Czechia · Grade 10 · Practice Sheet 42

1. 1.

   A triangle has sides a = 18 cm and b = 7 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 →
2. 2.

   Kč 2,100 is invested at 6% simple interest per year for 3 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

   View formula →
3. 3.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 4 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

   View formula →
4. 4.

   A bag has 25 equally likely marbles, of which 18 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 →
5. 5.

   Find the gravitational potential energy of a 46 kg object raised 29 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
6. 6.

   An object has mass 9.8 g and volume 7 cm³. Find its density.

   Formula:Density

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

   View formula →
7. 7.

   Find the force needed to accelerate a 12 kg mass at 7.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
8. 8.

   A force of 68 N moves an object 35 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
9. 9.

   A triangle has sides a = 14 cm and b = 16 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 →
10. 10.

    Find the gravitational potential energy of a 27 kg object raised 20 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
11. 11.

    A device runs at 134 V drawing 9.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
12. 12.

    A cylinder has radius 12 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

    View formula →
13. 13.

    Solve for x: 9x + 8 = 89.

    Formula:Solving a Linear Equation

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

    View formula →
14. 14.

    A cone has base radius 4 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

    View formula →
15. 15.

    Solve for x: 6x + 6 = 66.

    Formula:Solving a Linear Equation

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

    View formula →
16. 16.

    A body starts at 10 m/s and accelerates at 2.6 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
17. 17.

    A value changes from 149 to 42. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

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

    View formula →
18. 18.

    A 38 kg object moves at 24 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
19. 19.

    An object with initial velocity 7 m/s accelerates at 4.6 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
20. 20.

    An object has mass 347.8 g and volume 47 cm³. Find its density.

    Formula:Density

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

    View formula →

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