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UK Year 13 Mathematics (A Levels)
Y13
 
Algebra
Modulus function and its graph (90)
 
Modulus inequalities (17)
 
Arithmetic of polynomials (31)
 
Zeros of polynomials (50)
 
Division of polynomials (21)
 
Factor and remainder theorems (16)
 
Partial fractions (0)
 
Partial fractions and binomial expansions (0)
 
Logarithmic and exponential functions
Laws of logarithms (46)
 
Logarithms to different bases (20)
 
Logarithmic equations and inequalities (95)
 
Exponential equations and inequalities (18)
 
Natural logarithms (16)
 
Trigonometry
Cosecant, secant and cotangent ratios (7)
 
Compound angle formulae (38)
 
Double angle formulae (0)
 
Further trigonometric identities (0)
 
Differentiation
Product and quotient rules (86)
 
Derivatives of exponential functions (2)
 
Derivatives of natural logarithmic functions (1)
 
Derivatives of trigonometric functions (6)
 
Implicit differentiation (0)
 
Parametric differentiation (0)
 
Integration
Integration of exponential functions (5)
 
Integration of inverse functions (0)
 
Integration of algebraic fractions (10)
 
Integration of trigonometric functions (17)
 
The trapezium rule (0)
 
Integration by substitution (5)
 
Integration by parts (5)
 
Numerical solution of equations
Finding a starting point (0)
 
Improving your solution (0)
 
Vectors
Displacement or translation vectors (16)
 
Position vectors (3)
 
Scalar product (58)
 
Vector equation of a line (4)
 
Intersection of two lines (11)
 
Differential equations
Technique of separating the variables (0)
 
Forming a differential equation from a problem (0)
 
Complex numbers
Imaginary numbers (18)
 
Complex numbers (78)
 
Complex plane (31)
 
Complex number equations (8)
 
Momentum
Momentum as a vector (0)
 
Collision and conservation of momentum (0)
 
Newton’s laws of motion
Newton's laws of motion and linear motion (1)
 
Mass and weight (0)
 
Inclined planes (0)
 
Motion of connected particles (0)
 
Energy, work and power
Work done by a force (2)
 
Kinetic and potential energy (0)
 
Work-energy principle (0)
 
Principle of conservation of energy (0)
 
Power (0)
 
Poisson distribution
Adapting the Poisson distribution for different intervals (0)
 
Poisson distribution as an approximation to the binomial distribution (0)
 
Using the normal distribution as an approximation to the Poisson distribution (0)
 
Hypothesis testing with the Poisson distribution (0)
 
Linear combinations of random variables
Expectation and variance (0)
 
Sum and difference of independent random variables (0)
 
Working with normal distributions (0)
 
Linear combinations of Poisson distributions (0)
 
Continuous random variables
Finding the median and other percentiles of a continuous random variable (0)
 
Finding the expectation and variance (0)
 
Sampling and estimation
Distribution of sample means (0)
 
Unbiased estimates of population mean and variance (0)
 
Hypothesis testing of the population mean (0)
 
Confidence intervals for population mean (0)
 
Confidence intervals for population proportion (0)
 
Hypothesis tests
One-tailed and two-tailed hypothesis tests (0)
 
Type I and Type II errors (0)