New Zealand · Year 12 · Practice Sheet 32

1. 1.

   An object with initial velocity 6 m/s accelerates at 1.7 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
2. 2.

   A device runs at 63 V drawing 2.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
3. 3.

   A triangle has sides a = 20 cm and b = 14 cm with an included angle C = 60°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

   View formula →
4. 4.

   Find the population standard deviation of: 11, 4, 3, 15, 13 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
5. 5.

   Find the sum of the first 5 terms of a geometric series with first term a = 4 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

   View formula →
6. 6.

   Solve using the quadratic formula: x² − 7x + 12 = 0.

   Formula:Quadratic Formula

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

   View formula →
7. 7.

   A force of 12 N moves an object 28 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
8. 8.

   In a triangle, a = 18, b = 5 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

   View formula →
9. 9.

   A force of 485 N acts on an area of 9.6 m². Find the pressure.

   Formula:Pressure

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

   View formula →
10. 10.

    A triangle has sides a = 17 cm and b = 13 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 →
11. 11.

    A force of 22 N moves an object 37 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
12. 12.

    Find the momentum of a 6 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
13. 13.

    A cone has base radius 5 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

    View formula →
14. 14.

    Find the population standard deviation of: 11, 12, 20, 7, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
15. 15.

    Find the force needed to accelerate a 20 kg mass at 4.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
16. 16.

    Find the momentum of a 21 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
17. 17.

    Two masses 6,100 kg and 280 kg are 11 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 →
18. 18.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 4 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

    View formula →
19. 19.

    In a triangle, a = 11, b = 15 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

    View formula →
20. 20.

    Find the population standard deviation of: 16, 13, 12, 15, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →

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