Solving a Linear and a Non-linear system of equations

Solving two simultaneous linear equations

set up x- and y axises.

set linear equations and solve the simulatenous equations.

Displacement-time graphs are given and the student should select the correct velocity-time graphs from a list. Includes linear, piecewise linear and quadratic displacement-time functions.

Solve a pair of linear equations by writing an equivalent matrix equation.

Solve $p - t < \text{or}> q$

Manipulation of algebraic fractions

Linear combinations of $2 \times 2$ matrices. Three examples.

Linear combinations of $2 \times 2$ matrices. Three examples.

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

Identifying some of the basic properties (intercepts, asymptotes, quadrants) of a rational function (quadratic over linear)

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This exam covers 

• laws of indices
• using surds and rationalising the denominator
• expanding brackets
• simplifying expressions
• solving linear inequalities
• finding common factors
• dividing a polynomial with remainders, using algebraic division
• factor theorem
• remainder theorem
• inverse and composite functions

Shows how to define variables to stop degenerate examples.

Question assessing the students understanding of linear sequences.

Students are assessed on their ability to find the common difference and first term in a linear sequence and then find the nth term of the sequence using the arithmetic formula.

Solve a system of three simultaneous linear equations

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Solving linear equations to find the value of x.

Solve a system of three simultaneous linear equations

Basic solving of linear equations.

A question to practise the following skills in the context of Earth Sciences:

• graph-reading skills
• using a graph to find the equation of a line
• used adpative marking

Basic solving of linear equations.

This question allows you to practice identifying the coordinates of points on graphs.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

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Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Questions on linear programming techniques, with interactive graphics.

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by elimination 1 with parts' by Joshua Boddy.

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by elimination 1 with parts' by Joshua Boddy.