Belgium · Year 12 · Practice Sheet 16

1. 1.

   A triangle has sides a = 7 cm and b = 12 cm with an included angle C = 30°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

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

   View formula →
2. 2.

   Two masses 3,500 kg and 590 kg are 8 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 →
3. 3.

   Solve using the quadratic formula: x² + 10x + 24 = 0.

   Formula:Quadratic Formula

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

   View formula →
4. 4.

   Find the population standard deviation of: 19, 11, 19, 13, 7 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
5. 5.

   An object with initial velocity 4 m/s accelerates at 4.6 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
6. 6.

   In a triangle, a = 10, b = 14 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

   View formula →
7. 7.

   A population of 2,800 grows 5% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
8. 8.

   Find the sum of the first 8 terms of an arithmetic series with first term a = 7 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

   View formula →
9. 9.

   Solve using the quadratic formula: x² − 7x + 6 = 0.

   Formula:Quadratic Formula

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

   View formula →
10. 10.

    A cone has base radius 6 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

    View formula →
11. 11.

    A force of 93 N moves an object 18 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
12. 12.

    Find the gravitational potential energy of a 11 kg object raised 24 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
13. 13.

    A current of 4.3 A flows through a 54 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
14. 14.

    Two masses 8,900 kg and 850 kg are 9 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 →
15. 15.

    A wave has frequency 603 Hz and wavelength 1.93 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
16. 16.

    A force of 224 N acts on an area of 1.1 m². Find the pressure.

    Formula:Pressure

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

    View formula →
17. 17.

    A wave has frequency 782 Hz and wavelength 0.5 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
18. 18.

    Find the gravitational potential energy of a 3 kg object raised 28 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
19. 19.

    Two masses 4,800 kg and 850 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 →
20. 20.

    A triangle has sides a = 13 cm and b = 6 cm with an included angle C = 120°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

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

    View formula →

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