Practice questions: Core 1
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 |
| 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. | |
| Using the discriminant | Use the discriminant to find when a quadratic has exactly one root | |
| Using the discriminant | Use the discriminant to find when a quadratic has no real root | |
| 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. | |
| Sequences | ||
| Basic arithmetic series | Find the nth term and the sum of an arithmetic series. | |
| Basic arithmetic series | Find the value number of terms needed for an arithmetic series to reach a certain value. | |
| Calculus | ||
| 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. | |
| Indefinite integration | Find the equation of a curve passing through a given point and with a given gradient function. |
