Algebra worksheet — GCSE Foundation

1.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

2.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.

3.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

4.Simplify x + x + 4

5.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

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.A vertical line passes through the point (4, 7). Write down the equation of this line.

8.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

9.a = 2 and b = 5. Work out the value of a²b.

10.How many turning points does the graph of y = x² − 7x + 10 have?

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

12.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

13.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

14.Solve 5x² − 15x = 0.

15.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?