Algebra worksheet — GCSE Higher

1.A circle has equation x² + y² = 25. Does the point (3, 4) lie on this circle?

2.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

3.A circle has centre (0, 0) and radius 9. Work out the equation of the circle.

4.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

5.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

6.A student attempts to prove that the sum of any three consecutive integers is a multiple of 3. Line 1: Let the three consecutive integers be n, n + 1 and n + 2. Line 2: Their sum is n + (n + 1) + (n + 2) = 3n + 2. Line 3: 3n + 2 leaves a remainder of 2 when divided by 3, so it is not a multiple of 3. Line 4: So the sum of three consecutive integers is not always a multiple of 3. Which line contains the FIRST error?

7.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

8.Which of these equations is equivalent to 5x − 2 = 3x + 8?

9.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

10.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

11.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

12.Simplify (x² − 9) ÷ (x² + 5x + 6).

13.A geometric sequence has first term 3 and common ratio √2. Work out the 6th term of the sequence, giving your answer in the form a√2.

14.Which of these is an identity?

15.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.