New Zealand · Year 12 · Practice Sheet 35

1. 1.

   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 →
2. 2.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 7 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

   View formula →
3. 3.

   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 →
4. 4.

   A body starts at 7 m/s and accelerates at 4.5 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

   View formula →
5. 5.

   A population of 4,400 grows 10% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
6. 6.

   Find the force needed to accelerate a 26 kg mass at 0.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
7. 7.

   A current of 4.2 A flows through a 58 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
8. 8.

   Find the gravitational potential energy of a 24 kg object raised 18 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
9. 9.

   In a triangle, a = 12, b = 11 and the included angle C = 50°. 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 817 Hz and wavelength 2.01 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
11. 11.

    Find the sum of the first 12 terms of an arithmetic series with first term a = 6 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

    View formula →
12. 12.

    A force of 100 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
13. 13.

    A 9 kg object moves at 8 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
14. 14.

    A cone has base radius 6 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 →
15. 15.

    Find the momentum of a 37 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
16. 16.

    A device runs at 228 V drawing 0.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
17. 17.

    Find the force needed to accelerate a 55 kg mass at 5.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
18. 18.

    Find the population standard deviation of: 17, 17, 10, 19, 13 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
19. 19.

    A wave has frequency 249 Hz and wavelength 4.95 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
20. 20.

    A 38 kg object moves at 9 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →

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