Kenya · Grade 12 · Practice Sheet 15

1. 1.

   Solve using the quadratic formula: x² + 0x − 1 = 0.

   Formula:Quadratic Formula

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

   View formula →
2. 2.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
3. 3.

   A force of 41 N moves an object 26 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
4. 4.

   A cone has base radius 3 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
5. 5.

   Two masses 2,200 kg and 700 kg are 15 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 current of 3.1 A flows through a 4 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
7. 7.

   A body starts at 15 m/s and accelerates at 2.3 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

   View formula →
8. 8.

   A force of 61 N acts on an area of 1.5 m². Find the pressure.

   Formula:Pressure

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

   View formula →
9. 9.

   A force of 11 N moves an object 39 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
10. 10.

    Find the sum of the first 5 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 →
11. 11.

    Find the force needed to accelerate a 9 kg mass at 5.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
12. 12.

    Find the sum of the first 7 terms of a geometric series with first term a = 8 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

    View formula →
13. 13.

    In a triangle, a = 6, b = 9 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →
14. 14.

    Find the population standard deviation of: 11, 7, 12, 8, 18 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
15. 15.

    Find the momentum of a 24 kg object moving at 20 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
16. 16.

    An object with initial velocity 4 m/s accelerates at 4.4 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
17. 17.

    A triangle has sides a = 20 cm and b = 10 cm with an included angle C = 90°. 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.

    Two masses 7,600 kg and 540 kg are 11 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.

    A cone has base radius 4 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 →
20. 20.

    Find the force needed to accelerate a 35 kg mass at 2.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →

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