Algebra worksheet — GCSE Higher

1.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

2.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.

3.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

4.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

5.The diagram shows the graph of a function. Which equation could it represent?

6.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

7.Factorise 3x² + 10x − 8.

8.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

9.Solve 7x − 5 = 3x + 11

10.The graph of y = x³ − 5x is reflected in the y-axis. Work out the equation of the image.

11.Using the table of values of f(x) (x = 0, 1, 2, 3 gives f(x) = 5, 8, 4, 1), work out the value of −f(x) when x = 1.

12.The point (5, −12) lies on the circle x² + y² = 169, which has centre (0, 0). Work out the equation of the tangent to the circle at (5, −12), giving your answer in the form y = mx + c.

13.The curve y = x² − 3x. Use the chord between x = 1 and x = 4 to estimate the gradient of the curve at x = 2.5.

14.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

15.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.