Practice questions: Additional Mathematics
You can see below a collection of questions which will help you practise essential skills. If you are logged in, the last column will show your success rate in your last five attempts at each question. This is a great way to make sure that you master all the important skills.
| Question | Description | Last 5 |
| General algebra | ||
|---|---|---|
| Solving simultaneous equations | Solve simultaneous linear equations by elimination. | |
| Solving a quadratic equation by factorising | Solve a quadratic equation by factorising it first. | |
| Linear-quadratic simultaneous equations | Solve simultaneous equations, one being linear and the other quadratic. | |
| Using the quadratic formula | Solve a quadratic equation using the quadratic formula. | |
| Polynomial algebra | ||
| Polynomial division | Practise dividing a polynomial by a linear polynomial | |
| Factorising polynomials | Factorise a polynomial using the factor theorem and polynomial division | |
| Remainder theorem | Use the remainder theorem to find an unknown coefficient in a polynomial | |
| Remainder and factor theorems | Use the remainder and factor theorems to find unknown coefficients in a polynomial | |
| Surds | ||
| Simplifying expressions with surds | Simplify an expression containing surds | |
| Rationalising fractions | Rationalise a fraction containing surds | |
| Coordinate geometry | ||
| Finding the equation of a straight line | Given two points on a curve, find the equation of the straight line through those two points. | |
| Finding the equation of a perpendicular line | Given the equation of a straight line L and the coordinates of a point A, find the equation of the line through A which is perpendicular to L. | |
| Finding the equation of a perpendicular bisector | Find the equation of the perpendicular bisector of a line segment. | |
| Finding the equation of a circle | Given its diameter, find the equation of a circle. | |
| Rearranging the equation of a circle | Rearrange the equation of a circle to find the coordinates of its centre and its radius. | |
| Differentiation | ||
| Differentiating polynomials | Differentiate a simple polynomial functions. | |
| Differentiating brackets | Differentiate an expression with brackets. | |
| Finding a tangent | Given the equation of a curve, find the equation of the tangent to this curve at a certain point. | |
| Finding a normal | Given the equation of a curve, find the equation of the normal to this curve at a certain point. | |
| Finding stationary points | Given the equation of a curve, find its stationary points and their nature. | |
| Integration | ||
| Indefinite integration | Find the equation of a curve passing through a given point and with a given gradient function. | |
| Definite integration | Calculate a definite integral. | |
| Area under a curve | Calculate the area under (or above) a curve. | |
| Area between two graphs | Calculate the area between two curves. | |
| Binomial | ||
| Binomial expansion | Expand a binomial expression. | |
| Using the binomial expansion to estimate a power. | Expand a binomial expression and use your result to estimate the value of a power. | |
| Trigonometry | ||
| Sine and cosine rule | Find the value of a missing side in a scalene triangle using the sine or the cosine rule. | |
| Simple trigonomic equation | Solve a simple trigonomic equation. | |
| Trigonomic equation with transformation | Solve a trigonometric equation of the form e.g. sin(ax + b) = 0.5. | |
| Quadratic trigonometric equation | Solve a quadratic trigonometric equation. It seems difficult at first but it is always the same method. |
