China · Grade 12 · Practice Sheet 47

1. 1.

   A triangle has sides a = 6 cm and b = 9 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 →
2. 2.

   A body starts at 16 m/s and accelerates at 4 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

   View formula →
3. 3.

   A population of 6,100 grows 3% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
4. 4.

   A current of 6.5 A flows through a 46 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
5. 5.

   A 39 kg object moves at 17 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
6. 6.

   A device runs at 217 V drawing 4.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
7. 7.

   Find the momentum of a 17 kg object moving at 4 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
8. 8.

   A 35 kg object moves at 5 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
9. 9.

   Solve using the quadratic formula: x² − 1x − 30 = 0.

   Formula:Quadratic Formula

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

   View formula →
10. 10.

    Two masses 3,900 kg and 830 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 →
11. 11.

    Solve using the quadratic formula: x² + 2x − 8 = 0.

    Formula:Quadratic Formula

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

    View formula →
12. 12.

    A 3 kg object moves at 10 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
13. 13.

    A population of 5,200 grows 3% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
14. 14.

    Find the sum of the first 5 terms of a geometric series with first term a = 5 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

    View formula →
15. 15.

    Find the population standard deviation of: 15, 19, 6, 19, 6 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
16. 16.

    Find the force needed to accelerate a 18 kg mass at 4.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
17. 17.

    A population of 5,800 grows 5% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
18. 18.

    A body starts at 10 m/s and accelerates at 4.9 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
19. 19.

    A triangle has sides a = 6 cm and b = 11 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 →
20. 20.

    A force of 5 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →

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