United States · Grade 12 · Practice Sheet 48

1. 1.

   A population of 2,800 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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2. 2.

   Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   A 17 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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4. 4.

   Find the sum of the first 8 terms of a geometric series with first term a = 1 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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5. 5.

   A body starts at 19 m/s and accelerates at 1.2 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   Find the momentum of a 24 kg object moving at 2 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A wave has frequency 266 Hz and wavelength 2.56 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Two masses 8,400 kg and 550 kg are 7 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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9. 9.

   Find the force needed to accelerate a 57 kg mass at 1.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Find the momentum of a 47 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    In a triangle, a = 8, b = 14 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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12. 12.

    Find the gravitational potential energy of a 49 kg object raised 40 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Find the population standard deviation of: 11, 14, 2, 14, 16 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    A population of 8,700 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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15. 15.

    A device runs at 20 V drawing 8.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    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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17. 17.

    A device runs at 90 V drawing 7.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 12 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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19. 19.

    A body starts at 9 m/s and accelerates at 5.2 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 12 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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