Sweden · Grade 11 · Practice Sheet 45

1. 1.

   A population of 6,200 grows 3% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
2. 2.

   A triangle has sides a = 5 cm and b = 19 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 →
3. 3.

   Solve using the quadratic formula: x² − 3x + 2 = 0.

   Formula:Quadratic Formula

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

   View formula →
4. 4.

   A right-angled triangle has legs of 9 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

   View formula →
5. 5.

   A cylinder has radius 4 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

   View formula →
6. 6.

   In a triangle, a = 12, b = 7 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

   View formula →
7. 7.

   A triangle has sides a = 10 cm and b = 17 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 →
8. 8.

   A current of 4 A flows through a 56 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
9. 9.

   Find the force needed to accelerate a 10 kg mass at 1.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
10. 10.

    A force of 46 N moves an object 11 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
11. 11.

    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 →
12. 12.

    Find the sum of the first 10 terms of an arithmetic series with first term a = 3 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

    View formula →
13. 13.

    An object with initial velocity 4 m/s accelerates at 3.7 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
14. 14.

    A wave has frequency 430 Hz and wavelength 3.6 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
15. 15.

    Find the population standard deviation of: 18, 5, 9, 9, 19 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

    View formula →
16. 16.

    An object has mass 51 g and volume 17 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

    View formula →
17. 17.

    Find the gravitational potential energy of a 35 kg object raised 40 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
18. 18.

    A 37 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
19. 19.

    A device runs at 22 V drawing 5.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
20. 20.

    A wave has frequency 319 Hz and wavelength 4.96 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →

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