Tunisia · Grade 12 · Practice Sheet 27

1. 1.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 7 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

   View formula →
2. 2.

   Find the population standard deviation of: 19, 17, 16, 20, 13 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
3. 3.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 6 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

   View formula →
4. 4.

   A 16 kg object moves at 3 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
5. 5.

   Find the sum of the first 4 terms of a geometric series with first term a = 2 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

   View formula →
6. 6.

   A triangle has sides a = 13 cm and b = 8 cm with an included angle C = 90°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

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

   View formula →
7. 7.

   Two masses 8,300 kg and 900 kg are 4 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 →
8. 8.

   A cone has base radius 11 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
9. 9.

   A force of 61 N moves an object 9 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
10. 10.

    Find the gravitational potential energy of a 35 kg object raised 2 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
11. 11.

    A force of 314 N acts on an area of 10 m². Find the pressure.

    Formula:Pressure

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

    View formula →
12. 12.

    Find the gravitational potential energy of a 42 kg object raised 15 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
13. 13.

    A triangle has sides a = 18 cm and b = 16 cm with an included angle C = 60°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

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

    View formula →
14. 14.

    A 31 kg object moves at 21 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
15. 15.

    In a triangle, a = 5, b = 9 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →
16. 16.

    A force of 110 N moves an object 17 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
17. 17.

    Find the force needed to accelerate a 56 kg mass at 3.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
18. 18.

    Find the gravitational potential energy of a 19 kg object raised 8 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
19. 19.

    A device runs at 71 V drawing 2.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
20. 20.

    Find the momentum of a 39 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

    View formula →

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