Peru · Grado 11 · Practice Sheet 23

1. 1.

   A population of 8,000 grows 8% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   Find the force needed to accelerate a 16 kg mass at 6.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   Find the gravitational potential energy of a 37 kg object raised 33 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A wave has frequency 694 Hz and wavelength 0.82 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the momentum of a 32 kg object moving at 28 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Find the force needed to accelerate a 10 kg mass at 5.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A force of 55 N moves an object 33 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   A device runs at 222 V drawing 0.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A 18 kg object moves at 9 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

    Find the population standard deviation of: 15, 14, 17, 2, 2 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    A cylinder has radius 14 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 10 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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13. 13.

    Find the momentum of a 12 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A force of 94 N moves an object 17 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    A triangle has sides a = 6 cm and b = 17 cm with an included angle C = 120°. 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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16. 16.

    Find the gravitational potential energy of a 43 kg object raised 9 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Find the population standard deviation of: 17, 15, 19, 20, 4 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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18. 18.

    A force of 60 N acts on an area of 4.5 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Find the population standard deviation of: 8, 2, 15, 7, 13 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    A cone has base radius 3 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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