Nepal · Class 12 · Practice Sheet 24

1. 1.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 9 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

   View formula →
2. 2.

   A wave has frequency 489 Hz and wavelength 4.85 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
3. 3.

   A body starts at 7 m/s and accelerates at 5.4 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

   View formula →
4. 4.

   Rs 1,900 is invested at 3% 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 →
5. 5.

   An object with initial velocity 13 m/s accelerates at 3.4 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
6. 6.

   Find the momentum of a 24 kg object moving at 18 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
7. 7.

   Find the force needed to accelerate a 14 kg mass at 4.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
8. 8.

   A population of 6,300 grows 2% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
9. 9.

   Find the gravitational potential energy of a 18 kg object raised 33 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
10. 10.

    In a triangle, a = 17, b = 16 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →
11. 11.

    Find the gravitational potential energy of a 15 kg object raised 39 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
12. 12.

    Solve using the quadratic formula: x² − 1x − 30 = 0.

    Formula:Quadratic Formula

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

    View formula →
13. 13.

    In a triangle, a = 12, b = 17 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →
14. 14.

    A device runs at 171 V drawing 1.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
15. 15.

    Find the momentum of a 3 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
16. 16.

    An object with initial velocity 11 m/s accelerates at 2.5 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
17. 17.

    A population of 8,800 grows 3% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
18. 18.

    Find the gravitational potential energy of a 38 kg object raised 32 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
19. 19.

    Find the sum of the first 7 terms of a geometric series with first term a = 6 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

    View formula →
20. 20.

    A wave has frequency 327 Hz and wavelength 1.19 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →

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