Belgium · Year 12 · Practice Sheet 35

1. 1.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 9 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

   View formula →
2. 2.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
3. 3.

   A population of 3,000 grows 3% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
4. 4.

   Two masses 7,300 kg and 240 kg are 4 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

   View formula →
5. 5.

   Solve using the quadratic formula: x² + 6x + 8 = 0.

   Formula:Quadratic Formula

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

   View formula →
6. 6.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 8 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

   View formula →
7. 7.

   An object with initial velocity 2 m/s accelerates at 4.5 m/s² for 6 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
8. 8.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 3 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

   View formula →
9. 9.

   A 18 kg object moves at 24 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
10. 10.

    A wave has frequency 37 Hz and wavelength 3.4 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
11. 11.

    A force of 335 N acts on an area of 1.5 m². Find the pressure.

    Formula:Pressure

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

    View formula →
12. 12.

    Find the gravitational potential energy of a 5 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
13. 13.

    A cone has base radius 2 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

    View formula →
14. 14.

    €3,300 is invested at 4% compound interest per annum for 5 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 triangle has sides a = 8 cm and b = 17 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 →
16. 16.

    Find the gravitational potential energy of a 14 kg object raised 33 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
17. 17.

    Find the force needed to accelerate a 50 kg mass at 1.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
18. 18.

    Find the gravitational potential energy of a 18 kg object raised 14 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
19. 19.

    A wave has frequency 406 Hz and wavelength 2.13 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
20. 20.

    A current of 6.7 A flows through a 7 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →

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