Germany · Klasse 12 · Practice Sheet 11

1. 1.

   A cone has base radius 2 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
2. 2.

   Find the gravitational potential energy of a 13 kg object raised 6 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
3. 3.

   Find the momentum of a 27 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
4. 4.

   A force of 87 N moves an object 31 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
5. 5.

   Find the population standard deviation of: 16, 9, 8, 19, 15 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
6. 6.

   A wave has frequency 83 Hz and wavelength 4.56 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
7. 7.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 11 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

   View formula →
8. 8.

   Find the momentum of a 1 kg object moving at 16 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
9. 9.

   Find the sum of the first 3 terms of a geometric series with first term a = 2 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

   View formula →
10. 10.

    A device runs at 113 V drawing 1.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
11. 11.

    A triangle has sides a = 18 cm and b = 8 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 →
12. 12.

    €4,000 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 →
13. 13.

    Find the population standard deviation of: 2, 9, 18, 8, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
14. 14.

    Find the force needed to accelerate a 21 kg mass at 1.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
15. 15.

    Find the sum of the first 3 terms of a geometric series with first term a = 3 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

    View formula →
16. 16.

    A 11 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
17. 17.

    An object with initial velocity 7 m/s accelerates at 4.8 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
18. 18.

    Find the population standard deviation of: 7, 18, 15, 4, 10 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
19. 19.

    Find the force needed to accelerate a 23 kg mass at 7.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
20. 20.

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

    Formula:Sum of a Geometric Series

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

    View formula →

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