
- AQA 7357
- I2
- Edexcel 9MA0
- 9.2
Lesson 4 of 7
The Newton–Raphson Method
Derives the Newton–Raphson formula from the tangent to a curve and applies it to find roots. Students show that a root is correct to a given accuracy, and explain when and why the method fails.
- AQA 7357
- I2
- Edexcel 9MA0
- 9.3
Lesson 5 of 7
Numerical Methods in Context
Applies numerical methods to models of real situations, turning a question into an equation and solving it by change of sign, iteration or Newton–Raphson. Students answer in context with units and sensible rounding, and criticise the model.
- AQA 7357
- I4 (with I1, I2)
- Edexcel 9MA0
- 9.5 (with 9.1–9.3)
Lesson 6 of 7
The Trapezium Rule
Uses the trapezium rule to estimate the area under a curve, from a formula or a table of values. Students decide from the shape of the curve whether it overestimates or underestimates, improve the estimate with more strips, and find percentage errors and bounds for the area.
- AQA 7357
- I3 (with H4, I4)
- Edexcel 9MA0
- 9.4 (with 9.5)
Mixed review · Lesson 7 of 7
Unit review: Numerical Methods
Mixed exam-style practice across the whole Numerical Methods unit: change of sign, iteration with staircase and cobweb diagrams, Newton–Raphson, models in context and the trapezium rule. The focus is on naming the method first and knowing when each one fails.
- AQA 7357
- I1, I2, I3, I4
- Edexcel 9MA0
- 9.1, 9.2, 9.3, 9.4, 9.5
More A-Level Maths worksheets
Want one-to-one help with A-Level Maths or Further Maths?
Our qualified teachers tutor A-Level Maths and Further Maths one-to-one, online or face to face in Corby and nearby towns. Start with a free consultation.