Hong Kong · Grade 11 · Practice Sheet 13

1. 1.

   Find the population standard deviation of: 13, 17, 13, 7, 20 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
2. 2.

   A population of 7,400 grows 2% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
3. 3.

   A force of 311 N acts on an area of 5.6 m². Find the pressure.

   Formula:Pressure

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

   View formula →
4. 4.

   Find the force needed to accelerate a 11 kg mass at 6.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
5. 5.

   Solve using the quadratic formula: x² + 1x − 20 = 0.

   Formula:Quadratic Formula

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

   View formula →
6. 6.

   Find the sum of the first 3 terms of a geometric series with first term a = 2 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

   View formula →
7. 7.

   Find the population standard deviation of: 8, 12, 8, 7, 2 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
8. 8.

   A force of 95 N moves an object 38 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
9. 9.

   A device runs at 87 V drawing 9.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
10. 10.

    A triangle has sides a = 14 cm and b = 8 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 →
11. 11.

    A 40 kg object moves at 15 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

    View formula →
12. 12.

    A triangle has sides a = 15 cm and b = 10 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 →
13. 13.

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

    Formula:Quadratic Formula

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

    View formula →
14. 14.

    A device runs at 102 V drawing 7.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
15. 15.

    In a triangle, a = 11, b = 8 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 →
16. 16.

    A device runs at 173 V drawing 8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
17. 17.

    A body starts at 4 m/s and accelerates at 5.1 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
18. 18.

    A force of 472 N acts on an area of 5.2 m². Find the pressure.

    Formula:Pressure

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

    View formula →
19. 19.

    A triangle has sides a = 5 cm and b = 10 cm with an included angle C = 30°. 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.

    A cylinder has radius 3 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

    View formula →

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