HELM Book 1.5.2 Task 2. This is a fixed question, asking you to rearrange an equation.

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Shows how the "give a number which satisfies an equation" part type can be used to makr the student's number correct if it satisfies an equation of the form $f(x) = 0$.

Given an equation with variable x in the power on two different bases, students must solve for x. Hints are included in the question to aid the student as needed.

Given an equation where x is the base of a log term, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation involving x as a power on e, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation with log terms added together, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation with log terms added together, the student must solve for x. Hints are included in the question to aid the student as needed.

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Student is given two points defined symbolically, and must find the equation of the line they define, then use integration to find an equation for the area under the line, bounded by the x-axis and vertical lines through the two points.   

Separable equation for integration.

First order integral.

First order integral.

Practice question solving linear homogeneous second order differentials using the auxiliary equation method.

Solving an equation of the form $ax \equiv b\;\textrm{mod}\;n$ where $a$ and $n$ are coprime.

More difficult trigonometric equations with radians

Solving $\cos(nx)=a$ for $x\in (0,\pi)$, where $n$ is an integer and $a\in(0,1)$.

Solving a pair of simultaneous equations of the form $a_1x+b_1y=c_1$ and $a_2 x^2+b_2y^2=c_2$ by forming a quadratic equation.

Solving a pair of simultaneous equations of the form $a_1xy=c_1$ and $a_2x+b_2y=c_2$ by forming a quadratic equation.

Solving a pair of linear simultaneous equations with integer solutions.

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

Tests the ability to find the gradient and intercept of a straight line graph.

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Students enter equation and turning point

Solving a cubic equation of the form $ax^3+bx^2+cx+d=0$.

This exercise will help you rearrange some complex equations.

A question to practice equation line and finding gradients

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

SUVAT equation questions, for mechanics page in wiki. Uses $v=u+at$ and $s=((u+v)/2)t$.

Solve a logarithmic equation