Tanzania · Grade 12 · Practice Sheet 36

1. 1.

   A triangle has sides a = 14 cm and b = 12 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 →
2. 2.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 6 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

   View formula →
3. 3.

   Solve using the quadratic formula: x² + 8x + 12 = 0.

   Formula:Quadratic Formula

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

   View formula →
4. 4.

   A body starts at 5 m/s and accelerates at 2.9 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

   View formula →
5. 5.

   A 13 kg object moves at 22 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
6. 6.

   A force of 9 N moves an object 25 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
7. 7.

   Find the sum of the first 4 terms of a geometric series with first term a = 6 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

   View formula →
8. 8.

   Find the force needed to accelerate a 35 kg mass at 3.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
9. 9.

   Solve using the quadratic formula: x² − 4x − 5 = 0.

   Formula:Quadratic Formula

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

   View formula →
10. 10.

    A triangle has sides a = 7 cm and b = 6 cm with an included angle C = 60°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

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

    View formula →
11. 11.

    An object with initial velocity 1 m/s accelerates at 1.6 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
12. 12.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

    View formula →
13. 13.

    An object with initial velocity 2 m/s accelerates at 4.6 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
14. 14.

    Find the momentum of a 56 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
15. 15.

    Two masses 6,600 kg and 770 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 →
16. 16.

    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 →
17. 17.

    A current of 1.7 A flows through a 11 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
18. 18.

    Two masses 8,900 kg and 130 kg are 6 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 population of 2,100 grows 3% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
20. 20.

    A current of 7.8 A flows through a 6 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →

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