Question 1 of 3 · No calculator needed
Which conclusion follows deductively from the assumption that n is divisible by 6?
If n is divisible by 6, n = 6k = 3(2k) for some integer k. Hence n is divisible by 3.
Pearson Edexcel IAL · A LevelMathematics,
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Question 2 of 3 · No calculator needed
In the standard contradiction proof that √2 is irrational, suppose √2 = a/b in lowest terms. After showing a² is even, what follows?
If a² is even, then a must be even. Writing a = 2k and substituting back then shows b is even too, contradicting that a/b was in lowest terms.
Question 3 of 3 · No calculator needed
How many real solutions does x⁴ + 1 = 3x² have?
Let u = x². Then u² - 3u + 1 = 0 has two positive roots. Each positive value of u gives two real values x = ±√u, so there are four real solutions.
These tiles show your answers to three questions. They are a starting point, not a mastery score or grade prediction.
Proof
Correct answer: n is divisible by 3
If n is divisible by 6, n = 6k = 3(2k) for some integer k. Hence n is divisible by 3.
Proof by contradiction
Correct answer: a is even
If a² is even, then a must be even. Writing a = 2k and substituting back then shows b is even too, contradicting that a/b was in lowest terms.
Algebra and functions
Correct answer: 4
Let u = x². Then u² - 3u + 1 = 0 has two positive roots. Each positive value of u gives two real values x = ±√u, so there are four real solutions.
For parents: look at the explanation together. A correct answer is encouraging; a missed answer gives you something specific to work on. Broader practice over time is needed to understand progress.
YOUR TOPIC MAP
52 areasFind your starting point.
01Algorithms
Specification reference: D1.1 Algorithms
Algorithms requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Algorithms requires. Keep exact values until the final step and check signs, units and reasonableness.
02Minimum spanning trees and shortest paths
Specification reference: D1.2 Minimum spanning trees and shortest paths
Minimum spanning trees and shortest paths requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Minimum spanning trees and shortest paths requires. Keep exact values until the final step and check signs, units and reasonableness.
03Route inspection and travelling salesperson algorithms
Specification reference: D1.3 Route inspection and travelling salesperson algorithms
Route inspection and travelling salesperson algorithms requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Route inspection and travelling salesperson algorithms requires. Keep exact values until the final step and check signs, units and reasonableness.
04Critical path analysis
Specification reference: D1.4 Critical path analysis
Critical path analysis requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Critical path analysis requires. Keep exact values until the final step and check signs, units and reasonableness.
05Linear programming
Specification reference: D1.5 Linear programming
Linear programming requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Linear programming requires. Keep exact values until the final step and check signs, units and reasonableness.
06Mathematical models in mechanics
Specification reference: M1.1 Mathematical models in mechanics
Mathematical models in mechanics requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Mathematical models in mechanics requires. Keep exact values until the final step and check signs, units and reasonableness.
07Vectors in mechanics
Specification reference: M1.2 Vectors in mechanics
Vectors in mechanics requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Vectors in mechanics requires. Keep exact values until the final step and check signs, units and reasonableness.
08Straight-line kinematics
Specification reference: M1.3 Straight-line kinematics
Straight-line kinematics requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Straight-line kinematics requires. Keep exact values until the final step and check signs, units and reasonableness.
09Dynamics of a particle
Specification reference: M1.4 Dynamics of a particle
Dynamics of a particle requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Dynamics of a particle requires. Keep exact values until the final step and check signs, units and reasonableness.
10Statics of a particle
Specification reference: M1.5 Statics of a particle
Statics of a particle requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Statics of a particle requires. Keep exact values until the final step and check signs, units and reasonableness.
11Moments
Specification reference: M1.6 Moments
Moments requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Moments requires. Keep exact values until the final step and check signs, units and reasonableness.
12Kinematics in a straight line or plane
Specification reference: M2.1 Kinematics in a straight line or plane
Kinematics in a straight line or plane requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Kinematics in a straight line or plane requires. Keep exact values until the final step and check signs, units and reasonableness.
13Centres of mass
Specification reference: M2.2 Centres of mass
Centres of mass requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Centres of mass requires. Keep exact values until the final step and check signs, units and reasonableness.
14Work and energy
Specification reference: M2.3 Work and energy
Work and energy requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Work and energy requires. Keep exact values until the final step and check signs, units and reasonableness.
15Collisions
Specification reference: M2.4 Collisions
Collisions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Collisions requires. Keep exact values until the final step and check signs, units and reasonableness.
16Statics of rigid bodies
Specification reference: M2.5 Statics of rigid bodies
Statics of rigid bodies requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Statics of rigid bodies requires. Keep exact values until the final step and check signs, units and reasonableness.
17Algebra and functions
Specification reference: P1.1 Algebra and functions
Algebra and functions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Algebra and functions requires. Keep exact values until the final step and check signs, units and reasonableness.
18Coordinate geometry in the (x, y) plane
Specification reference: P1.2 Coordinate geometry in the (x, y) plane
Coordinate geometry in the (x, y) plane requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Coordinate geometry in the (x, y) plane requires. Keep exact values until the final step and check signs, units and reasonableness.
19Trigonometry
Specification reference: P1.3 Trigonometry
Trigonometry requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Trigonometry requires. Keep exact values until the final step and check signs, units and reasonableness.
20Differentiation
Specification reference: P1.4 Differentiation
Differentiation requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Differentiation requires. Keep exact values until the final step and check signs, units and reasonableness.
21Integration
Specification reference: P1.5 Integration
Integration requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Integration requires. Keep exact values until the final step and check signs, units and reasonableness.
22Proof
Specification reference: P2.1 Proof
Proof requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Proof requires. Keep exact values until the final step and check signs, units and reasonableness.
23Algebra and functions
Specification reference: P2.2 Algebra and functions
Algebra and functions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Algebra and functions requires. Keep exact values until the final step and check signs, units and reasonableness.
24Coordinate geometry of the circle
Specification reference: P2.3 Coordinate geometry of the circle
Coordinate geometry of the circle requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Coordinate geometry of the circle requires. Keep exact values until the final step and check signs, units and reasonableness.
25Sequences and series
Specification reference: P2.4 Sequences and series
Sequences and series requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Sequences and series requires. Keep exact values until the final step and check signs, units and reasonableness.
26Exponentials and logarithms
Specification reference: P2.5 Exponentials and logarithms
Exponentials and logarithms requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Exponentials and logarithms requires. Keep exact values until the final step and check signs, units and reasonableness.
27Trigonometry
Specification reference: P2.6 Trigonometry
Trigonometry requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Trigonometry requires. Keep exact values until the final step and check signs, units and reasonableness.
28Differentiation
Specification reference: P2.7 Differentiation
Differentiation requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Differentiation requires. Keep exact values until the final step and check signs, units and reasonableness.
29Integration
Specification reference: P2.8 Integration
Integration requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Integration requires. Keep exact values until the final step and check signs, units and reasonableness.
30Algebra and functions
Specification reference: P3.1 Algebra and functions
Algebra and functions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Algebra and functions requires. Keep exact values until the final step and check signs, units and reasonableness.
31Trigonometry
Specification reference: P3.2 Trigonometry
Trigonometry requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Trigonometry requires. Keep exact values until the final step and check signs, units and reasonableness.
32Exponentials and logarithms
Specification reference: P3.3 Exponentials and logarithms
Exponentials and logarithms requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Exponentials and logarithms requires. Keep exact values until the final step and check signs, units and reasonableness.
33Differentiation
Specification reference: P3.4 Differentiation
Differentiation requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Differentiation requires. Keep exact values until the final step and check signs, units and reasonableness.
34Integration
Specification reference: P3.5 Integration
Integration requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Integration requires. Keep exact values until the final step and check signs, units and reasonableness.
35Numerical methods
Specification reference: P3.6 Numerical methods
Numerical methods requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Numerical methods requires. Keep exact values until the final step and check signs, units and reasonableness.
36Proof by contradiction
Specification reference: P4.1 Proof by contradiction
Proof by contradiction requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Proof by contradiction requires. Keep exact values until the final step and check signs, units and reasonableness.
37Partial fractions
Specification reference: P4.2 Partial fractions
Partial fractions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Partial fractions requires. Keep exact values until the final step and check signs, units and reasonableness.
38Parametric equations
Specification reference: P4.3 Parametric equations
Parametric equations requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Parametric equations requires. Keep exact values until the final step and check signs, units and reasonableness.
39Binomial expansion for rational powers
Specification reference: P4.4 Binomial expansion for rational powers
Binomial expansion for rational powers requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Binomial expansion for rational powers requires. Keep exact values until the final step and check signs, units and reasonableness.
40Implicit and parametric differentiation and differential equations
Specification reference: P4.5 Implicit and parametric differentiation and differential equations
Implicit and parametric differentiation and differential equations requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Implicit and parametric differentiation and differential equations requires. Keep exact values until the final step and check signs, units and reasonableness.
41Advanced integration
Specification reference: P4.6 Advanced integration
Advanced integration requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Advanced integration requires. Keep exact values until the final step and check signs, units and reasonableness.
42Vectors
Specification reference: P4.7 Vectors
Vectors requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Vectors requires. Keep exact values until the final step and check signs, units and reasonableness.
43Mathematical models in probability and statistics
Specification reference: S1.1 Mathematical models in probability and statistics
Mathematical models in probability and statistics requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Mathematical models in probability and statistics requires. Keep exact values until the final step and check signs, units and reasonableness.
44Representation and summary of data
Specification reference: S1.2 Representation and summary of data
Representation and summary of data requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Representation and summary of data requires. Keep exact values until the final step and check signs, units and reasonableness.
45Probability
Specification reference: S1.3 Probability
Probability requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Probability requires. Keep exact values until the final step and check signs, units and reasonableness.
46Correlation and regression
Specification reference: S1.4 Correlation and regression
Correlation and regression requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Correlation and regression requires. Keep exact values until the final step and check signs, units and reasonableness.
47Discrete random variables
Specification reference: S1.5 Discrete random variables
Discrete random variables requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Discrete random variables requires. Keep exact values until the final step and check signs, units and reasonableness.
48The Normal distribution
Specification reference: S1.6 The Normal distribution
The Normal distribution requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what The Normal distribution requires. Keep exact values until the final step and check signs, units and reasonableness.
49The Binomial and Poisson distributions
Specification reference: S2.1 The Binomial and Poisson distributions
The Binomial and Poisson distributions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what The Binomial and Poisson distributions requires. Keep exact values until the final step and check signs, units and reasonableness.
50Continuous random variables
Specification reference: S2.2 Continuous random variables
Continuous random variables requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Continuous random variables requires. Keep exact values until the final step and check signs, units and reasonableness.
51Continuous distributions and Normal approximations
Specification reference: S2.3 Continuous distributions and Normal approximations
Continuous distributions and Normal approximations requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Continuous distributions and Normal approximations requires. Keep exact values until the final step and check signs, units and reasonableness.
52Samples and hypothesis tests
Specification reference: S2.4 Samples and hypothesis tests
Samples and hypothesis tests requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Samples and hypothesis tests requires. Keep exact values until the final step and check signs, units and reasonableness.
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Pearson Edexcel IAL · A Level · Mathematics · YMA01
Issue 3 (April 2019; current PDF modified April 2025)
Source checked: 2026-08-27. The current official specification controls assessment requirements and option choices.
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It shows the outcome of these three answers and gives a specific skill to discuss or practise next. It is not a full assessment, a mastery score or a grade prediction. Broader practice over time is needed to understand progress.
What does the Pearson Edexcel IAL A Level Mathematics route cover?
LearningP currently maps 52 assessed areas for specification YMA01. The visible topic map below is derived from the verified route; the current official specification remains controlling.
How many LearningP questions support this route?
The verified source bank contains 587 original LearningP question records for this route. Every mapped area meets the current publication minimum and passed the latest blocker and review audit.
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