Czechia · Grade 12 · Practice Sheet 16

1. 1.

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

   Formula:Quadratic Formula

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

   View formula →
2. 2.

   A cone has base radius 3 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 →
3. 3.

   Find the momentum of a 16 kg object moving at 26 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
4. 4.

   A force of 275 N acts on an area of 7.3 m². Find the pressure.

   Formula:Pressure

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

   View formula →
5. 5.

   A cone has base radius 10 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
6. 6.

   A force of 227 N acts on an area of 4.4 m². Find the pressure.

   Formula:Pressure

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

   View formula →
7. 7.

   An object with initial velocity 13 m/s accelerates at 2.3 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
8. 8.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 11 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

   View formula →
9. 9.

   A 25 kg object moves at 8 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
10. 10.

    A force of 253 N acts on an area of 7.4 m². Find the pressure.

    Formula:Pressure

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

    View formula →
11. 11.

    A triangle has sides a = 16 cm and b = 16 cm with an included angle C = 45°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

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

    View formula →
12. 12.

    A current of 6.6 A flows through a 21 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
13. 13.

    A wave has frequency 180 Hz and wavelength 0.42 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
14. 14.

    Two masses 3,800 kg and 150 kg are 12 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 →
15. 15.

    Find the gravitational potential energy of a 6 kg object raised 21 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
16. 16.

    Two masses 1,200 kg and 530 kg are 10 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 →
17. 17.

    An object with initial velocity 3 m/s accelerates at 3.9 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
18. 18.

    In a triangle, a = 15, b = 15 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 →
19. 19.

    A population of 4,400 grows 5% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
20. 20.

    A force of 447 N acts on an area of 8.4 m². Find the pressure.

    Formula:Pressure

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

    View formula →

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