Norway · Grade 12 · Practice Sheet 25

1. 1.

   Solve using the quadratic formula: x² + 3x − 10 = 0.

   Formula:Quadratic Formula

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

   View formula →
2. 2.

   A cone has base radius 6 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
3. 3.

   A population of 4,800 grows 8% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
4. 4.

   Find the force needed to accelerate a 40 kg mass at 1.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
5. 5.

   A triangle has sides a = 19 cm and b = 6 cm with an included angle C = 120°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

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

   View formula →
6. 6.

   Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
7. 7.

   A current of 5.4 A flows through a 47 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
8. 8.

   Find the sum of the first 8 terms of a geometric series with first term a = 1 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

   View formula →
9. 9.

   Find the population standard deviation of: 5, 9, 13, 17, 8 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
10. 10.

    Solve using the quadratic formula: x² + 1x − 12 = 0.

    Formula:Quadratic Formula

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

    View formula →
11. 11.

    A force of 278 N acts on an area of 9.9 m². Find the pressure.

    Formula:Pressure

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

    View formula →
12. 12.

    A current of 4.6 A flows through a 16 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
13. 13.

    Find the population standard deviation of: 10, 17, 17, 19, 18 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
14. 14.

    A current of 1.9 A flows through a 17 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
15. 15.

    Find the sum of the first 3 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 →
16. 16.

    A 14 kg object moves at 8 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
17. 17.

    Find the force needed to accelerate a 23 kg mass at 7.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
18. 18.

    A wave has frequency 52 Hz and wavelength 4.66 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
19. 19.

    A body starts at 9 m/s and accelerates at 2.3 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
20. 20.

    kr 2,600 is invested at 5% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

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

    View formula →

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