CAMBRIDGE IGCSE MATHS (0580)

Question 1:
Solve the equation \( 4x - 12 = 2(11 - 3x) \)

Question 2:
Solve the equation \( 5(2y - 17) = 60 \)

Question 3:
Solve the equation \( 5 - 2x = 3x - 19 \)

Question 4:
Solve the equation \( 1 + 2x = -15 \)

Question 5:
Solve the equation \( \frac{n-8}{2} = 11 \)

Question 6:
Solve the equation \( \frac{x+5}{x} = \frac{7}{3} \)

Question 7:
Solve the equation \( \frac{2x + 5}{3} = 8 \)

Question 8:
Solve the equation \( 3(x+4) = 2(4x - 1) \)

Question 9:
Solve the equation \( 6(y+1) = 9 \)

Question 10:
Solve the equation \( 6(k - 8) = 78 \)

Question 11:
Solve \( 2 - x = 5x + 1 \)

Question 12:
Solve the following equations:
a) \( 7 - 3n = 11n + 2 \)
b) \( \frac{p - 3}{5} = 3 \)

Question 13:
Solve \( \frac{1-p}{3} = 4 \)

Question 14:
Solve \( 3w - 7 = 32 \)

Question 15:
Solve the equation: \( 4(x - 3) + 2(2x + 1) = 3(x + 5) - 2 \)

Question 16:
Solve the equation: \( \frac{5(y + 4)}{3} - \frac{2(y - 1)}{2} = 7 \)

Question 17:
Solve the equation: \( \frac{3}{4}(2z - 5) = \frac{1}{2}(z + 7) + 5 \)

Question 18:
Solve the equation: \( 6(3a - 2) - 4 = 5(a + 7) + 3a \)

Question 19:
Solve the equation: \( 4x + 3 = 2(x + 5) + 3(x - 2) \)

Question 20:
Solve the following system of equations: \( 3x - 4y + 5 = 0 \) \( 2x + y - 3 = 0 \)
Find:

• a) The values of \(x\) and \(y\).
• b) Verify your solution by substituting the values into both equations.

Question 21:
The line \( 3x - 4y + 5 = 0 \) intersects the x-axis and y-axis at points \(A\) and \(B\) respectively. Calculate:

• i) The coordinates of \(A\) and \(B\).
• ii) The length of the line segment \(AB\).

Question 22:
The line \(5x - 2y + 10 = 0\) intersects the x-axis at point \(A\) and the y-axis at point \(B\).

1. Find the coordinates of points \(A\) and \(B\).
2. Determine the equation of a line perpendicular to \(5x - 2y + 10 = 0\) that passes through the origin.

Question 23:
Solve the following system of equations:

1. \(2x + 3y = 12\)
2. \(4x - y = 9\)

Question 24:
Find the value of \(k\) if the line \(kx - 3y + 5 = 0\) is parallel to the line \(2x - 6y + 10 = 0\).

Question 25:
Solve for \(x\) and \(y\) if:

1. \(3x + 4y = 20\)
2. \(x - 2y = 1\)