Chile · Grado 12 · Practice Sheet 43

1. 1.

   In a triangle, a = 17, b = 14 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

   View formula →
2. 2.

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

   Formula:Quadratic Formula

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

   View formula →
3. 3.

   A force of 495 N acts on an area of 3.3 m². Find the pressure.

   Formula:Pressure

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

   View formula →
4. 4.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 6 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

   View formula →
5. 5.

   A device runs at 7 V drawing 9.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
6. 6.

   $4,000 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 →
7. 7.

   A triangle has sides a = 19 cm and b = 14 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 wave has frequency 455 Hz and wavelength 2.45 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
9. 9.

   Two masses 8,700 kg and 330 kg are 9 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 force of 82 N moves an object 33 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
11. 11.

    An object with initial velocity 7 m/s accelerates at 4.1 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
12. 12.

    A current of 1.3 A flows through a 29 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
13. 13.

    A triangle has sides a = 13 cm and b = 6 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 →
14. 14.

    A force of 48 N acts on an area of 2.8 m². Find the pressure.

    Formula:Pressure

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

    View formula →
15. 15.

    A population of 8,900 grows 5% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
16. 16.

    Find the gravitational potential energy of a 50 kg object raised 20 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
17. 17.

    A body starts at 4 m/s and accelerates at 4.5 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
18. 18.

    An object with initial velocity 10 m/s accelerates at 3.5 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
19. 19.

    Find the gravitational potential energy of a 19 kg object raised 28 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
20. 20.

    Solve using the quadratic formula: x² − 1x − 30 = 0.

    Formula:Quadratic Formula

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

    View formula →

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