Taiwan · Grade 11 · Practice Sheet 13

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.

   An object has mass 63.6 g and volume 12 cm³. Find its density.

   Formula:Density

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

   View formula →
3. 3.

   An object with initial velocity 11 m/s accelerates at 1.1 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
4. 4.

   Find the population standard deviation of: 10, 10, 18, 16, 16 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
5. 5.

   A force of 17 N moves an object 39 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
6. 6.

   A population of 1,100 grows 3% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
7. 7.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 4 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

   View formula →
8. 8.

   A cone has base radius 10 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
9. 9.

   Find the population standard deviation of: 11, 14, 12, 5, 19 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
10. 10.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 1 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

    View formula →
11. 11.

    Find the gravitational potential energy of a 35 kg object raised 9 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
12. 12.

    Find the momentum of a 1 kg object moving at 30 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
13. 13.

    An object with initial velocity 6 m/s accelerates at 3.3 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
14. 14.

    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 →
15. 15.

    A wave has frequency 355 Hz and wavelength 3.85 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
16. 16.

    A force of 30 N moves an object 23 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
17. 17.

    A population of 8,900 grows 3% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
18. 18.

    Two masses 7,300 kg and 420 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 →
19. 19.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 5 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

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

    View formula →
20. 20.

    Find the sum of the first 5 terms of a geometric series with first term a = 7 and common ratio r = 2.

    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.