SAT · Practice Sheet 30

1. 1.

   Quantitative Aptitude

   A vehicle covers 400 km in 8 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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2. 2.

   Mathematics

   Find the sum of the first 3 terms of a GP with first term 6 and common ratio 2.

   Formula:GP Sum of n Terms

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

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3. 3.

   Mathematics

   If f(x) = 3x³ + 5x² + 5x, find f′(4).

   Formula:Derivative of a Polynomial

   $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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4. 4.

   Mathematics

   Find the distance between the points (2, -4) and (-6, -1).

   Formula:Distance Between Two Points

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

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5. 5.

   Quantitative Aptitude

   Pipe A fills a tank in 11 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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6. 6.

   Mathematics

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

   Formula:Distance Between Two Points

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

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7. 7.

   Mathematics

   Evaluate ∫ from 2 to 3 of 1x^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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8. 8.

   Quantitative Aptitude

   An item is bought for $300 and sold for $330. Find the profit percentage.

   Formula:Profit Percentage

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

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9. 9.

   Mathematics

   Find the sum of the first 21 terms of an AP with first term 11 and common difference 8.

   Formula:AP Sum of n Terms

   $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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10. 10.

    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 2.)

    Formula:Permutations

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

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11. 11.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 3.)

    Formula:Combinations

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

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12. 12.

    Quantitative Aptitude

    Two varieties costing $29 and $83 per kg are mixed to give a mixture worth $38 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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13. 13.

    Quantitative Aptitude

    Divide $1,470 between two people in the ratio 4:6. 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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14. 14.

    Mathematics

    Find the distance between the points (2, -8) and (5, -3).

    Formula:Distance Between Two Points

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

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15. 15.

    Quantitative Aptitude

    A value changes from 200 to 250. Find the percentage increase.

    Formula:Percentage Change

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

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16. 16.

    Quantitative Aptitude

    A can finish a job in 13 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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17. 17.

    Mathematics

    Find the slope of the line through (2, 4) and (6, 7).

    Formula:Slope of a Line

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

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18. 18.

    Mathematics

    In an arithmetic progression with first term 6 and common difference 5, find term number 19.

    Formula:AP nth Term

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

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19. 19.

    Quantitative Aptitude

    Pipe A fills a tank in 12 hours and pipe B in 11 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

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20. 20.

    Quantitative Aptitude

    The marked price of an item is $800. After a 15% discount, find the selling price.

    Formula:Discount & Selling Price

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

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