Cambodia · Grade 12 · Practice Sheet 36

1. 1.

   Find the population standard deviation of: 10, 3, 19, 18, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
2. 2.

   In a triangle, a = 13, b = 10 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 →
3. 3.

   Two masses 2,300 kg and 650 kg are 14 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 →
4. 4.

   Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
5. 5.

   A cone has base radius 5 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
6. 6.

   A wave has frequency 578 Hz and wavelength 0.83 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
7. 7.

   A device runs at 88 V drawing 7.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
8. 8.

   An object with initial velocity 15 m/s accelerates at 1.2 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
9. 9.

   Find the momentum of a 4 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
10. 10.

    Find the sum of the first 4 terms of a geometric series with first term a = 5 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

    View formula →
11. 11.

    Solve using the quadratic formula: x² − 6x + 8 = 0.

    Formula:Quadratic Formula

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

    View formula →
12. 12.

    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 →
13. 13.

    Two masses 2,700 kg and 690 kg are 4 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 →
14. 14.

    Find the force needed to accelerate a 53 kg mass at 2.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
15. 15.

    A body starts at 1 m/s and accelerates at 4.1 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
16. 16.

    Find the force needed to accelerate a 38 kg mass at 1.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
17. 17.

    ៛ 600 is invested at 6% 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 →
18. 18.

    A device runs at 175 V drawing 5.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
19. 19.

    A triangle has sides a = 12 cm and b = 7 cm with an included angle C = 45°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

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

    View formula →
20. 20.

    An object with initial velocity 10 m/s accelerates at 1.4 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →

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