United Kingdom · Year 11 · Practice Sheet 7

1. 1.

   A triangle has sides a = 5 cm and b = 7 cm with an included angle C = 30°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

   View formula →
2. 2.

   Find the population standard deviation of: 18, 9, 8, 13, 16 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
3. 3.

   A force of 112 N moves an object 37 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
4. 4.

   Find the momentum of a 9 kg object moving at 29 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
5. 5.

   A right-angled triangle has legs of 10 cm and 19 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

   View formula →
6. 6.

   Find the gravitational potential energy of a 48 kg object raised 13 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
7. 7.

   Two masses 2,300 kg and 790 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 →
8. 8.

   An object has mass 170 g and volume 50 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

   View formula →
9. 9.

   A wave has frequency 680 Hz and wavelength 2.95 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
10. 10.

    A current of 2.1 A flows through a 8 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
11. 11.

    A cylinder has radius 2 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

    View formula →
12. 12.

    A force of 15 N moves an object 3 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
13. 13.

    Find the sum of the first 3 terms of a geometric series with first term a = 5 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

    View formula →
14. 14.

    Find the sum of the first 8 terms of an arithmetic series with first term a = 11 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

    View formula →
15. 15.

    A population of 1,100 grows 10% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
16. 16.

    A force of 60 N moves an object 26 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
17. 17.

    An object with initial velocity 9 m/s accelerates at 2 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
18. 18.

    Find the force needed to accelerate a 30 kg mass at 1.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
19. 19.

    Two masses 2,800 kg and 570 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 →
20. 20.

    Find the sum of the first 3 terms of a geometric series with first term a = 3 and common ratio r = 3.

    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.