ACT · Practice Sheet 17

1. 1.

   Quantitative Aptitude

   A can finish a job in 14 days and B in 18 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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2. 2.

   Quantitative Aptitude

   What is 25% of 960?

   Formula:Percentage of a Number

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

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3. 3.

   Mathematics

   Find the slope of the line through (1, 5) and (2, -6).

   Formula:Slope of a Line

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

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4. 4.

   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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5. 5.

   Quantitative Aptitude

   The marked price of an item is $300. After a 40% discount, find the selling price.

   Formula:Discount & Selling Price

   $SP = MP\left(1-\dfrac{d}{100}\right)$

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6. 6.

   Physics

   If 4,684 J of work is done in 37 s, find the power.

   Formula:Power

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

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7. 7.

   Mathematics

   Find the binomial coefficient C(10, 4) — the coefficient of x^4 in (1 + x)^10.

   Formula:Binomial Coefficient

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

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8. 8.

   Physics

   Find the momentum of a 35 kg body moving at 26 m/s.

   Formula:Linear Momentum

   $p = mv$

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9. 9.

   Physics

   An object starts at 0 m/s and accelerates at 2 m/s² for 2 s. Find its final velocity.

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

   $v = u + at$

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10. 10.

    Quantitative Aptitude

    Find the average of these 5 numbers: 81, 23, 32, 87, 51.

    Formula:Arithmetic Mean

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

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11. 11.

    Quantitative Aptitude

    An item is bought for $200 and sold for $250. Find the profit percentage.

    Formula:Profit Percentage

    $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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12. 12.

    Quantitative Aptitude

    The marked price of an item is $800. After a 20% discount, find the selling price.

    Formula:Discount & Selling Price

    $SP = MP\left(1-\dfrac{d}{100}\right)$

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13. 13.

    Mathematics

    Find term number 5 of a geometric progression with first term 3 and common ratio 3.

    Formula:GP nth Term

    $a_n = a\,r^{\,n-1}$

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14. 14.

    Physics

    A force of 699 N acts on an area of 9 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    Quantitative Aptitude

    The sum of the ages of two people is 27 years, and one is 5 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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16. 16.

    Mathematics

    Find the slope of the line through (6, -8) and (-7, -7).

    Formula:Slope of a Line

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

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17. 17.

    Mathematics

    Find the distance between the points (-3, -5) and (-7, -1).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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18. 18.

    Quantitative Aptitude

    Find the HCF and LCM of 35 and 35.

    Formula:LCM & HCF

    $\text{LCM}\times\text{HCF} = a\times b$

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19. 19.

    Quantitative Aptitude

    A vehicle covers 236 km in 4 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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20. 20.

    Physics

    A constant force of 92 N moves an object 43 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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