Ireland · Year 12 · Practice Sheet 49

1. 1.

   In a triangle, a = 5, b = 6 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

   View formula →
2. 2.

   Find the gravitational potential energy of a 3 kg object raised 32 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
3. 3.

   Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
4. 4.

   Find the momentum of a 17 kg object moving at 16 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
5. 5.

   Solve using the quadratic formula: x² − 8x + 12 = 0.

   Formula:Quadratic Formula

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

   View formula →
6. 6.

   Find the force needed to accelerate a 26 kg mass at 5.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
7. 7.

   A current of 7.6 A flows through a 9 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
8. 8.

   A body starts at 7 m/s and accelerates at 3.7 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

   View formula →
9. 9.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
10. 10.

    A device runs at 191 V drawing 1.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
11. 11.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

    View formula →
12. 12.

    €2,400 is invested at 4% 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 →
13. 13.

    A triangle has sides a = 20 cm and b = 12 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 →
14. 14.

    A population of 5,000 grows 3% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
15. 15.

    A wave has frequency 261 Hz and wavelength 0.98 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
16. 16.

    Find the gravitational potential energy of a 9 kg object raised 7 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
17. 17.

    A device runs at 16 V drawing 7.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
18. 18.

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

    Formula:Quadratic Formula

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

    View formula →
19. 19.

    A force of 228 N acts on an area of 3.9 m². Find the pressure.

    Formula:Pressure

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

    View formula →
20. 20.

    A 39 kg object moves at 5 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →

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