India · Class 12 · Practice Sheet 42

1. 1.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 2 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

   View formula →
2. 2.

   A force of 301 N acts on an area of 8.3 m². Find the pressure.

   Formula:Pressure

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

   View formula →
3. 3.

   A wave has frequency 81 Hz and wavelength 2.45 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
4. 4.

   In a triangle, a = 11, b = 7 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

   View formula →
5. 5.

   A cone has base radius 9 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
6. 6.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 12 and common difference d = 7.

   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 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
8. 8.

   Find the gravitational potential energy of a 38 kg object raised 18 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
9. 9.

   Solve using the quadratic formula: x² − 3x + 0 = 0.

   Formula:Quadratic Formula

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

   View formula →
10. 10.

    A force of 170 N acts on an area of 2.1 m². Find the pressure.

    Formula:Pressure

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

    View formula →
11. 11.

    A wave has frequency 440 Hz and wavelength 4.46 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
12. 12.

    A force of 106 N acts on an area of 3.9 m². Find the pressure.

    Formula:Pressure

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

    View formula →
13. 13.

    Find the gravitational potential energy of a 10 kg object raised 3 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
14. 14.

    Find the sum of the first 5 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 →
15. 15.

    Find the gravitational potential energy of a 47 kg object raised 38 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
16. 16.

    Find the population standard deviation of: 17, 16, 7, 17, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
17. 17.

    A force of 343 N acts on an area of 8 m². Find the pressure.

    Formula:Pressure

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

    View formula →
18. 18.

    Find the momentum of a 21 kg object moving at 16 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
19. 19.

    Solve using the quadratic formula: x² − 4x + 3 = 0.

    Formula:Quadratic Formula

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

    View formula →
20. 20.

    A force of 36 N moves an object 37 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →

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