Mongolia · Grade 12 · Practice Sheet 32

1. 1.

   In a triangle, a = 11, b = 11 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 →
2. 2.

   A body starts at 2 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 →
3. 3.

   A triangle has sides a = 16 cm and b = 20 cm with an included angle C = 120°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

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

   View formula →
4. 4.

   A wave has frequency 168 Hz and wavelength 2.6 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
5. 5.

   Two masses 2,600 kg and 550 kg are 13 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 →
6. 6.

   A 18 kg object moves at 19 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
7. 7.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 8 and common difference d = 3.

   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 12 cm and height 20 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 sum of the first 20 terms of an arithmetic series with first term a = 12 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

   View formula →
10. 10.

    A force of 359 N acts on an area of 3.8 m². Find the pressure.

    Formula:Pressure

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

    View formula →
11. 11.

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

    Formula:Volume of a Cone

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

    View formula →
12. 12.

    Solve using the quadratic formula: x² − 9x + 20 = 0.

    Formula:Quadratic Formula

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

    View formula →
13. 13.

    Find the sum of the first 8 terms of a geometric series with first term a = 4 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

    View formula →
14. 14.

    A population of 7,600 grows 5% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
15. 15.

    Find the momentum of a 54 kg object moving at 30 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
16. 16.

    Find the force needed to accelerate a 44 kg mass at 4.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
17. 17.

    A triangle has sides a = 6 cm and b = 12 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 →
18. 18.

    A current of 5.2 A flows through a 12 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
19. 19.

    Find the force needed to accelerate a 24 kg mass at 6.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
20. 20.

    Find the population standard deviation of: 15, 15, 10, 4, 16 (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.