Sweden · Grade 12 · Practice Sheet 27

1. 1.

   A body starts at 13 m/s and accelerates at 5.6 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

   View formula →
2. 2.

   A triangle has sides a = 13 cm and b = 17 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 →
3. 3.

   In a triangle, a = 5, b = 18 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 →
4. 4.

   Find the momentum of a 30 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
5. 5.

   Find the population standard deviation of: 20, 19, 12, 15, 4 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
6. 6.

   Find the sum of the first 8 terms of an arithmetic series with first term a = 10 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

   View formula →
7. 7.

   A triangle has sides a = 5 cm and b = 17 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 →
8. 8.

   Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
9. 9.

   In a triangle, a = 8, b = 9 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

   View formula →
10. 10.

    Find the gravitational potential energy of a 29 kg object raised 28 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
11. 11.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

    View formula →
12. 12.

    A population of 2,900 grows 3% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
13. 13.

    In a triangle, a = 18, b = 15 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →
14. 14.

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

    Two masses 1,000 kg and 150 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 →
16. 16.

    A population of 4,400 grows 10% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
17. 17.

    A force of 426 N acts on an area of 4.2 m². Find the pressure.

    Formula:Pressure

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

    View formula →
18. 18.

    A wave has frequency 470 Hz and wavelength 0.35 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
19. 19.

    Solve using the quadratic formula: x² − 3x − 10 = 0.

    Formula:Quadratic Formula

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

    View formula →
20. 20.

    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 →

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