Hong Kong · Grade 10 · Practice Sheet 2

1. 1.

   Solve for x: 2x + 15 = 31.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

   View formula →
2. 2.

   In a triangle, a = 6, b = 10 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 →
3. 3.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 3 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

   View formula →
4. 4.

   Solve for x: 5x + 12 = 57.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

   View formula →
5. 5.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
6. 6.

   A cylinder has radius 2 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

   View formula →
7. 7.

   Solve for x: 5x + 2 = 57.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

   View formula →
8. 8.

   Solve using the quadratic formula: x² − 10x + 24 = 0.

   Formula:Quadratic Formula

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

   View formula →
9. 9.

   Find the momentum of a 20 kg object moving at 9 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
10. 10.

    A force of 44 N moves an object 27 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
11. 11.

    A triangle has sides a = 17 cm and b = 9 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 →
12. 12.

    Solve for x: 9x + 17 = 116.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

    View formula →
13. 13.

    Find the sum of the first 15 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 →
14. 14.

    A force of 40 N moves an object 37 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
15. 15.

    An object has mass 207 g and volume 30 cm³. Find its density.

    Formula:Density

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

    View formula →
16. 16.

    A bag has 23 equally likely marbles, of which 11 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

    View formula →
17. 17.

    A wave has frequency 627 Hz and wavelength 2.65 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
18. 18.

    Find the gravitational potential energy of a 41 kg object raised 35 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
19. 19.

    A 12 kg object moves at 15 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
20. 20.

    A body starts at 6 m/s and accelerates at 5.3 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →

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