Switzerland · Grade 10 · Practice Sheet 6

1. 1.

   An object has mass 103.2 g and volume 43 cm³. Find its density.

   Formula:Density

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

   View formula →
2. 2.

   A value changes from 186 to 151. Find the percentage change (to 2 d.p.).

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

   View formula →
3. 3.

   Solve for x: 2x + 20 = 34.

   Formula:Solving a Linear Equation

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

   View formula →
4. 4.

   In a triangle, a = 13, b = 18 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 →
5. 5.

   A triangle has sides a = 8 cm and b = 17 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 →
6. 6.

   Find the force needed to accelerate a 52 kg mass at 5.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
7. 7.

   Solve using the quadratic formula: x² + 7x + 12 = 0.

   Formula:Quadratic Formula

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

   View formula →
8. 8.

   A wave has frequency 422 Hz and wavelength 1.71 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
9. 9.

   A bag has 19 equally likely marbles, of which 9 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 →
10. 10.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 5 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

    View formula →
11. 11.

    In a triangle, a = 8, b = 9 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 →
12. 12.

    A wave has frequency 392 Hz and wavelength 4.51 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
13. 13.

    A 37 kg object moves at 19 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
14. 14.

    A body starts at 5 m/s and accelerates at 5.6 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
15. 15.

    An object has mass 324 g and volume 40 cm³. Find its density.

    Formula:Density

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

    View formula →
16. 16.

    A bag has 16 equally likely marbles, of which 8 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.

    Find the gravitational potential energy of a 22 kg object raised 39 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
18. 18.

    A force of 228 N acts on an area of 7.8 m². Find the pressure.

    Formula:Pressure

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

    View formula →
19. 19.

    Solve using the quadratic formula: x² + 5x + 6 = 0.

    Formula:Quadratic Formula

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

    View formula →
20. 20.

    A population of 1,300 grows 2% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →

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