ACT · Practice Sheet 27

1. 1.

   Quantitative Aptitude

   An item is bought for $600 and sold for $900. Find the profit percentage.

   Formula:Profit Percentage

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

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2. 2.

   Mathematics

   Find term number 6 of a geometric progression with first term 3 and common ratio 2.

   Formula:GP nth Term

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

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3. 3.

   Physics

   Calculate the potential energy of a 30 kg object at a height of 3 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Quantitative Aptitude

   Find the HCF and LCM of 19 and 32.

   Formula:LCM & HCF

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

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5. 5.

   Mathematics

   Find the distance between the points (3, 3) and (3, 2).

   Formula:Distance Between Two Points

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

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6. 6.

   Mathematics

   Find the slope of the line through (7, -1) and (4, 0).

   Formula:Slope of a Line

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

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7. 7.

   Quantitative Aptitude

   A vehicle covers 513 km in 9 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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8. 8.

   Mathematics

   Evaluate ∫ from 1 to 4 of 4x^3 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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9. 9.

   Quantitative Aptitude

   The marked price of an item is $1,300. After a 50% discount, find the selling price.

   Formula:Discount & Selling Price

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

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10. 10.

    Quantitative Aptitude

    A can finish a job in 16 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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11. 11.

    Physics

    A force of 896 N acts on an area of 46 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    Quantitative Aptitude

    Find the HCF and LCM of 18 and 26.

    Formula:LCM & HCF

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

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13. 13.

    Quantitative Aptitude

    An item is bought for $800 and sold for $1,000. Find the profit percentage.

    Formula:Profit Percentage

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

    View formula →
14. 14.

    Mathematics

    Evaluate ∫ from 1 to 4 of 3x^1 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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15. 15.

    Quantitative Aptitude

    An item is bought for $900 and sold for $1,260. Find the profit percentage.

    Formula:Profit Percentage

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

    View formula →
16. 16.

    Physics

    A body moving at 2 m/s accelerates at 4 m/s² for 3 s. Find the distance travelled.

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

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

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17. 17.

    Quantitative Aptitude

    Find the average of these 6 numbers: 60, 22, 66, 30, 70, 47.

    Formula:Arithmetic Mean

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

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18. 18.

    Quantitative Aptitude

    A value changes from 700 to 595. Find the percentage decrease.

    Formula:Percentage Change

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

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19. 19.

    Quantitative Aptitude

    An item is bought for $200 and sold for $240. Find the profit percentage.

    Formula:Profit Percentage

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

    View formula →
20. 20.

    Physics

    Find the momentum of a 4 kg body moving at 9 m/s.

    Formula:Linear Momentum

    $p = mv$

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