Cambodia · Grade 11 · Practice Sheet 18

1. 1.

   Find the sum of the first 8 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 →
2. 2.

   Find the force needed to accelerate a 40 kg mass at 8 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
3. 3.

   A force of 73 N moves an object 23 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
4. 4.

   A wave has frequency 586 Hz and wavelength 1.07 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
5. 5.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 6 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

   View formula →
6. 6.

   Find the sum of the first 8 terms of a geometric series with first term a = 6 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

   View formula →
7. 7.

   In a triangle, a = 11, b = 5 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

   View formula →
8. 8.

   Find the momentum of a 30 kg object moving at 12 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
9. 9.

   ៛ 4,000 is invested at 4% compound interest per annum for 5 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

   View formula →
10. 10.

    A population of 6,600 grows 5% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
11. 11.

    Find the population standard deviation of: 8, 5, 2, 18, 4 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
12. 12.

    Two masses 2,900 kg and 480 kg are 15 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

    View formula →
13. 13.

    An object has mass 354.2 g and volume 46 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

    View formula →
14. 14.

    A force of 30 N moves an object 35 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
15. 15.

    A triangle has sides a = 16 cm and b = 7 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 →
16. 16.

    A cylinder has radius 4 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

    View formula →
17. 17.

    Find the sum of the first 12 terms of an arithmetic series with first term a = 5 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

    View formula →
18. 18.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

    View formula →
19. 19.

    Find the force needed to accelerate a 56 kg mass at 7.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
20. 20.

    A triangle has sides a = 15 cm and b = 11 cm with an included angle C = 60°. 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.