United States · Grade 11 · Practice Sheet 39

1. 1.

   Find the sum of the first 7 terms of a geometric series with first term a = 4 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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2. 2.

   A device runs at 16 V drawing 5.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   $700 is invested at 4% compound interest per annum for 5 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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4. 4.

   A wave has frequency 812 Hz and wavelength 2.21 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   In a triangle, a = 5, b = 9 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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6. 6.

   A wave has frequency 452 Hz and wavelength 2.79 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the population standard deviation of: 3, 9, 9, 19, 14 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   Two masses 2,200 kg and 790 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 momentum of a 55 kg object moving at 21 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A wave has frequency 110 Hz and wavelength 0.83 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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12. 12.

    A 40 kg object moves at 17 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    A cylinder has radius 7 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.

    An object has mass 22 g and volume 22 cm³. Find its density.

    Formula:Density

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

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15. 15.

    Find the gravitational potential energy of a 27 kg object raised 32 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    Find the momentum of a 56 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    $1,100 is invested at 5% compound interest per annum for 5 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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18. 18.

    Find the gravitational potential energy of a 43 kg object raised 35 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A force of 161 N acts on an area of 8.6 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    $2,800 is invested at 5% compound interest per annum for 2 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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