Austria · Klasse 10 · Practice Sheet 3

1. 1.

   An object has mass 295.2 g and volume 36 cm³. Find its density.

   Formula:Density

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

   View formula →
2. 2.

   A triangle has sides a = 12 cm and b = 5 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 →
3. 3.

   Solve for x: 2x + 13 = 33.

   Formula:Solving a Linear Equation

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

   View formula →
4. 4.

   An object has mass 110.7 g and volume 27 cm³. Find its density.

   Formula:Density

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

   View formula →
5. 5.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
6. 6.

   A cone has base radius 6 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
7. 7.

   Find the gravitational potential energy of a 8 kg object raised 27 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
8. 8.

   Solve using the quadratic formula: x² − 9x + 20 = 0.

   Formula:Quadratic Formula

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

   View formula →
9. 9.

   €1,500 is invested at 4% simple interest per year for 3 years. Find the interest earned.

   Formula:Simple Interest

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

   View formula →
10. 10.

    A force of 85 N moves an object 32 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
11. 11.

    Find the force needed to accelerate a 52 kg mass at 8.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
12. 12.

    A force of 33 N acts on an area of 3.8 m². Find the pressure.

    Formula:Pressure

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

    View formula →
13. 13.

    An object has mass 268.8 g and volume 42 cm³. Find its density.

    Formula:Density

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

    View formula →
14. 14.

    A triangle has sides a = 19 cm and b = 11 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 →
15. 15.

    €2,700 is invested at 3% 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 →
16. 16.

    A wave has frequency 726 Hz and wavelength 1.83 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
17. 17.

    Find the momentum of a 60 kg object moving at 30 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
18. 18.

    A right-angled triangle has legs of 20 cm and 8 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

    View formula →
19. 19.

    A body starts at 18 m/s and accelerates at 4.6 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
20. 20.

    A bag has 26 equally likely marbles, of which 2 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 →

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