Ireland · Year 10 · Practice Sheet 49

1. 1.

   A body starts at 6 m/s and accelerates at 3.8 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

   View formula →
2. 2.

   A wave has frequency 171 Hz and wavelength 3.21 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
3. 3.

   A triangle has sides a = 18 cm and b = 17 cm with an included angle C = 60°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

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

   View formula →
4. 4.

   In a triangle, a = 8, b = 13 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 →
5. 5.

   Find the gravitational potential energy of a 16 kg object raised 3 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
6. 6.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 6 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

   View formula →
7. 7.

   A force of 115 N moves an object 25 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
8. 8.

   Find the force needed to accelerate a 11 kg mass at 2.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
9. 9.

   A population of 2,800 grows 8% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
10. 10.

    Find the force needed to accelerate a 20 kg mass at 2.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
11. 11.

    A population of 4,100 grows 2% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
12. 12.

    Solve using the quadratic formula: x² + 6x + 0 = 0.

    Formula:Quadratic Formula

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

    View formula →
13. 13.

    A value changes from 144 to 64. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

    View formula →
14. 14.

    Find the momentum of a 12 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
15. 15.

    An object with initial velocity 8 m/s accelerates at 4.5 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
16. 16.

    Find the gravitational potential energy of a 39 kg object raised 8 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
17. 17.

    Solve using the quadratic formula: x² − 2x − 8 = 0.

    Formula:Quadratic Formula

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

    View formula →
18. 18.

    A 2 kg object moves at 4 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
19. 19.

    €1,000 is invested at 7.5% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

    View formula →
20. 20.

    A value changes from 186 to 21. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

    View formula →

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