CAMBRIDGE IGCSE MATHS (0580)

Question 1:
\( m = \frac{1}{4} \left(3h^2 + 8ah + 3a^2\right) \)
Calculate the exact value of \( m \) when \( h = 20 \) and \( a = -5 \).

Question 2:
\( y = \sqrt{8 + \frac{4}{x}} \)
Find the value of \( y \) correct to 4 decimal places when \( x = 2 \).

Question 3:
\( y = \frac{2}{x^2} + \frac{x^2}{2} \)
Find the value of \( y \) when \( x = 6 \). Give your answer as a mixed number in its simplest form.

Question 4:
Simplify the expression:
\( 1 - 2u + u + 4 \).

Question 5:
\( y = mx + c \)
Find the value of \( y \) when \( m = -2 \), \( x = -7 \), and \( c = -3 \).

Question 6:
Write as a single fraction:
\( 1 - \frac{2}{p} - \frac{3}{t} \).

Question 7:
\( y = p^2 + qr \)
a) Find \( y \) when \( p = -5 \), \( q = 3 \), and \( r = -7 \).
b) Write \( p \) in terms of \( q, r, \) and \( y \).

Question 8:
Find the value of \( 5a - 3b \) when \( a = 7 \) and \( b = -2 \).

Question 9:
Find the value of \( 7x + 3y \) when \( x = 12 \) and \( y = -6 \).

Question 10:
Complete these statements:
a) When \( w = \_\_\_\_ \), \( 10w = 70 \).
b) When \( 5x = 15 \), \( 12x = 36 \).

Question 11:
Simplify the expression:
\( 2p - q - 3q - 5p \).

Question 12:
\( y = mx + c \)
Find the value of \( y \) when \( m = -2 \), \( x = -7 \), and \( c = -3 \).

Question 13:
Simplify and calculate the value of:
\( m = \frac{1}{5} \left( 4x^2 - 3xy + 5y^2 \right) \)
Find \( m \) when \( x = -6 \) and \( y = 2 \).

Question 14:
Solve:
\( z = \sqrt{12 + \frac{8}{x}} \)
Find \( z \) when \( x = 4 \). Give your answer correct to 3 decimal places.

Question 15:
Simplify and calculate:
\( t = \frac{3}{x^2} + \frac{x^2}{3} \)
Find \( t \) when \( x = -9 \). Express your answer as a mixed number in its simplest form.

Question 16:
Simplify the expression:
\( 1 - 3u + 2u - 5 + u^2 \)

Question 17:
\( y = mx + c^2 \)
Find \( y \) when \( m = -4 \), \( x = 5 \), and \( c = -3 \).

Question 18:
Write \( 1 - \frac{4}{a} + \frac{5}{b} \) as a single fraction.

Question 19:
Given \( y = p^2 - q \cdot r \):
a) Calculate \( y \) when \( p = -8 \), \( q = 6 \), and \( r = -4 \).
b) Write \( p \) in terms of \( y \), \( q \), and \( r \).

Question 20:
Evaluate:
\( 3x - 4y + 2z \)
when \( x = -3 \), \( y = 7 \), and \( z = -2 \).

Question 21:
Evaluate:
\( 10x - 3y + z \)
when \( x = 15 \), \( y = -10 \), and \( z = 5 \).

Question 22:
Complete these statements:
a) When \( v = \) ____, \( 7v = 84 \).
b) When \( 8x = 32 \), \( 5x = \) ____.

Question 23:
Simplify:
\( 4p - 2q + 5p - 6q \)

Question 24:
Find the value of \( y \):
\( y = mx^2 + c \)
when \( m = 2 \), \( x = -3 \), and \( c = 5 \).

Question 25:
Find the value of \( \frac{2x}{y} + \frac{z}{y} \)
when \( x = -4 \), \( y = 6 \), and \( z = -3 \).