New Zealand · Year 12 · Practice Sheet 45

1. 1.

   A force of 102 N moves an object 2 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
2. 2.

   A force of 327 N acts on an area of 8.5 m². Find the pressure.

   Formula:Pressure

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

   View formula →
3. 3.

   Find the population standard deviation of: 18, 2, 14, 19, 7 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
4. 4.

   Two masses 3,500 kg and 840 kg are 13 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 →
5. 5.

   Solve using the quadratic formula: x² − 8x + 12 = 0.

   Formula:Quadratic Formula

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

   View formula →
6. 6.

   A 33 kg object moves at 12 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
7. 7.

   An object with initial velocity 2 m/s accelerates at 1.2 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
8. 8.

   Find the sum of the first 5 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 →
9. 9.

   Find the population standard deviation of: 5, 15, 16, 4, 2 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
10. 10.

    Find the momentum of a 54 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
11. 11.

    $1,700 is invested at 3% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

    View formula →
12. 12.

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

    Formula:Sum of a Geometric Series

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

    View formula →
13. 13.

    Find the population standard deviation of: 14, 15, 15, 17, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
14. 14.

    A device runs at 233 V drawing 8.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
15. 15.

    A cone has base radius 10 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 →
16. 16.

    An object with initial velocity 4 m/s accelerates at 3.6 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
17. 17.

    Find the force needed to accelerate a 23 kg mass at 3.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
18. 18.

    An object with initial velocity 2 m/s accelerates at 1.1 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
19. 19.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 8 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

    View formula →
20. 20.

    Find the sum of the first 5 terms of a geometric series with first term a = 2 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

    View formula →

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