Algebra worksheet — GCSE Foundation

1.y = x + 10. Work out the value of y when x = 0.

2.Solve x² + 3x − 10 = 0.

3.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

4.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

5.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

6.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

7.Which of these quadratic graphs does NOT cross the x-axis at all?

8.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

9.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

10.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

11.Expand 2(x + 12)

12.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

13.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

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

15.The formula for the energy stored in a stretched spring is E = (1/2)kx², where E is in joules, k is the spring constant in N/m and x is the extension in m. A spring with a spring constant of 40 N/m is stretched so that its extension is 0.3 m. Work out the energy stored in the spring.