Algebra worksheet — GCSE Higher

1.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

2.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?

3.Factorise 6x² − 7x − 3.

4.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

5.A candidate solves the simultaneous equations y = x − 2 and y = x² − 4x + 2 by substitution. They write: "x − 2 = x² − 4x + 2, so x² − 3x + 4 = 0." Which of these is a correct comment on the candidate's working?

6.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

7.By completing the square, show that the curve y = x² − 14x + 50 never crosses the x-axis. Which statement gives the correct reason?

8.A student claims: 'For every positive integer n, n² + n + 1 is a prime number.' Which value of n shows that this claim is false?

9.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

10.Which expression is equivalent to 3(2x − 5) + 4x?

11.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

12.n = 3. Work out the value of (2n)².

13.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.

14.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

15.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.