Advanced Higher Maths Questions by Topic


Differentiating exponential and natural logarithmic functions

Differentiating functions using the chain rule

Differentiating functions given in the form of a product and in the form of a quotient

Differentiating inverse trigonometric functions

Finding the derivative where relationships are defined implicitly

Finding the derivative where relationships are defined parametrically

Applying differentiation to problems in context

Integrating expressions using standard results

Integrating by substitution

Integrating by parts

Applying integration to problems in context

Solving first-order differential equations with variables separable

Solving first-order linear differential equations using an integrating factor

Solving second-order differential equations

Algebra, proof and number theory

Decomposing a rational function into a sum of partial fractions (denominator of degree at most three)

Finding the asymptotes to the graphs of rational functions

Investigating features of graphs and sketching graphs of functions

Expanding expressions using the binomial theorem

Finding the general term and summing arithmetic and geometric progressions

Applying summation formulae

Using the Maclaurin expansion to find specified terms of the power series for simple functions

Disproving a conjecture by providing a counterexample

Using indirect or direct proof in straightforward examples

Using proof by induction

Using Euclid’s algorithm to find the greatest common divisor of two positive integers

Matrices, vectors and complex numbers

Using Gaussian elimination to solve a 3 X 3 system of linear equations

Understanding and using matrix algebra

Calculating the determinant of a matrix

Finding the inverse of a matrix

Using transformation matrices

Calculating a vector product

Working with lines in three dimensions

Working with planes

Performing algebraic operations on complex numbers

Performing geometric operations on complex numbers