Belgium · Year 12 · Practice Sheet 18

1. 1.

   A body starts at 5 m/s and accelerates at 3.6 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   A population of 7,900 grows 10% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   Find the force needed to accelerate a 31 kg mass at 4.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A force of 82 N moves an object 36 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A current of 1.5 A flows through a 46 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A force of 233 N acts on an area of 6.4 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A force of 9 N moves an object 13 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   Find the sum of the first 8 terms of a geometric series with first term a = 6 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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9. 9.

   In a triangle, a = 18, b = 8 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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10. 10.

    A cone has base radius 2 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    A 9 kg object moves at 12 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    A wave has frequency 281 Hz and wavelength 0.45 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the force needed to accelerate a 39 kg mass at 8.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    Find the momentum of a 59 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Two masses 5,800 kg and 640 kg are 11 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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16. 16.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 11 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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17. 17.

    In a triangle, a = 16, b = 5 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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18. 18.

    €3,600 is invested at 8% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

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

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19. 19.

    A current of 4.6 A flows through a 45 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    Find the population standard deviation of: 20, 12, 19, 4, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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