Netherlands · Year 12 · Practice Sheet 20

1. 1.

   A population of 2,000 grows 2% 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.

   Find the gravitational potential energy of a 12 kg object raised 5 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   Find the population standard deviation of: 19, 15, 19, 8, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   A wave has frequency 524 Hz and wavelength 3.66 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   Find the momentum of a 18 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A population of 3,800 grows 2% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   A force of 305 N acts on an area of 8.1 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   An object with initial velocity 1 m/s accelerates at 2.4 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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10. 10.

    Find the force needed to accelerate a 51 kg mass at 1.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A device runs at 186 V drawing 6.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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13. 13.

    Find the sum of the first 6 terms of a geometric series with first term a = 4 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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14. 14.

    Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    A wave has frequency 888 Hz and wavelength 1.56 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    An object with initial velocity 2 m/s accelerates at 1.1 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    €3,400 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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18. 18.

    A device runs at 163 V drawing 4.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A force of 481 N acts on an area of 8.6 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    A population of 3,700 grows 3% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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