Thailand · Grade 11 · Practice Sheet 23

1. 1.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 1 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.

   In a triangle, a = 5, b = 17 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

   View formula →
3. 3.

   A force of 112 N moves an object 17 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
4. 4.

   Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

   View formula →
5. 5.

   A force of 63 N moves an object 8 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
6. 6.

   Find the gravitational potential energy of a 3 kg object raised 34 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
7. 7.

   A 40 kg object moves at 4 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
8. 8.

   Find the force needed to accelerate a 25 kg mass at 2.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
9. 9.

   A right-angled triangle has legs of 4 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

   View formula →
10. 10.

    In a triangle, a = 17, b = 16 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 →
11. 11.

    Find the force needed to accelerate a 28 kg mass at 3.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
12. 12.

    A cone has base radius 12 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 →
13. 13.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 7 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

    View formula →
14. 14.

    Solve using the quadratic formula: x² + 0x − 16 = 0.

    Formula:Quadratic Formula

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

    View formula →
15. 15.

    Find the force needed to accelerate a 26 kg mass at 2.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
16. 16.

    A device runs at 165 V drawing 1.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
17. 17.

    Find the sum of the first 7 terms of a geometric series with first term a = 6 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

    View formula →
18. 18.

    An object with initial velocity 8 m/s accelerates at 1.6 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
19. 19.

    A wave has frequency 191 Hz and wavelength 2.46 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
20. 20.

    Find the population standard deviation of: 5, 5, 12, 6, 19 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →

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