SAT · Practice Sheet 45

1. 1.

   Mathematics

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

   Formula:Slope of a Line

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

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2. 2.

   Mathematics

   Evaluate log base 5 of 125.

   Formula:Logarithm Evaluation

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

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3. 3.

   Quantitative Aptitude

   What is 10% of 520?

   Formula:Percentage of a Number

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

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4. 4.

   Quantitative Aptitude

   A value changes from 200 to 260. Find the percentage increase.

   Formula:Percentage Change

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

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5. 5.

   Mathematics

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

   Formula:Slope of a Line

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

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6. 6.

   Quantitative Aptitude

   Find the HCF and LCM of 28 and 23.

   Formula:LCM & HCF

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

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7. 7.

   Mathematics

   Find the sum of the first 22 terms of an AP with first term 20 and common difference 10.

   Formula:AP Sum of n Terms

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

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8. 8.

   Quantitative Aptitude

   A invests $10,000 and B invests $6,000 for the same period. If the total profit is $14,000, find A's share.

   Formula:Partnership (profit share)

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

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9. 9.

   Mathematics

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

   Formula:Slope of a Line

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

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10. 10.

    Mathematics

    In an arithmetic progression with first term 3 and common difference 6, find term number 17.

    Formula:AP nth Term

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

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11. 11.

    Quantitative Aptitude

    The marked price of an item is $600. After a 20% discount, find the selling price.

    Formula:Discount & Selling Price

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

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12. 12.

    Quantitative Aptitude

    Find the average of these 8 numbers: 31, 51, 49, 82, 83, 30, 23, 73.

    Formula:Arithmetic Mean

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

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13. 13.

    Quantitative Aptitude

    Find the simple interest on $48,000 at 6% per annum for 5 year(s).

    Formula:Simple Interest

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

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14. 14.

    Quantitative Aptitude

    A vehicle covers 344 km in 4 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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15. 15.

    Quantitative Aptitude

    A value changes from 200 to 300. Find the percentage increase.

    Formula:Percentage Change

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

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16. 16.

    Mathematics

    Find the distance between the points (7, -8) and (-8, 3).

    Formula:Distance Between Two Points

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

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17. 17.

    Quantitative Aptitude

    A value changes from 500 to 375. Find the percentage decrease.

    Formula:Percentage Change

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

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18. 18.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)

    Formula:Permutations

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

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19. 19.

    Mathematics

    Evaluate log base 3 of 729.

    Formula:Logarithm Evaluation

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

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20. 20.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 3.)

    Formula:Combinations

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

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