Singapore · Grade 11 · Practice Sheet 38

1. 1.

   A wave has frequency 761 Hz and wavelength 0.91 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A cylinder has radius 11 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   A wave has frequency 859 Hz and wavelength 3.09 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A 36 kg object moves at 22 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   A force of 42 N moves an object 29 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   In a triangle, a = 11, b = 17 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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7. 7.

   Find the sum of the first 5 terms of a geometric series with first term a = 6 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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8. 8.

   A population of 2,800 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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9. 9.

   A 32 kg object moves at 12 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

    A cone has base radius 10 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    A wave has frequency 481 Hz and wavelength 4.85 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Find the population standard deviation of: 17, 20, 13, 19, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    A current of 6.8 A flows through a 25 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A force of 179 N acts on an area of 0.7 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    A wave has frequency 887 Hz and wavelength 3.38 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Solve using the quadratic formula: x² − 5x + 6 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    Find the population standard deviation of: 18, 13, 17, 5, 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 population of 1,300 grows 10% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    A force of 73 N acts on an area of 3.3 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    Find the gravitational potential energy of a 22 kg object raised 5 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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