ACT · Practice Sheet 21

1. 1.

   Physics

   If 3,877 J of work is done in 10 s, find the power.

   Formula:Power

   $P = \dfrac{W}{t}$

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2. 2.

   Mathematics

   Find the slope of the line through (-6, 6) and (6, -8).

   Formula:Slope of a Line

   $m = \dfrac{y_2-y_1}{x_2-x_1}$

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3. 3.

   Physics

   A force of 260 N acts on an area of 11 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   Physics

   If 2,809 J of work is done in 45 s, find the power.

   Formula:Power

   $P = \dfrac{W}{t}$

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5. 5.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 6?

   Formula:Probability (two dice)

   $P = \dfrac{\text{favourable}}{\text{total}}$

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6. 6.

   Physics

   A constant force of 187 N moves an object 29 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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7. 7.

   Physics

   Find the kinetic energy of a 9 kg object moving at 26 m/s.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2}mv^{2}$

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8. 8.

   Physics

   Calculate the potential energy of a 9 kg object at a height of 42 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   Mathematics

   Find the slope of the line through (0, -5) and (-2, 5).

   Formula:Slope of a Line

   $m = \dfrac{y_2-y_1}{x_2-x_1}$

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10. 10.

    Quantitative Aptitude

    What is 10% of 1,120?

    Formula:Percentage of a Number

    $\text{Value} = \dfrac{P}{100}\times N$

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11. 11.

    Quantitative Aptitude

    Divide $564 between two people in the ratio 3:3. How much does each receive?

    Formula:Sharing in a Ratio

    $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

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12. 12.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 3.)

    Formula:Combinations

    $^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$

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13. 13.

    Quantitative Aptitude

    A invests $4,000 and B invests $9,000 for the same period. If the total profit is $24,000, find A's share.

    Formula:Partnership (profit share)

    $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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14. 14.

    Quantitative Aptitude

    Find the simple interest on $14,000 at 12% per annum for 5 year(s).

    Formula:Simple Interest

    $SI = \dfrac{P\times R\times T}{100}$

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15. 15.

    Quantitative Aptitude

    Divide $1,008 between two people in the ratio 2:5. How much does each receive?

    Formula:Sharing in a Ratio

    $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

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16. 16.

    Quantitative Aptitude

    Find the average of these 10 numbers: 42, 76, 36, 51, 60, 90, 47, 78, 61, 27.

    Formula:Arithmetic Mean

    $\bar{x} = \dfrac{\sum x}{n}$

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17. 17.

    Mathematics

    In an arithmetic progression with first term 3 and common difference 7, find term number 21.

    Formula:AP nth Term

    $a_n = a + (n-1)d$

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18. 18.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

    Formula:Probability (two dice)

    $P = \dfrac{\text{favourable}}{\text{total}}$

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19. 19.

    Mathematics

    Evaluate ∫ from 2 to 3 of 4x^2 dx.

    Formula:Definite Integral of a Power

    $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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20. 20.

    Quantitative Aptitude

    Find the average of these 5 numbers: 69, 54, 46, 29, 64.

    Formula:Arithmetic Mean

    $\bar{x} = \dfrac{\sum x}{n}$

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