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Tags: algebra, equations (linear), equations (quadratic)

Last updated Sep 2019

Topics:
Algebra, Calculus, Trigonometeric Equations, Complex numbers & Partial Derivatives

Students must complete the exam within 120 mins (standard time).

Questions have variables to produce randomised questions.

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Solve linear equations with unkowns on both sides. Including brackets and fractions.

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

An application of quadratic functions based on the Golden Gate Bridge in San Francisco, USA. Student is given an equation representing the suspension cable of the bridge and asked to find the width between the towers and the minimum height of the cable above the roadway. Requires and understanding of the quadratic function and where and how to apply correct formulae.

Student needs to solve a quadratic equation to calculate time taken for a diver to hit the water after diving from a diving board. Height of the board and initial upward velocity of the diver are randomly generated values. student needs to know that surface of the water is height 0, and only positive root of quadratic has physical meaning. Question is set to always give one positieve and one negative root.

Real numbers $a,\;b,\;c$ and $d$ are such that $a+b+c+d=1$ and for the given vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3,\;\textbf{v}_4$ $a\textbf{v}_1+b\textbf{v}_2+c\textbf{v}_3+d\textbf{v}_4=\textbf{0}$. Find $a,\;b,\;c,\;d$.

Find the equation of the line that passes through given points

Extra practice on some basic algebra skills, including solving linear equations. You can try as many times as you like and also generate new versions of the questions for extra practice.

The student is given the equations of a line and a circle, and has to find the coordinates of the points of intersection. They're always at integer coordinates.

Solve a problem using a linear equation.

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This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

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

Straightforward solving linear equations question

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

A simultaneous equations question with integers only

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Sometimes randomisation creates error with variable: c4

Students enter equation and turning point

Basic solving of linear equations

Solving linear equations

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Students enter equation and turning point

Straightforward solving linear equations question

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Basic solving of linear equations