Kenya · Grade 12 · Practice Sheet 3

1. 1.

   A cone has base radius 12 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

   View formula →
2. 2.

   A population of 3,500 grows 8% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

   View formula →
3. 3.

   A cone has base radius 5 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

   View formula →
4. 4.

   Find the momentum of a 40 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
5. 5.

   Find the gravitational potential energy of a 36 kg object raised 38 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
6. 6.

   Solve using the quadratic formula: x² − 4x + 0 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

   View formula →
7. 7.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 3 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

   View formula →
8. 8.

   A population of 7,100 grows 3% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

   View formula →
9. 9.

   Find the force needed to accelerate a 2 kg mass at 6.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
10. 10.

    A device runs at 94 V drawing 2.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
11. 11.

    A 29 kg object moves at 13 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

    View formula →
12. 12.

    A triangle has sides a = 16 cm and b = 19 cm with an included angle C = 30°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

    View formula →
13. 13.

    A cone has base radius 5 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

    View formula →
14. 14.

    In a triangle, a = 5, b = 17 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

    View formula →
15. 15.

    A device runs at 61 V drawing 3.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
16. 16.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 7 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

    View formula →
17. 17.

    A wave has frequency 339 Hz and wavelength 1.33 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
18. 18.

    A population of 5,400 grows 3% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

    View formula →
19. 19.

    A force of 39 N moves an object 21 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
20. 20.

    A triangle has sides a = 11 cm and b = 12 cm with an included angle C = 120°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.