Japan · Grade 12 · Practice Sheet 9

1. 1.

   Two masses 3,500 kg and 450 kg are 20 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 device runs at 57 V drawing 1.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
3. 3.

   A force of 89 N acts on an area of 8.2 m². Find the pressure.

   Formula:Pressure

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

   View formula →
4. 4.

   A population of 5,900 grows 10% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
5. 5.

   Find the sum of the first 3 terms of a geometric series with first term a = 6 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

   View formula →
6. 6.

   A body starts at 12 m/s and accelerates at 4 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

   View formula →
7. 7.

   A 30 kg object moves at 10 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
8. 8.

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

   Formula:Quadratic Formula

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

   View formula →
9. 9.

   A population of 2,200 grows 8% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
10. 10.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 2 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

    View formula →
11. 11.

    A force of 79 N moves an object 29 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
12. 12.

    Find the sum of the first 6 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 →
13. 13.

    A device runs at 91 V drawing 8.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
14. 14.

    A cone has base radius 10 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

    View formula →
15. 15.

    In a triangle, a = 18, b = 12 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.

    Two masses 4,500 kg and 820 kg are 16 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 →
17. 17.

    Find the momentum of a 13 kg object moving at 20 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
18. 18.

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

    A wave has frequency 195 Hz and wavelength 3.81 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
20. 20.

    An object with initial velocity 14 m/s accelerates at 4.6 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →

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