Cambridge IGCSE · Mathematics (0580)

Equations: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Equations.

10 questions27 marksFree, no account

Question 1

1 mark

Solve the equation $$\frac{x}{4} + 7 = 12$$.

Question 2

1 mark

Solve the fractional equation for \(x\):
\( \frac{2x + 5}{3} = x - 1 \)

Question 3

1 mark

Solve the equation \( \frac{2x}{x - 3} - \frac{1}{x + 2} = 3 \).
Give your answers correct to 2 decimal places.

Question 4

1 mark

Make \( t \) the subject of the formula:
\( v = u + at \)

Question 5

1 mark

Solve the following simultaneous linear equations to find the value of \(x\):
\(3x + 2y = 12\)
\(x - y = 4\)

Question 6

2 marks

Change the subject of the formula \(P = 2l + 2w\) to \(w\).

Write your answer out first, then check it against the worked solution.

Question 7

3 marks

Solve the equation \(7m - 1 = 3m + 15\).

Write your answer out first, then check it against the worked solution.

Question 8

6 marks

Solve the quadratic equation \(3x^2 - 4x - 5 = 0\).
Give your answers correct to 2 decimal places.

Write your answer out first, then check it against the worked solution.

Question 9

4 marks

(a) Solve the equation:
\( 8(x - 3) = 2x + 6 \)

(b) Solve the following simultaneous equations:
\( 5x + 2y = 19 \)
\( 3x - 2y = 5 \)

Write your answer out first, then check it against the worked solution.

Question 10

7 marks

Solve the simultaneous equations:
\(y = 2x - 5\)
\(x^2 + y^2 = 25\)

Write your answer out first, then check it against the worked solution.

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