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KCSE Mathematics practice questions
Ten questions in the style of KCSE Mathematics Paper 1: order of operations, algebraic fractions, indices, percentages, straight lines, area, polygons, logarithms, rates and volume. Each one has a worked solution.
Preguntas originales escritas por profesores de Studoli al estilo del examen KCSE. No son exámenes oficiales.
Tema: Numbers
1. Evaluate (−8 + 3 × 4) ÷ 2.
Solución
B. 2
- Multiplication comes before addition: 3 × 4 = 12.
- −8 + 12 = 4, then 4 ÷ 2 = 2.
Tema: Algebra
2. Simplify (x² − 4) ÷ (x + 2).
Solución
B. x − 2
- Factorise the top as a difference of two squares: (x − 2)(x + 2).
- Cancel (x + 2): the answer is x − 2.
Tema: Indices
3. Solve 3^(2x) = 81.
Solución
B. x = 2
- Write 81 as a power of 3: 81 = 3⁴.
- So 2x = 4 and x = 2.
Tema: Commercial arithmetic
4. A radio is marked at Ksh 4,000. A discount of 15% is given. Find the selling price.
Solución
B. Ksh 3,400
- Discount = 15% of 4,000 = Ksh 600.
- Selling price = 4,000 − 600 = Ksh 3,400.
Tema: Straight lines
5. Find the gradient of the line 2y − 6x = 8.
Solución
C. 3
- Make y the subject: 2y = 6x + 8, so y = 3x + 4.
- The gradient is the coefficient of x: 3.
Tema: Area
6. Find the area of a triangle with base 10 cm and height 6 cm.
Solución
B. 30 cm²
- Area = ½ × base × height.
- ½ × 10 × 6 = 30 cm².
Tema: Geometry
7. What is the sum of the interior angles of a hexagon?
Solución
C. 720°
- Sum of interior angles = (n − 2) × 180°.
- A hexagon has 6 sides: (6 − 2) × 180° = 720°.
Tema: Logarithms
8. Find x if log₂ x = 5.
Solución
C. 32
- log₂ x = 5 means 2⁵ = x.
- x = 32.
Tema: Rates
9. Convert 72 km/h to metres per second.
Solución
B. 20 m/s
- 72 km/h = 72,000 m in 3,600 s.
- 72,000 ÷ 3,600 = 20 m/s. A quick rule is to divide by 3.6.
Tema: Volume
10. Find the volume of a cylinder of radius 7 cm and height 10 cm. (Take π = 22/7)
Solución
B. 1,540 cm³
- Volume = πr²h.
- 22/7 × 7 × 7 × 10 = 22 × 7 × 10 = 1,540 cm³.
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