ACT · Practice Sheet 40

1. 1.

   Physics

   Find the density of an object with mass 134 g and volume 39 cm³.

   Formula:Density

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

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2. 2.

   Physics

   A body moving at 14 m/s accelerates at 8 m/s² for 9 s. Find the distance travelled.

   Formula:Equation of Motion (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^{2}$

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3. 3.

   Physics

   If 2,270 J of work is done in 6 s, find the power.

   Formula:Power

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

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4. 4.

   Quantitative Aptitude

   A can finish a job in 11 days and B in 20 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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5. 5.

   Mathematics

   Find the binomial coefficient C(7, 3) — the coefficient of x^3 in (1 + x)^7.

   Formula:Binomial Coefficient

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

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6. 6.

   Physics

   A force of 239 N acts on an area of 24 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Physics

   Find the force required to accelerate a 32 kg mass at 17 m/s².

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

   $F = ma$

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8. 8.

   Quantitative Aptitude

   Pipe A fills a tank in 4 hours and pipe B in 5 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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9. 9.

   Quantitative Aptitude

   A invests $10,000 and B invests $4,000 for the same period. If the total profit is $15,000, find A's share.

   Formula:Partnership (profit share)

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

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10. 10.

    Quantitative Aptitude

    A value changes from 300 to 330. Find the percentage increase.

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$

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11. 11.

    Mathematics

    Find the slope of the line through (-5, -7) and (6, -5).

    Formula:Slope of a Line

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

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12. 12.

    Mathematics

    For the quadratic 2x² + 8x + 1 = 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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13. 13.

    Physics

    Find the force required to accelerate a 18 kg mass at 16 m/s².

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

    $F = ma$

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14. 14.

    Physics

    Calculate the potential energy of a 38 kg object at a height of 18 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Quantitative Aptitude

    What is 15% of 140?

    Formula:Percentage of a Number

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

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16. 16.

    Quantitative Aptitude

    Two varieties costing $33 and $76 per kg are mixed to give a mixture worth $55 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)

    $\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$

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17. 17.

    Quantitative Aptitude

    A invests $2,000 and B invests $7,000 for the same period. If the total profit is $9,000, find A's share.

    Formula:Partnership (profit share)

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

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18. 18.

    Mathematics

    Find the sum of the first 3 terms of a GP with first term 1 and common ratio 3.

    Formula:GP Sum of n Terms

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

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19. 19.

    Quantitative Aptitude

    The marked price of an item is $600. After a 40% discount, find the selling price.

    Formula:Discount & Selling Price

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

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20. 20.

    Physics

    If 4,175 J of work is done in 4 s, find the power.

    Formula:Power

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

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