China · Grade 12 · Practice Sheet 7

1. 1.

   A 12 kg object moves at 2 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
2. 2.

   Solve using the quadratic formula: x² − 6x + 8 = 0.

   Formula:Quadratic Formula

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

   View formula →
3. 3.

   A wave has frequency 162 Hz and wavelength 1.5 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
4. 4.

   Find the momentum of a 52 kg object moving at 3 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
5. 5.

   Two masses 4,600 kg and 760 kg are 14 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.

   Find the sum of the first 3 terms of a geometric series with first term a = 1 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

   View formula →
7. 7.

   Find the population standard deviation of: 6, 20, 4, 11, 7 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
8. 8.

   Find the gravitational potential energy of a 21 kg object raised 37 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
9. 9.

   In a triangle, a = 14, 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 →
10. 10.

    A wave has frequency 268 Hz and wavelength 3.39 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    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.

    Find the sum of the first 8 terms of a geometric series with first term a = 1 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

    View formula →
13. 13.

    A wave has frequency 607 Hz and wavelength 4.31 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
14. 14.

    Find the sum of the first 5 terms of a geometric series with first term a = 7 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

    View formula →
15. 15.

    A force of 53 N moves an object 8 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
16. 16.

    Solve using the quadratic formula: x² + 5x + 6 = 0.

    Formula:Quadratic Formula

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

    View formula →
17. 17.

    Find the force needed to accelerate a 12 kg mass at 7.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
18. 18.

    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 →
19. 19.

    A population of 1,000 grows 8% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
20. 20.

    Find the force needed to accelerate a 25 kg mass at 1.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →

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