A variety of trigonometric equations which can be solved using inverse operations.

Find the eigenfunctions of an irregular Sturm–Liouville problem and hence solve an inhomogeneous boundary value problem by writing the solution as an eigenfunction expansion.

Solve equations involving logs and exponential functions, by using inverse operations.

Solve linear equations with unknowns on one. Including brackets and fractions. Solutions may require rounding.

Solve linear equations with one unknown. Including brackets and fractions.

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

Solve an ODE by first writing it in canonical form.

Solve linear equations with one unknown. Including brackets and fractions.

Solving a quadratic equation via factorisation (or otherwise) with the $x^2$-term having a coefficient of 1.

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

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

Solving a quadratic equation via factorisation, with the $x^2$-term having a coefficient of 1.

Solving simple linear equations in $\mathbb{Q}$ and $\mathbb{Z}_n$ for $n= 13, \;17$ or $19$.

Use the simplex method to solve a linear program.

In this question the students have to solve a linear recurrence of order 1. The sequence is asked in recurrence form and the goal is to find its closed form.

In this question the students have to solve a linear recurrence of order 2. The sequence is asked in recurrence form and the goal is to find its closed form.

Copy the problem parameters into the handout provided and solve the Building Fabric heat loss problem by hand. Enter your answers into this quiz to get your score. Upload a copy of your written answer to the submission on Brightspace. Good Luck!

Questions to test if the student knows the inverse of an even power (and how to solve equations that contain a single power that is even). 

Questions to test if the student knows the inverse of an odd power (and how to solve equations that contain a single power that is odd). 

Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them). 

Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.

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. 

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 $a,\;b,\;c,\;d$.

Solving a system of simultaneous congruences using the Chinese Remainder Theorem.

An explore mode question which allows you to write a solution straight away, or break it down into steps.

After solving a system of three congruences, you can ask for a new problem with more congruences.

Solve a problem using a linear equation.

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.

Basic solving of linear equations

Solving linear equations