Algebra worksheet — GCSE Foundation

1.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

2.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

3.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

4.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

5.A person's body mass index is given by the formula B = m ÷ h², where m is the mass in kg and h is the height in metres. Work out B, to 1 decimal place, when m = 68 and h = 1.6.

6.a = 2 and b = 5. Work out the value of ab².

7.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

8.A square has sides of length y cm. Write down an expression for the perimeter of the square.

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

10.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

11.Solve 4x − (2x − 6) = 18

12.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

13.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

14.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

15.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.