Canada · Grade 12 · Practice Sheet 29

1. 1.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 2 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

   View formula →
2. 2.

   A current of 1.2 A flows through a 18 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
3. 3.

   A wave has frequency 337 Hz and wavelength 0.63 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
4. 4.

   Find the gravitational potential energy of a 7 kg object raised 29 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
5. 5.

   A body starts at 16 m/s and accelerates at 5.1 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

   View formula →
6. 6.

   A 5 kg object moves at 17 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
7. 7.

   A current of 2.7 A flows through a 35 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
8. 8.

   A device runs at 204 V drawing 8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
9. 9.

   A wave has frequency 538 Hz and wavelength 1.1 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
10. 10.

    Find the population standard deviation of: 5, 15, 9, 9, 12 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

    View formula →
11. 11.

    A population of 3,000 grows 8% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
12. 12.

    A cone has base radius 11 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

    View formula →
13. 13.

    Solve using the quadratic formula: x² − 3x + 0 = 0.

    Formula:Quadratic Formula

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

    View formula →
14. 14.

    Find the gravitational potential energy of a 43 kg object raised 5 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
15. 15.

    A wave has frequency 787 Hz and wavelength 0.65 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
16. 16.

    Find the momentum of a 43 kg object moving at 17 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
17. 17.

    In a triangle, a = 9, b = 15 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →
18. 18.

    Two masses 4,200 kg and 840 kg are 15 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 →
19. 19.

    $900 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 →
20. 20.

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

    Formula:Sum of a Geometric Series

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

    View formula →

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