Ecuador · Grado 12 · Practice Sheet 21

1. 1.

   Find the gravitational potential energy of a 39 kg object raised 33 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
2. 2.

   Find the sum of the first 3 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 →
3. 3.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 12 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

   View formula →
4. 4.

   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 →
5. 5.

   A wave has frequency 653 Hz and wavelength 0.49 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
6. 6.

   Find the sum of the first 4 terms of a geometric series with first term a = 1 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

   View formula →
7. 7.

   A force of 9 N moves an object 32 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
8. 8.

   A wave has frequency 728 Hz and wavelength 3.36 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
9. 9.

   In a triangle, a = 5, b = 13 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.

    A body starts at 20 m/s and accelerates at 2.9 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
11. 11.

    A 33 kg object moves at 7 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
12. 12.

    An object with initial velocity 3 m/s accelerates at 3.8 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
13. 13.

    A force of 126 N acts on an area of 7 m². Find the pressure.

    Formula:Pressure

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

    View formula →
14. 14.

    Find the gravitational potential energy of a 27 kg object raised 9 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
15. 15.

    Find the sum of the first 3 terms of a geometric series with first term a = 6 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

    View formula →
16. 16.

    In a triangle, a = 6, b = 12 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 →
17. 17.

    Find the momentum of a 42 kg object moving at 24 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
18. 18.

    An object with initial velocity 4 m/s accelerates at 1.6 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
19. 19.

    Find the population standard deviation of: 17, 5, 4, 14, 3 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
20. 20.

    Find the gravitational potential energy of a 49 kg object raised 20 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →

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