India · Class 12 · Practice Sheet 49

1. 1.

   Find the sum of the first 8 terms of a geometric series with first term a = 5 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

   View formula →
2. 2.

   Solve using the quadratic formula: x² + 5x + 4 = 0.

   Formula:Quadratic Formula

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

   View formula →
3. 3.

   A current of 2.1 A flows through a 53 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
4. 4.

   Solve using the quadratic formula: x² − 4x − 5 = 0.

   Formula:Quadratic Formula

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

   View formula →
5. 5.

   A device runs at 207 V drawing 3.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
6. 6.

   Find the gravitational potential energy of a 25 kg object raised 35 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
7. 7.

   Find the sum of the first 7 terms of an arithmetic series with first term a = 1 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

   View formula →
8. 8.

   A force of 28 N moves an object 36 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
9. 9.

   A current of 4 A flows through a 42 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
10. 10.

    A body starts at 15 m/s and accelerates at 2.5 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
11. 11.

    Find the gravitational potential energy of a 15 kg object raised 14 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
12. 12.

    A force of 91 N moves an object 5 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
13. 13.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 4 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

    View formula →
14. 14.

    A force of 429 N acts on an area of 1.1 m². Find the pressure.

    Formula:Pressure

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

    View formula →
15. 15.

    Find the population standard deviation of: 17, 19, 4, 18, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
16. 16.

    A cone has base radius 5 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

    View formula →
17. 17.

    Find the momentum of a 9 kg object moving at 17 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
18. 18.

    An object with initial velocity 3 m/s accelerates at 3.9 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
19. 19.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

    View formula →
20. 20.

    A triangle has sides a = 8 cm and b = 14 cm with an included angle C = 90°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

    View formula →

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