Hong Kong · Grade 12 · Practice Sheet 23

1. 1.

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

   Formula:Quadratic Formula

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

   View formula →
2. 2.

   A triangle has sides a = 10 cm and b = 20 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 →
3. 3.

   Find the gravitational potential energy of a 31 kg object raised 26 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
4. 4.

   A 13 kg object moves at 24 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
5. 5.

   A force of 98 N moves an object 14 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
6. 6.

   Find the gravitational potential energy of a 12 kg object raised 5 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
7. 7.

   A device runs at 157 V drawing 8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
8. 8.

   Find the gravitational potential energy of a 33 kg object raised 19 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
9. 9.

   A population of 2,200 grows 8% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
10. 10.

    A current of 5.8 A flows through a 8 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
11. 11.

    A wave has frequency 876 Hz and wavelength 2.96 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
12. 12.

    Find the sum of the first 4 terms of a geometric series with first term a = 8 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

    View formula →
13. 13.

    A force of 46 N moves an object 18 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
14. 14.

    A force of 402 N acts on an area of 2.6 m². Find the pressure.

    Formula:Pressure

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

    View formula →
15. 15.

    Find the sum of the first 6 terms of a geometric series with first term a = 3 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

    View formula →
16. 16.

    HK$ 3,500 is invested at 4% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

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

    View formula →
17. 17.

    A current of 2 A flows through a 11 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
18. 18.

    A cone has base radius 7 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

    View formula →
19. 19.

    A triangle has sides a = 7 cm and b = 14 cm with an included angle C = 120°. 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.

    In a triangle, a = 15, b = 8 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 →

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