SAT · Practice Sheet 31

1. 1.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 4.)

   Formula:Combinations

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

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2. 2.

   Mathematics

   Find the distance between the points (-5, -7) and (6, 6).

   Formula:Distance Between Two Points

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

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3. 3.

   Mathematics

   Evaluate ∫ from 0 to 5 of 3x^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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4. 4.

   Quantitative Aptitude

   A vehicle covers 252 km in 7 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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5. 5.

   Quantitative Aptitude

   Find the average of these 8 numbers: 84, 81, 34, 41, 89, 48, 52, 59.

   Formula:Arithmetic Mean

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

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6. 6.

   Mathematics

   Find the slope of the line through (-1, 7) and (-7, -2).

   Formula:Slope of a Line

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

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7. 7.

   Quantitative Aptitude

   Divide AED 837 between two people in the ratio 7:2. 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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8. 8.

   Mathematics

   If f(x) = 2x³ + 4x² + 3x, find f′(4).

   Formula:Derivative of a Polynomial

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

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9. 9.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 5?

   Formula:Probability (two dice)

   $P = \dfrac{\text{favourable}}{\text{total}}$

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10. 10.

    Quantitative Aptitude

    What is 15% of 80?

    Formula:Percentage of a Number

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

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11. 11.

    Quantitative Aptitude

    Find the simple interest on AED 43,000 at 6% per annum for 3 year(s).

    Formula:Simple Interest

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

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12. 12.

    Mathematics

    Evaluate ∫ from 1 to 4 of 4x^2 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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13. 13.

    Mathematics

    Evaluate log base 3 of 243.

    Formula:Logarithm Evaluation

    $\log_{b}(b^{k}) = k$

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14. 14.

    Quantitative Aptitude

    A can finish a job in 12 days and B in 19 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

    A vehicle covers 528 km in 6 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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16. 16.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 3.)

    Formula:Permutations

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

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17. 17.

    Mathematics

    Evaluate log base 10 of 100,000.

    Formula:Logarithm Evaluation

    $\log_{b}(b^{k}) = k$

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18. 18.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 5 and common ratio 2.

    Formula:GP Sum of n Terms

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

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19. 19.

    Mathematics

    Find term number 7 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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20. 20.

    Quantitative Aptitude

    A value changes from 900 to 720. Find the percentage decrease.

    Formula:Percentage Change

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

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