Algebra worksheet — GCSE Foundation

1.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

2.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

3.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

4.Which expression means 'add 3 to n, then multiply the result by 4'?

5.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

6.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

7.Write down the gradient of the line with equation y = 6 + 4x.

8.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

9.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

10.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

11.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

12.The formula for the profit, £P, made on an item is P = S − C, where S is the selling price and C is the cost price. Make S the subject of the formula.

13.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

14.Solve the inequality 3x + 6 ≤ 0.

15.Simplify p + p + p.