Find a regression equation.

Find the solution of $\displaystyle \frac{dy}{dx}=\frac{1+y^2}{a+bx}$ which satisfies $y(1)=c$

rebelmaths

Practice rationalising a binomial denominator which contains surds.

Adapted from 'Surds 3' by Joshua Boddy.

Given a table of the number of days in which sales were between £x1000 and £(x+1)1000 find the relative percentage frequencies of these volume of sales.

rebelmaths

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force is applied in the negative $x$ and negative $y$ direction.

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force is applied in the negative $x$ and negative $y$ direction.

5 questions which introduce the student to the Numbas system:

1. Input 1

2. Input 2

3. Input 3         

4. Input 4       

5. Input 5                                                                                  

Calculate the expression $\frac{12}{4}a+\frac{3}{5}a$. One of the following is not correct, which one?

A few questions which show off the new matrix entry part.

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force is applied in the negative $x$ direction but the positive $y$. 

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force is applied in the negative $x$ and negative $y$ direction.

A mass is inside a box which is suspended vertically by a cord. Question uses $F=ma$ for different accelerations.

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force acts in the positive $x$ and positive $y$ direction.

Practice rationalising a binomial denominator which contains surds.

Adapted from 'Surds 3' by Joshua Boddy.

Single example with detailed solution for rationalising a binomial denominator which contains surds.

Adapted from 'Surds: rationalising the denominator conjugate' by Ben Brawn.

Two particles connected by a string which passes over a pulley at the top of an inclined plane. Find the acceleration of the masses and the tension in the string. Can not model the whole system as a single particle.

Finding the acceleration of a particle on an inclined plane which is at an angle to the horizontal. Smooth then with value for coefficient of friction.

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

6 questions which introduce the student to the Numbas system.

rebelmaths

Finding the values which satisfy an inequality containing two linear factors. 

Finding values which satisfy an inequality.

This test has a mixture of fundamentals questions.  You can use this to see which areas you need to practice.

Equations which can be written in the form

\[\dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(y),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x)f(y)\]

can all be solved by integration.

In each case it is possible to separate the $x$'s to one side of the equation and the $y$'s to the other

Solving such equations is therefore known as solution by separation of variables

Questions which rely on knowledge of standard integrals.

A really simple question which asks the student to multiply two matrices.

3 questions on factorising quadratics. The second question also asks for the roots of the quadratic. The third question involves factorising quartic polynomials but which are quadratics in $x^2$.

13 questions on combining algebraic fractions. An area in which students often need practice. 

Given a set $A$, elements of which may also be sets, determine if the given elements or subsets are in $A$.

English sentences which are propositions are given and for each the appropriate statement involving quantifiers is to be chosen. 

English sentences which are propositions are given and the appropriate logical expression chosen for the negation of the sentence.