Ireland · Year 12 · Practice Sheet 48

1. 1.

   A cone has base radius 10 cm and height 9 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 wave has frequency 37 Hz and wavelength 3.64 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
3. 3.

   Two masses 8,200 kg and 860 kg are 2 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 →
4. 4.

   A force of 465 N acts on an area of 5.1 m². Find the pressure.

   Formula:Pressure

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

   View formula →
5. 5.

   A wave has frequency 752 Hz and wavelength 2.71 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
6. 6.

   Solve using the quadratic formula: x² − 4x − 12 = 0.

   Formula:Quadratic Formula

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

   View formula →
7. 7.

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

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
8. 8.

   A population of 1,200 grows 8% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
9. 9.

   A cone has base radius 4 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
10. 10.

    In a triangle, a = 12, b = 6 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

    View formula →
11. 11.

    Find the gravitational potential energy of a 25 kg object raised 30 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
12. 12.

    Find the force needed to accelerate a 38 kg mass at 2.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
13. 13.

    €2,700 is invested at 8% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

    View formula →
14. 14.

    A current of 3.8 A flows through a 25 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
15. 15.

    Two masses 8,100 kg and 500 kg are 19 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 →
16. 16.

    Find the sum of the first 4 terms of a geometric series with first term a = 4 and common ratio r = 2.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

    View formula →
17. 17.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 12 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

    View formula →
18. 18.

    A wave has frequency 62 Hz and wavelength 4.94 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
19. 19.

    Two masses 3,500 kg and 520 kg are 14 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 →
20. 20.

    Find the force needed to accelerate a 37 kg mass at 7.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →

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