Taiwan · Grade 12 · Practice Sheet 4

1. 1.

   Two masses 3,000 kg and 640 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 →
2. 2.

   A triangle has sides a = 13 cm and b = 8 cm with an included angle C = 45°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

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

   View formula →
3. 3.

   A device runs at 126 V drawing 6.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
4. 4.

   Solve using the quadratic formula: x² + 2x − 3 = 0.

   Formula:Quadratic Formula

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

   View formula →
5. 5.

   A wave has frequency 822 Hz and wavelength 3.1 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
6. 6.

   Find the gravitational potential energy of a 20 kg object raised 27 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
7. 7.

   A cone has base radius 4 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
8. 8.

   A force of 43 N moves an object 40 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
9. 9.

   Find the momentum of a 20 kg object moving at 2 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
10. 10.

    A cone has base radius 6 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

    View formula →
11. 11.

    An object with initial velocity 13 m/s accelerates at 1.3 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

    View formula →
12. 12.

    Find the force needed to accelerate a 50 kg mass at 7.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
13. 13.

    A wave has frequency 836 Hz and wavelength 0.39 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
14. 14.

    An object with initial velocity 9 m/s accelerates at 3.9 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

    View formula →
15. 15.

    Find the population standard deviation of: 5, 9, 13, 7, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
16. 16.

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

    Formula:Sum of a Geometric Series

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

    View formula →
17. 17.

    Two masses 7,700 kg and 650 kg are 10 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.

    A device runs at 31 V drawing 4.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
19. 19.

    Find the sum of the first 5 terms of a geometric series with first term a = 2 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

    View formula →
20. 20.

    Find the momentum of a 3 kg object moving at 14 m/s.

    Formula:Momentum

    $p = mv$

    View formula →

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