Algebra worksheet — GCSE Foundation

1.Solve 2x + 7 = x + 13

2.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

3.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

4.Write down the number of terms in the expression 4x² − 7x + 3.

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.n = 3. Work out the value of (2n)².

7.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

8.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

9.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

10.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

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

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

13.The point A is at (5, −3). In which quadrant does A lie?

14.Simplify x + x + 4

15.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.