Chile · Grado 11 · Practice Sheet 13

1. 1.

   An object has mass 253.5 g and volume 39 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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2. 2.

   Find the gravitational potential energy of a 3 kg object raised 32 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   A cylinder has radius 12 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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4. 4.

   An object has mass 220.5 g and volume 45 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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5. 5.

   A device runs at 144 V drawing 8.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   Find the momentum of a 10 kg object moving at 2 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   In a triangle, a = 15, b = 17 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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8. 8.

   A 38 kg object moves at 8 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   Find the momentum of a 28 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A force of 326 N acts on an area of 9.7 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A wave has frequency 258 Hz and wavelength 0.38 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Find the sum of the first 5 terms of a geometric series with first term a = 2 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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13. 13.

    A cylinder has radius 6 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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14. 14.

    Find the population standard deviation of: 12, 11, 3, 14, 18 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    A population of 6,300 grows 8% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    $3,200 is invested at 6% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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17. 17.

    A wave has frequency 368 Hz and wavelength 2.51 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Find the momentum of a 23 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A right-angled triangle has legs of 5 cm and 19 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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20. 20.

    A force of 453 N acts on an area of 4.4 m². Find the pressure.

    Formula:Pressure

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

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