Germany · Klasse 11 · Practice Sheet 25

1. 1.

   Find the sum of the first 5 terms of a geometric series with first term a = 7 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

   View formula →
2. 2.

   Find the population standard deviation of: 15, 10, 4, 8, 5 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
3. 3.

   A cone has base radius 5 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 →
4. 4.

   Find the momentum of a 37 kg object moving at 4 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
5. 5.

   A force of 23 N moves an object 27 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
6. 6.

   A current of 2.4 A flows through a 22 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
7. 7.

   Find the population standard deviation of: 5, 20, 4, 8, 9 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
8. 8.

   A population of 1,500 grows 8% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
9. 9.

   Find the momentum of a 32 kg object moving at 10 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
10. 10.

    A cone has base radius 11 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.

    Find the force needed to accelerate a 41 kg mass at 3.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
12. 12.

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

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
13. 13.

    A population of 5,600 grows 5% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
14. 14.

    Find the population standard deviation of: 9, 2, 13, 18, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
15. 15.

    An object has mass 39.9 g and volume 19 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

    View formula →
16. 16.

    Find the sum of the first 7 terms of a geometric series with first term a = 8 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

    View formula →
17. 17.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 9 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

    View formula →
18. 18.

    In a triangle, a = 13, 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 →
19. 19.

    Find the momentum of a 34 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
20. 20.

    An object has mass 24.6 g and volume 6 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

    View formula →

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