Ecuador · Grado 12 · Practice Sheet 31

1. 1.

   A population of 4,600 grows 8% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
2. 2.

   An object with initial velocity 15 m/s accelerates at 2.4 m/s² for 6 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
3. 3.

   Find the population standard deviation of: 12, 12, 15, 8, 10 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
4. 4.

   A device runs at 217 V drawing 6.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
5. 5.

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

   Formula:Quadratic Formula

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

   View formula →
6. 6.

   A force of 192 N acts on an area of 4.3 m². Find the pressure.

   Formula:Pressure

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

   View formula →
7. 7.

   Two masses 2,000 kg and 760 kg are 4 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 →
8. 8.

   A cone has base radius 3 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
9. 9.

   Two masses 1,700 kg and 400 kg are 17 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 →
10. 10.

    A current of 7.8 A flows through a 39 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
11. 11.

    $1,400 is invested at 5% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

    View formula →
12. 12.

    A current of 0.6 A flows through a 34 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
13. 13.

    Two masses 4,400 kg and 830 kg are 7 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 →
14. 14.

    An object with initial velocity 12 m/s accelerates at 4.4 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
15. 15.

    Find the momentum of a 52 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
16. 16.

    Find the force needed to accelerate a 18 kg mass at 3 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
17. 17.

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

    Formula:Quadratic Formula

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

    View formula →
18. 18.

    A triangle has sides a = 14 cm and b = 15 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 →
19. 19.

    A body starts at 19 m/s and accelerates at 5.1 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
20. 20.

    A population of 2,900 grows 10% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →

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