Mexico · Grado 12 · Practice Sheet 25

1. 1.

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

   Formula:Sum of a Geometric Series

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

   View formula →
2. 2.

   A body starts at 1 m/s and accelerates at 4.4 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

   View formula →
3. 3.

   In a triangle, a = 14, b = 13 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

   View formula →
4. 4.

   A 27 kg object moves at 23 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
5. 5.

   A cone has base radius 2 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 →
6. 6.

   A device runs at 36 V drawing 5.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
7. 7.

   Find the population standard deviation of: 14, 13, 17, 6, 3 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
8. 8.

   Find the momentum of a 17 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
9. 9.

   Find the gravitational potential energy of a 32 kg object raised 9 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
10. 10.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 7 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

    View formula →
11. 11.

    A device runs at 101 V drawing 8.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
12. 12.

    A force of 74 N moves an object 26 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
13. 13.

    A 11 kg object moves at 16 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
14. 14.

    A current of 6 A flows through a 59 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
15. 15.

    A force of 100 N moves an object 24 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
16. 16.

    A population of 8,200 grows 2% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
17. 17.

    A force of 54 N acts on an area of 0.6 m². Find the pressure.

    Formula:Pressure

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

    View formula →
18. 18.

    Solve using the quadratic formula: x² + 3x − 4 = 0.

    Formula:Quadratic Formula

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

    View formula →
19. 19.

    A device runs at 223 V drawing 6.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
20. 20.

    Find the force needed to accelerate a 32 kg mass at 5.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →

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