Germany · Klasse 12 · Practice Sheet 4

1. 1.

   A triangle has sides a = 12 cm and b = 18 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.

   In a triangle, a = 10, b = 12 and the included angle C = 70°. 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 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 →
4. 4.

   A device runs at 21 V drawing 6.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
5. 5.

   Find the force needed to accelerate a 49 kg mass at 8.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
6. 6.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 11 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

   View formula →
7. 7.

   A population of 5,600 grows 10% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
8. 8.

   €800 is invested at 5% compound interest per annum for 3 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 sum of the first 7 terms of an arithmetic series with first term a = 1 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

   View formula →
10. 10.

    A force of 67 N moves an object 22 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
11. 11.

    A device runs at 240 V drawing 3.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
12. 12.

    Find the population standard deviation of: 15, 9, 11, 9, 4 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
13. 13.

    A wave has frequency 657 Hz and wavelength 4.3 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
14. 14.

    A force of 199 N acts on an area of 8.3 m². Find the pressure.

    Formula:Pressure

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

    View formula →
15. 15.

    A current of 2.2 A flows through a 42 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
16. 16.

    Find the force needed to accelerate a 50 kg mass at 4 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
17. 17.

    A device runs at 35 V drawing 0.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
18. 18.

    A force of 345 N acts on an area of 8.7 m². Find the pressure.

    Formula:Pressure

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

    View formula →
19. 19.

    Two masses 2,200 kg and 450 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 →
20. 20.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 4 and common difference d = 8.

    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.