Algebra worksheet — GCSE Foundation

1.The point A lies on the x-axis. Which statement about A must be true?

2.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

3.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

4.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.

5.Which of these is an equation, rather than an expression, a formula or an identity?

6.x = 5. Work out the value of 3x² − 4.

7.Write down the expression that means the same as p + p + p + q.

8.Factorise fully 12x² + 18x.

9.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.

10.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

11.Expand 2(x − 13)

12.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

13.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

14.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

15.Simplify 5x + 3y − 2x + y.