Algebra worksheet — GCSE Foundation

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 distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

3.Work out the value of m² + 3m when m = −2

4.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

5.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?

6.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

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

9.Solve x² − x − 12 = 0.

10.x = 5. Work out the value of 3x² − 4.

11.Work out the equation of the straight line through the points (−2, 1) and (0, 7).

12.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

13.Which of these equations describes a vertical line?

14.Make x the subject of the formula y = 2x − 9.

15.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.