Portugal · Ano 10 · Practice Sheet 49

1. 1.

   A cone has base radius 7 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
2. 2.

   A triangle has sides a = 9 cm and b = 18 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 →
3. 3.

   A device runs at 208 V drawing 7.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
4. 4.

   An object has mass 289.8 g and volume 42 cm³. Find its density.

   Formula:Density

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

   View formula →
5. 5.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 9 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

   View formula →
6. 6.

   An object with initial velocity 3 m/s accelerates at 4.8 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
7. 7.

   A device runs at 159 V drawing 8.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
8. 8.

   A body starts at 15 m/s and accelerates at 3.4 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

   View formula →
9. 9.

   A bag has 14 equally likely marbles, of which 12 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.

    Solve using the quadratic formula: x² − 11x + 30 = 0.

    Formula:Quadratic Formula

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

    View formula →
11. 11.

    A triangle has sides a = 10 cm and b = 16 cm with an included angle C = 45°. 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.

    Find the gravitational potential energy of a 10 kg object raised 35 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
13. 13.

    A force of 53 N acts on an area of 8.6 m². Find the pressure.

    Formula:Pressure

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

    View formula →
14. 14.

    €3,300 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 →
15. 15.

    A force of 46 N moves an object 2 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
16. 16.

    Find the gravitational potential energy of a 15 kg object raised 9 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
17. 17.

    A current of 4.8 A flows through a 19 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
18. 18.

    A wave has frequency 377 Hz and wavelength 4.38 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
19. 19.

    A body starts at 1 m/s and accelerates at 3.5 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
20. 20.

    Find the force needed to accelerate a 35 kg mass at 3.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →

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