Australia · Year 12 · Practice Sheet 46

1. 1.

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

   Formula:Quadratic Formula

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

   View formula →
2. 2.

   Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

   View formula →
3. 3.

   A force of 111 N moves an object 39 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
4. 4.

   A force of 405 N acts on an area of 6.4 m². Find the pressure.

   Formula:Pressure

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

   View formula →
5. 5.

   A 3 kg object moves at 14 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
6. 6.

   Find the force needed to accelerate a 39 kg mass at 0.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
7. 7.

   A wave has frequency 306 Hz and wavelength 0.53 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
8. 8.

   Two masses 1,300 kg and 300 kg are 12 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 →
9. 9.

   Find the gravitational potential energy of a 17 kg object raised 15 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
10. 10.

    A population of 8,300 grows 10% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
11. 11.

    A cone has base radius 8 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

    View formula →
12. 12.

    Find the momentum of a 39 kg object moving at 16 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
13. 13.

    A population of 7,400 grows 5% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
14. 14.

    A 29 kg object moves at 15 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
15. 15.

    A triangle has sides a = 10 cm and b = 15 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 →
16. 16.

    A population of 8,900 grows 2% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
17. 17.

    A device runs at 84 V drawing 1.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
18. 18.

    Find the momentum of a 56 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
19. 19.

    A wave has frequency 313 Hz and wavelength 0.8 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
20. 20.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 1 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

    View formula →

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