MEI AS Pure Maths Tests

Each of the Tests opens in a new window. Tests marked +-*/ link to the Test (in a new window).

All Tests have full Worked Solutions

AS Level Pure Mathematics TESTS.
If you find any bugs or have comments, please email Dr Ron Knott .
For problems with a specific Test, always mention the test reference (a web address) shown in the bottom right hand corner of each Test.

A page to check that this browser correctly displays the maths symbols etc used in these Tests

Powers and Logarithms

Bases of Logs
Solving for Powers +-*/
Modelling Population Growth +-*/ logs and exponentials

Graphs

Curve Sketching: Shape degree 2 and 3
Equations from Log-x and Log-Log graphs +-*/
Equations from Log-x graphs, Equations from Log-Log graphs
Graph Transformations

Sequences and Series

Arithmetic Series: Terms +-*/
Given first 3 Terms , Given the common difference and first term
Arithmetic Series: Sum +-*/
Arithmetic Series: Formula manipulation +-*/
Find S given a,d,n qu=s | Find d given S,a,n qu=d| Find a given S,d,n qu=a| Find n given S,a,d:n is unique qu=n| Find n given S,a,d:n not unique qu=n
Geometric Series: Terms +-*/
Geometric Series: Sum +-*/ e.g. infinite or finite series
Geometric Series: Formula Manipulation+-*/
Given r,sum of an infinite GP find a | Given a,sum of an infinite GP find r | Given r,sum of n terms, find a | Given r,sum and a, find n | Given r, a, find n to exceed a given sum

Review of Algebra

Collecting Terms
Simplifying Products
Simplifying Surds 4 types of question:
Sum, Product, Division, Power (2 or 3)
Forming and Solving Equations +-*/ 7 question types
e.g. 1 2 3 4 5 6 7
Quadratics - Completing The Square
Algebraically, to find turning point
Factorize Quadratic Equations:
e.g. constant term is 0, Difference of two squares, coeff of x² is 1, coeff of x² is not 1
Solve Quadratic Equations
Form and Solve Quadratic Equations +-*/ finds roots using the Formula:
e.g. Field (factors), Field (formula)or Ball (formula), Ball (factors)
Partial Fractions

Simultaneous Equations

Solving Simultaneous Linear Equations
Forming and Solving Simultaneous Linear Equations
Quadratic and Line Intersection
Circle and Line Intersection e.g. 0, 1, 2 points in common

Solving Inequalities

Coordinate Geometry

Trigonometry

Polynomials

Binomial Coefficient Evaluation
Binomial Coefficient Expansion
Division
Remainder Theorem
Given a divisor find remainder, Given the remainder find the polynomial
Differentiation
Differentiation: Gradient and Normal
Differentiation: Rules
Product Rule, Quotient Rule, Chain Rule
Tangent and Normal Lines +-*/
Integration
Definite Integration +-*/
Polynomial from Roots
Sum and Product of Roots
Polynomials with New Roots Quadratic, Cubic or Quartic
Quadratic only, Quadratic or Cubic only

Differential Equations

First order, constant coefficient, homogeneous (separation of variables)
Second Order, constant coefficient, homogeneous (auxiliary quadratic equation, distinct real roots, general or particular solutions)
- Particular solutions only
- General solutions only

Complex Numbers

Addition and Subtraction
Multiplication
Division
Conjugate
Polar Form +-*/ convert x-y form to and from polar form:
Modulus and Argument (special angles) to x+yj form, x+yj to polar , x+yj to Mod and Arg
Polar Multiplication and Division +-*/

Vectors

By adding parameters to the URLs these tests can be particularised to only 2D vector, only 3D vectors, magnitude-direction form only, ij form only, column vectors only and position vectors only. By omitting the parameters, the tests randomly choose the values of the parameters.
eg 2D position vectors for the Magnitude Of Vectors test has URL VectorsMag.html?DIM=2,qu=pts2
Resting your mouse over the URLs below reveals the full URL in the Status bar at the foot of this window.

2D and 3D

Magnitude 2D and 3D
magnitude-direction | ij | column vector | position vector
Operations 2D and 3D
add | subtract | dot (scalar) product | scalar multiple
+-*/ Angle between two vectors 2D and 3D
Magnitude-direction | ij | column vector | position vector

2D only

3D only

Magnitude 3D
magnitude-direction | ij | column vector | position vector
Operations 3D
add | subtract | dot (scalar) product | scalar multiple
+-*/ Angle between two 3D vectors
Magnitude-direction | ij | column vector | position vector
Vector Plane Equation using the Normal including 2 zeros, and 1 zero

Matrices

Mechanics

Statistics

Mean and SD +-*/
Linear Coding +-*/

Changes

Author : Dr Ron Knott : all enquiries to