Ireland · Year 12 · Practice Sheet 32

1. 1.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

   View formula →
2. 2.

   A body starts at 12 m/s and accelerates at 2.4 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

   View formula →
3. 3.

   A 33 kg object moves at 23 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
4. 4.

   A wave has frequency 180 Hz and wavelength 4.32 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
5. 5.

   A population of 7,500 grows 3% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
6. 6.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

   View formula →
7. 7.

   A population of 5,600 grows 2% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
8. 8.

   Find the population standard deviation of: 15, 13, 2, 4, 20 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

   View formula →
9. 9.

   A cone has base radius 3 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
10. 10.

    A current of 2.8 A flows through a 51 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
11. 11.

    Find the force needed to accelerate a 54 kg mass at 8.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
12. 12.

    A device runs at 212 V drawing 5.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
13. 13.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 8 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

    View formula →
14. 14.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

    View formula →
15. 15.

    A triangle has sides a = 11 cm and b = 13 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 →
16. 16.

    Find the sum of the first 8 terms of a geometric series with first term a = 7 and common ratio r = 2.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

    View formula →
17. 17.

    Find the gravitational potential energy of a 21 kg object raised 15 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
18. 18.

    A device runs at 85 V drawing 2.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
19. 19.

    Find the momentum of a 5 kg object moving at 13 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
20. 20.

    A cone has base radius 5 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

    View formula →

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