Egypt · Grade 12 · Practice Sheet 49

1. 1.

   A wave has frequency 801 Hz and wavelength 2.97 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A population of 3,200 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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3. 3.

   Find the population standard deviation of: 10, 8, 10, 20, 17 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   Find the sum of the first 4 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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5. 5.

   A force of 60 N acts on an area of 3.9 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   A body starts at 7 m/s and accelerates at 1.9 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   Find the force needed to accelerate a 54 kg mass at 6.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A force of 87 N moves an object 28 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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10. 10.

    A force of 85 N moves an object 16 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    A population of 1,900 grows 2% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    Find the gravitational potential energy of a 18 kg object raised 24 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    A wave has frequency 69 Hz and wavelength 3.42 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A population of 3,300 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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15. 15.

    Find the momentum of a 11 kg object moving at 21 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

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

    Formula:Quadratic Formula

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

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17. 17.

    A body starts at 2 m/s and accelerates at 1.6 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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19. 19.

    A device runs at 144 V drawing 2.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the sum of the first 10 terms of an arithmetic series with first term a = 9 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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