A-Level Maths Revision Guides
A-Level
A-Level Maths Revision Guides
Six guides covering Pure Mathematics, Mechanics and Statistics. Every method explained step by step, then practised against questions with answers and full worked solutions.
- A-Level
- All boards
- 173 methods
- Worked solutions
The guides come in two kinds. An Explanation Guide sets out how each method works, step by step.
A Practice Guide holds the questions on those methods, each with its answer and a full worked solution. There is one of each for all three strands.
What the six guides cover
28 areas of the A-Level Maths specification, 173 named methods, and the practice questions that go with them.
| Strand | Areas | Methods | Practice questions |
|---|---|---|---|
| Pure Mathematics | 15 | 120 | over 1,500 |
| Mechanics | 8 | 28 | 296 |
| Statistics | 5 | 25 | 271 |
A-Level Maths content is common across the main boards, so the guides are used with AQA, Edexcel, OCR and MEI alike.
Three examples from the guides
One question from each Practice Guide, with its answer and worked solution. Attempt it first, then open the answer.
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Pure Mathematics · Proof by direct algebra
Prove that the sum of any eight consecutive integers is divisible by 2.
Answer
8n + 28 = 2(4n + 14), divisible by 2 for every integer n.
Worked solution
Represent the integers. Let the first of the eight consecutive integers be n, where n is any integer. The eight consecutive integers are then
n, n + 1, n + 2, n + 3, n + 4, n + 5, n + 6, n + 7.
Add and simplify. Add the eight integers and collect like terms:
n + (n + 1) + (n + 2) + (n + 3) + (n + 4) + (n + 5) + (n + 6) + (n + 7) = 8n + 28.
Factor out 2. Take out the common factor of 2:
8n + 28 = 2(4n + 14).
Conclude. Since n is an integer, 4n + 14 is also an integer, so 2(4n + 14) is a multiple of 2. Therefore the sum of any eight consecutive integers is divisible by 2 for every integer n.
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Mechanics · Constant acceleration in a straight line (SUVAT)
A car is moving along a straight horizontal road with speed 4 m s−1. The car then moves with constant acceleration 5 m s−2. (a) Find the speed of the car after 5 s. (b) Find the distance travelled by the car in the first 5 s.
The method, from the Explanation Guide
- List the SUVAT variables. Write down s, u, v, a, t; mark the three that are known and the one to be found.
- Fix the positive direction. State which direction is positive so that every quantity carries a consistent sign.
- Choose the equation. Pick the SUVAT equation containing the three known values and the single unknown, leaving out the variable not involved.
- Substitute and solve. Put in the numbers and solve for the unknown.
The Explanation Guide works this same car through those four steps before the Practice Guide asks for it.
Answer
(a) v = 29 m s−1 (b) s = 82.5 m
Worked solution
Setting up. The motion is in a straight line with constant acceleration, so the SUVAT equations apply with u = 4 m s−1, a = 5 m s−2 and t = 5 s.
(a) Speed after the given time. Using v = u + at:
v = 4 + 5 × 5 = 29 m s−1.
(b) Distance travelled. Using s = ut + ½at2:
s = 4 × 5 + ½ × 5 × 52 = 82.5 m.
Why that works. The distance is the area beneath the velocity-time graph, which is a straight line because the acceleration is constant.
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Statistics · Binomial distribution
The random variable X ∼ B(8, 0.3). (a) Find P(X = 3). (b) Find P(X ≤ 4). (c) Find P(X ≥ 6). Give each probability to 4 significant figures.
Answer
(a) P(X = 3) = 0.2541 (b) P(X ≤ 4) = 0.9420 (c) P(X ≥ 6) = 0.01129
Worked solution
Setting up. X ∼ B(8, 0.3), so
P(X = x) = 8Cx (0.3)x (0.7)8−x for x = 0, 1, …, 8.
(a) P(X = 3). A single term of the distribution. Evaluate the binomial coefficient and the two powers, then multiply:
P(X = 3) = 8C3 (0.3)3 (0.7)5 = 56 × 0.027 × 0.16807 = 0.2541.
(b) P(X ≤ 4). Sum the probabilities from 0 to 4:
P(X ≤ 4) = 0.9420.
(c) P(X ≥ 6). Use the complement:
P(X ≥ 6) = 1 − P(X ≤ 5) = 0.01129.
The 3-step active recall method
Re-reading notes is a futile process when your aim is to remember the information and successfully apply it in exam settings. Active recall is the method you use to ensure the information sticks for a long period of time.
But even active recall can be futile unless you have a structured way of implementing it. This is where the 3-step active recall method comes in, a structured method that is signature to the Levo Learning guides.
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Step 1
Answer up to 10 questions cold, closed book, even if you are unsure on the topic.
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Step 2
Answer the same questions again, but open book. Write the correct answer down even if it seems pointless.
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Step 3
Repeat as step 1 and answer the questions closed book again.
The same applies to method. The steps have to be produced without the worked solution in front of you.
The Complete Maths Bundle
All six guides together: the Explanation Guide and the Practice Guide for Pure Mathematics, Mechanics and Statistics. £45, against £50 bought separately.
Or buy the guides individually
Each strand has an Explanation Guide and a Practice Guide, sold separately.
Pure Mathematics
120 methods · over 1,500 questionsThe compulsory core, carrying two thirds of the qualification. Algebra and proof through to coordinate geometry, trigonometry, calculus and vectors.
Mechanics
28 methods · 296 questionsKinematics by SUVAT, motion graphs, projectiles, forces and friction, connected particles and moments.
Statistics
25 methods · 271 questionsSampling, data presentation, probability, the distributions and hypothesis testing.
Questions
What is the difference between the Explanation Guide and the Practice Guide?
The Explanation Guide works through each method step by step, with a worked example and the mistakes that lose marks. The Practice Guide holds the questions, each with its answer and a full worked solution.
How many guides are there, and do I need all six?
Six: an Explanation Guide and a Practice Guide for each of Pure, Mechanics and Statistics. They are sold separately, and the Complete Maths Bundle holds all six for £45 against £50 individually.
Which exam board are the maths guides for?
A-Level Maths content is common across the main boards, so the guides are used with AQA, Edexcel, OCR and MEI alike.
How do I use active recall with maths?
Work the Practice Guide in three passes: closed book, then open book writing the correct working down, then closed book again. The method has to be produced without the solution in front of you.
What format are the guides in?
Digital PDF, sent to the email address on the order.