Australia · Year 12 · Practice Sheet 38

1. 1.

   A population of 2,200 grows 10% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   A 6 kg object moves at 5 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   A device runs at 111 V drawing 2.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Find the gravitational potential energy of a 30 kg object raised 15 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A population of 6,600 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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6. 6.

   Find the gravitational potential energy of a 8 kg object raised 36 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A device runs at 148 V drawing 8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A population of 7,200 grows 5% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   Find the gravitational potential energy of a 29 kg object raised 9 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    In a triangle, a = 8, b = 12 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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11. 11.

    An object with initial velocity 13 m/s accelerates at 2.4 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    A population of 1,900 grows 5% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    A device runs at 84 V drawing 2.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 7 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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15. 15.

    A body starts at 6 m/s and accelerates at 4.1 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    An object with initial velocity 9 m/s accelerates at 2.6 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    A population of 6,300 grows 5% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    A force of 78 N acts on an area of 9.5 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Find the momentum of a 21 kg object moving at 12 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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