Algebra worksheet — GCSE Foundation

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

2.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.

3.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.

4.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

5.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

6.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.

7.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

8.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

9.The point A lies on the x-axis. Which statement about A must be true?

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

11.Solve (2x + 1)/3 = 5

12.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

13.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

14.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

15.The graph of y = (x − 2)(x + 5) crosses the x-axis at two points. Work out the x-coordinates of these two points.