Netherlands · Year 12 · Practice Sheet 36

1. 1.

   A population of 7,300 grows 10% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   A force of 13 N moves an object 37 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   A triangle has sides a = 19 cm and b = 12 cm with an included angle C = 45°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

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

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4. 4.

   €2,600 is invested at 4% compound interest per annum for 5 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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5. 5.

   A force of 111 N moves an object 32 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A wave has frequency 718 Hz and wavelength 3.66 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A population of 1,800 grows 8% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   Solve using the quadratic formula: x² − 1x − 6 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   Find the momentum of a 1 kg object moving at 28 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A force of 461 N acts on an area of 9.8 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A wave has frequency 538 Hz and wavelength 4.18 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A force of 115 N moves an object 15 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    €1,600 is invested at 8% compound interest per annum for 5 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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14. 14.

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

    Formula:Quadratic Formula

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

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15. 15.

    Two masses 1,500 kg and 840 kg are 12 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 force needed to accelerate a 41 kg mass at 5.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A cone has base radius 12 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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18. 18.

    Find the force needed to accelerate a 10 kg mass at 3.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    Find the momentum of a 42 kg object moving at 6 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A 18 kg object moves at 6 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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