Calculus, logarithms and probability
Write your reasoning, then compare it with the indicative marking points. Check your own exam-board specification for required coverage.
- Calculus
- Logarithms
- Probability
Practice betaUsable beta practice. Treat marking points as a helpful practice guide, not a certified answer key.
AS/A Level · Learning hub
Mathematics
About this subject
Original concept practice. Limited preview, not a complete syllabus or official past-paper collection.
Topics & subtopics
Integration and mathematical modelling
Original application practice with worked explanations and indicative self-marking points. Not an official exam paper or a board-specific assessment.
- Integration
- Area interpretation
- Mathematical models
Algebra and functions
Modulus, composite and inverse functions, partial fractions, transformations and exponential equations.
- Inverse and composite functions
- Partial fractions
- Transformations and equations
Differentiation and its applications
Product, quotient and chain rules, implicit differentiation, optimisation and related rates.
- Differentiation rules
- Optimisation
- Related rates
Integration techniques
Standard integrals, definite integrals, substitution, integration by parts, partial fractions and volumes of revolution.
- Substitution
- Integration by parts
- Definite integrals and volumes
Trigonometry
Exact values, identities, the R sin(x + alpha) form, trigonometric equations and sectors.
- Trigonometric identities
- Trigonometric equations
- Radians and sectors
Sequences, series and the binomial expansion
Arithmetic and geometric sequences, sum to infinity, sigma notation and binomial expansions for any rational power.
- Arithmetic and geometric sequences
- Series and sigma notation
- Binomial expansions
Vectors and coordinate geometry
Circles, scalar product, vector equations of lines in three dimensions, intersection and tangents to curves.
- Vector operations
- Spatial lines
- Circles and tangents
Statistics: probability, distributions and hypothesis tests
Binomial and normal distributions, conditional probability, hypothesis tests and regression.
- Probability distributions
- Hypothesis tests
- Regression
Mechanics: motion, forces and moments
Constant acceleration, Newton's laws, projectiles, connected particles, moments and variable acceleration.
- Motion and acceleration
- Forces and connected particles
- Moments
Parametric calculus and differential models
Tangents, curvature, integration techniques and separable equations.
- Parametric derivatives and tangents
- Integration and separable differential equations
Statistics and modelling: decisions and limits
Hypothesis tests, motion, distribution cutoffs and constrained optimisation.
- Normal and binomial inference
- Motion, growth and optimisation
Structured progression
Revision Ladder
Start with foundations, then move through application and challenge. Stages use activity marks and complexity.
Stage 1
Start stage Foundation
Recall core ideas and establish reliable methods.
22 questions available0/22 completedStage 2
Start stage Apply
Connect concepts and apply them in exam-style contexts.
23 questions available0/23 completedStage 3
Start stage Challenge
Tackle advanced reasoning and multi-step questions.
21 questions available0/21 completedProgress dashboard
Topic practice
Recommended next: Calculus, logarithms and probability
01
Calculus, logarithms and probability
Not startedWrite your reasoning, then compare it with the indicative marking points. Check your own exam-board specification for required coverage.
0%0/3 complete
02Integration and mathematical modelling
Not startedOriginal application practice with worked explanations and indicative self-marking points. Not an official exam paper or a board-specific assessment.
0%0/3 complete
03Algebra and functions
Not startedModulus, composite and inverse functions, partial fractions, transformations and exponential equations.
0%0/6 complete
04Differentiation and its applications
Not startedProduct, quotient and chain rules, implicit differentiation, optimisation and related rates.
0%0/6 complete
05Integration techniques
Not startedStandard integrals, definite integrals, substitution, integration by parts, partial fractions and volumes of revolution.
0%0/6 complete
06Trigonometry
Not startedExact values, identities, the R sin(x + alpha) form, trigonometric equations and sectors.
0%0/6 complete
07Sequences, series and the binomial expansion
Not startedArithmetic and geometric sequences, sum to infinity, sigma notation and binomial expansions for any rational power.
0%0/6 complete
08Vectors and coordinate geometry
Not startedCircles, scalar product, vector equations of lines in three dimensions, intersection and tangents to curves.
0%0/6 complete
09Statistics: probability, distributions and hypothesis tests
Not startedBinomial and normal distributions, conditional probability, hypothesis tests and regression.
0%0/6 complete
10Mechanics: motion, forces and moments
Not startedConstant acceleration, Newton's laws, projectiles, connected particles, moments and variable acceleration.
0%0/6 complete
11Parametric calculus and differential models
Not startedTangents, curvature, integration techniques and separable equations.
0%0/6 complete
12Statistics and modelling: decisions and limits
Not startedHypothesis tests, motion, distribution cutoffs and constrained optimisation.
0%0/6 complete
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