Algebra worksheet — GCSE Higher

1.Solve the inequality x² − 5x + 6 < 0.

2.The point (9, 40) lies on the circle x² + y² = 1681, which has centre (0, 0). Work out the equation of the tangent to the circle at (9, 40), giving your answer in the form ax + by = c.

3.Which expression means 'y squared, multiplied by 3'?

4.A proof that (n + 3)² − (n − 3)² is always a multiple of a certain number begins: Line 1: (n + 3)² − (n − 3)² = (n² + 6n + 9) − (n² − 6n + 9). Which expression correctly completes Line 2?

5.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

6.The tangent to a curve at the point (5, 2) is the line y = mx + c. This tangent crosses the y-axis at (0, −8). Work out the gradient, m, of the tangent.

7.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

8.A line has equation y = −4x + 1. Work out the equation of the line perpendicular to it that passes through the point (0, 3).

9.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.

10.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

11.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

12.Simplify 2/(x + 1) + 3/(x − 2), giving your answer as a single fraction.

13.Subtract, giving your answer as a single fraction in its simplest form: 4/(x − 1) − 2/(x + 3)

14.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

15.Which of these statements is an equation with exactly one solution?