Sri Lanka · Grade 12 · Practice Sheet 8

1. 1.

   Find the population standard deviation of: 13, 10, 8, 10, 17 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
2. 2.

   A current of 7.1 A flows through a 44 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
3. 3.

   Two masses 5,700 kg and 560 kg are 12 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 12 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
5. 5.

   In a triangle, a = 15, b = 16 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 →
6. 6.

   A population of 3,700 grows 8% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
7. 7.

   A current of 0.8 A flows through a 57 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
8. 8.

   An object with initial velocity 15 m/s accelerates at 2.2 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
9. 9.

   Find the sum of the first 5 terms of a geometric series with first term a = 1 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

   View formula →
10. 10.

    A body starts at 7 m/s and accelerates at 4.5 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
11. 11.

    A cone has base radius 6 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 →
12. 12.

    Two masses 4,700 kg and 180 kg are 18 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.

    In a triangle, a = 8, b = 5 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 →
14. 14.

    A force of 185 N acts on an area of 7.5 m². Find the pressure.

    Formula:Pressure

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

    View formula →
15. 15.

    A force of 30 N moves an object 6 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
16. 16.

    In a triangle, a = 10, b = 11 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →
17. 17.

    A population of 5,900 grows 10% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
18. 18.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 1 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

    View formula →
19. 19.

    A force of 316 N acts on an area of 9.7 m². Find the pressure.

    Formula:Pressure

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

    View formula →
20. 20.

    A triangle has sides a = 8 cm and b = 11 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.