Mathematics Practice Problem
Sheet
Algebra • Geometry • Trigonometry • Basic Calculus
Designed for exam practice and concept strengthening
Section 1: Algebra Problems
1. Solve: 2x + 7 = 19
2. Factorize: x² − 9x + 20
3. Solve using quadratic formula: x² − 5x + 6 = 0
4. Simplify: (a + b)² − (a − b)²
5. If log(a) + log(b) = log(20) and a = 4, find b.
Section 2: Geometry Problems
6. Find the area of a triangle with base 10 cm and height 8 cm.
7. Calculate the circumference of a circle with radius 7 cm.
8. A rectangle has length 12 cm and width 5 cm. Find its area and
perimeter.
9. Find the volume of a cube with side length 4 cm.
Section 3: Trigonometry Problems
10. If sin θ = 3/5, find cos θ.
11. Prove that sin²θ + cos²θ = 1 for θ = 45°.
12. Find tan θ if sin θ = 5/13 and cos θ = 12/13.
Section 4: Calculus Problems
13. Differentiate: f(x) = 3x² + 5x + 2
14. Find derivative of: y = x³
15. Evaluate: ∫ 2x dx
