Algebra worksheet — GCSE Foundation

1.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

2.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

3.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

4.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.

5.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

6.Solve 4x − (2x − 6) = 18

7.Which of these is a formula, rather than an expression, an equation, or an identity?

8.Work out the value of n² − n when n = −3

9.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

10.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

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

12.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

13.y = x + 4. Work out the value of y when x = 3.

14.Solve 6x − 5 = 3x + 13.

15.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.