United Kingdom · Year 12 · Practice Sheet 36

1. 1.

   A wave has frequency 597 Hz and wavelength 3.03 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
2. 2.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 4 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

   View formula →
3. 3.

   A force of 203 N acts on an area of 9.6 m². Find the pressure.

   Formula:Pressure

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

   View formula →
4. 4.

   In a triangle, a = 6, b = 8 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 →
5. 5.

   An object with initial velocity 2 m/s accelerates at 2.6 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
6. 6.

   Find the momentum of a 47 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
7. 7.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 1 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

   View formula →
8. 8.

   A device runs at 137 V drawing 0.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
9. 9.

   Solve using the quadratic formula: x² + 6x + 5 = 0.

   Formula:Quadratic Formula

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

   View formula →
10. 10.

    An object with initial velocity 6 m/s accelerates at 4.4 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
11. 11.

    Two masses 3,800 kg and 380 kg are 17 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 →
12. 12.

    A wave has frequency 124 Hz and wavelength 2.59 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
13. 13.

    Find the force needed to accelerate a 46 kg mass at 1.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
14. 14.

    Find the population standard deviation of: 8, 14, 19, 7, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
15. 15.

    A wave has frequency 879 Hz and wavelength 2.14 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
16. 16.

    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 →
17. 17.

    A body starts at 11 m/s and accelerates at 1.2 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
18. 18.

    Solve using the quadratic formula: x² − 2x − 24 = 0.

    Formula:Quadratic Formula

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

    View formula →
19. 19.

    Find the momentum of a 39 kg object moving at 24 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
20. 20.

    In a triangle, a = 18, b = 14 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →

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