Algebra worksheet — GCSE Foundation

1.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.

2.Write down the expression that means the same as w ÷ 6.

3.Write down 0.2x with its coefficient written as a fraction in its simplest form.

4.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

5.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

6.Work out the gradient of the straight line with equation 3y = 12 − 6x.

7.Write down the gradient of the line with equation y = 7x − 2.

8.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

9.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

10.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.

11.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?

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

13.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

14.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.

15.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.