Belgium · Year 12 · Practice Sheet 14

1. 1.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 8 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

   View formula →
2. 2.

   A population of 7,000 grows 5% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
3. 3.

   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 →
4. 4.

   A triangle has sides a = 17 cm and b = 10 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 →
5. 5.

   Two masses 1,000 kg and 730 kg are 5 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

   View formula →
6. 6.

   A force of 234 N acts on an area of 8.4 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

   View formula →
7. 7.

   Solve using the quadratic formula: x² + 4x + 3 = 0.

   Formula:Quadratic Formula

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

   View formula →
8. 8.

   A 14 kg object moves at 24 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
9. 9.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
10. 10.

    Find the gravitational potential energy of a 9 kg object raised 33 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
11. 11.

    A triangle has sides a = 19 cm and b = 17 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 →
12. 12.

    A force of 288 N acts on an area of 9.7 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

    View formula →
13. 13.

    A body starts at 7 m/s and accelerates at 2.9 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
14. 14.

    Find the momentum of a 20 kg object moving at 24 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
15. 15.

    Two masses 3,800 kg and 500 kg are 12 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

    View formula →
16. 16.

    A wave has frequency 827 Hz and wavelength 2.72 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
17. 17.

    Two masses 3,200 kg and 340 kg are 17 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

    View formula →
18. 18.

    Find the force needed to accelerate a 42 kg mass at 6.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
19. 19.

    Find the gravitational potential energy of a 48 kg object raised 12 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
20. 20.

    A 33 kg object moves at 18 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →

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