Algebra worksheet — GCSE Foundation

1.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.

2.A cinema sells adult tickets and child tickets. On one evening, 40 tickets are sold in total. There are 8 more adult tickets sold than child tickets. Work out the number of child tickets sold.

3.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.

4.Which of these is a factor of 15x + 20?

5.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

6.Which of these numbers is a cube number?

7.Make a the subject of the formula b = 20 − a.

8.Work out the value of 5y + 9 when y = 0

9.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.

10.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

11.Factorise fully 5x + 5y − 5

12.Write down the coefficient of p in the expression 7 − 4p + 9q.

13.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.

14.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

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.