ACT · Practice Sheet 38

1. 1.

   Physics

   Calculate the potential energy of a 30 kg object at a height of 45 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Physics

   Find the force required to accelerate a 49 kg mass at 11 m/s².

   Formula:Newton's Second Law (F = ma)

   $F = ma$

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3. 3.

   Physics

   Calculate the potential energy of a 18 kg object at a height of 16 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Physics

   Find the electrical power when 232 V drives a current of 13 A.

   Formula:Electrical Power

   $P = VI$

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5. 5.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 3.)

   Formula:Combinations

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

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6. 6.

   Mathematics

   For the quadratic 2x² − 8x + 0 = 0, find the sum and product of its roots.

   Formula:Vieta's Formulas (roots)

   $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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7. 7.

   Physics

   If 3,213 J of work is done in 37 s, find the power.

   Formula:Power

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

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8. 8.

   Quantitative Aptitude

   A vehicle covers 648 km in 9 hours. Find its average speed.

   Formula:Speed, Distance & Time

   $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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9. 9.

   Quantitative Aptitude

   Pipe A fills a tank in 7 hours and pipe B in 12 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

   $T = \dfrac{xy}{x+y}$

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10. 10.

    Quantitative Aptitude

    Find the average of these 8 numbers: 22, 50, 71, 59, 73, 89, 37, 40.

    Formula:Arithmetic Mean

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

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11. 11.

    Mathematics

    For the quadratic 2x² + 7x + 3 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)

    $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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12. 12.

    Physics

    An object starts at 13 m/s and accelerates at 10 m/s² for 9 s. Find its final velocity.

    Formula:Equation of Motion (v = u + at)

    $v = u + at$

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13. 13.

    Quantitative Aptitude

    A vehicle covers 280 km in 5 hours. Find its average speed.

    Formula:Speed, Distance & Time

    $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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14. 14.

    Quantitative Aptitude

    A can finish a job in 19 days and B in 8 days. Working together, how long will they take?

    Formula:Time & Work (combined)

    $T = \dfrac{xy}{x+y}$

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15. 15.

    Quantitative Aptitude

    Pipe A fills a tank in 5 hours and pipe B in 13 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

    $T = \dfrac{xy}{x+y}$

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16. 16.

    Quantitative Aptitude

    The sum of the ages of two people is 90 years, and one is 14 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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17. 17.

    Physics

    Find the kinetic energy of a 19 kg object moving at 3 m/s.

    Formula:Kinetic Energy

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

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18. 18.

    Quantitative Aptitude

    Find the simple interest on $18,000 at 10% per annum for 6 year(s).

    Formula:Simple Interest

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

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19. 19.

    Quantitative Aptitude

    Find the compound interest on $1,000 at 20% per annum compounded annually for 3 years.

    Formula:Compound Interest

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

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20. 20.

    Quantitative Aptitude

    What is 75% of 200?

    Formula:Percentage of a Number

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

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