Peru · Grado 12 · Practice Sheet 28

1. 1.

   A wave has frequency 318 Hz and wavelength 1.28 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
2. 2.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 4 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

   View formula →
3. 3.

   A cone has base radius 12 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
4. 4.

   A current of 6 A flows through a 10 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
5. 5.

   Solve using the quadratic formula: x² − 10x + 24 = 0.

   Formula:Quadratic Formula

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

   View formula →
6. 6.

   Find the momentum of a 27 kg object moving at 20 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
7. 7.

   Find the force needed to accelerate a 48 kg mass at 7.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
8. 8.

   Find the sum of the first 6 terms of a geometric series with first term a = 5 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

   View formula →
9. 9.

   A force of 65 N moves an object 31 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
10. 10.

    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 →
11. 11.

    Solve using the quadratic formula: x² − 5x + 0 = 0.

    Formula:Quadratic Formula

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

    View formula →
12. 12.

    Two masses 1,100 kg and 190 kg are 9 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 →
13. 13.

    A body starts at 11 m/s and accelerates at 1.5 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
14. 14.

    An object with initial velocity 4 m/s accelerates at 1.6 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
15. 15.

    A population of 5,300 grows 2% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
16. 16.

    In a triangle, a = 5, b = 14 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →
17. 17.

    S/ 3,500 is invested at 6% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

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

    View formula →
18. 18.

    Find the force needed to accelerate a 12 kg mass at 4.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
19. 19.

    A device runs at 231 V drawing 1.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
20. 20.

    A body starts at 11 m/s and accelerates at 2.8 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →

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