United States · Grade 11 · Practice Sheet 42

1. 1.

   A force of 80 N moves an object 9 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   $1,600 is invested at 6% compound interest per annum for 4 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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3. 3.

   A wave has frequency 747 Hz and wavelength 3.39 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A 25 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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5. 5.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 6 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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6. 6.

   A wave has frequency 744 Hz and wavelength 4.76 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A 8 kg object moves at 7 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   Find the force needed to accelerate a 56 kg mass at 2.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Find the population standard deviation of: 16, 10, 6, 2, 14 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    Find the gravitational potential energy of a 12 kg object raised 14 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A device runs at 91 V drawing 4.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A population of 7,100 grows 2% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    A 40 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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14. 14.

    Find the sum of the first 4 terms of a geometric series with first term a = 2 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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15. 15.

    Find the population standard deviation of: 14, 8, 6, 2, 2 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    Find the force needed to accelerate a 26 kg mass at 8.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    Find the sum of the first 8 terms of a geometric series with first term a = 6 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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18. 18.

    $2,400 is invested at 3% compound interest per annum for 4 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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19. 19.

    In a triangle, a = 5, b = 13 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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20. 20.

    Solve using the quadratic formula: x² − 11x + 30 = 0.

    Formula:Quadratic Formula

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

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