Germany · Klasse 12 · Practice Sheet 9

1. 1.

   A 5 kg object moves at 13 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
2. 2.

   In a triangle, a = 15, b = 8 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 →
3. 3.

   Find the gravitational potential energy of a 9 kg object raised 31 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
4. 4.

   A device runs at 181 V drawing 3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
5. 5.

   €3,000 is invested at 3% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

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

   View formula →
6. 6.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 1 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

   View formula →
7. 7.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
8. 8.

   €1,500 is invested at 4% 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 →
9. 9.

   Find the momentum of a 18 kg object moving at 8 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
10. 10.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 9 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

    View formula →
11. 11.

    Find the gravitational potential energy of a 40 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
12. 12.

    A wave has frequency 112 Hz and wavelength 0.8 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
13. 13.

    Two masses 6,700 kg and 820 kg are 4 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 →
14. 14.

    A wave has frequency 337 Hz and wavelength 1.88 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
15. 15.

    Solve using the quadratic formula: x² + 5x − 6 = 0.

    Formula:Quadratic Formula

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

    View formula →
16. 16.

    Find the momentum of a 18 kg object moving at 4 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
17. 17.

    A population of 7,400 grows 8% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
18. 18.

    A current of 5.9 A flows through a 49 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
19. 19.

    Two masses 4,700 kg and 310 kg are 17 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.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 2 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

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

    View formula →

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