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SAT · Practice Sheet 25

Sheet code: SAT-US-S25 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Divide $1,666 between two people in the ratio 2:5. 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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2.
Mathematics
If f(x) = 1x³ + 2x² + 2x, find f′(5).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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3.
Quantitative Aptitude
Two varieties costing $31 and $61 per kg are mixed to give a mixture worth $39 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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4.
Quantitative Aptitude
A value changes from 700 to 490. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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5.
Quantitative Aptitude
Find the average of these 6 numbers: 36, 36, 88, 74, 24, 42.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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6.
Mathematics
Find the slope of the line through (2, -1) and (8, 0).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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7.
Mathematics
If f(x) = 1x³ + 4x² + 8x, find f′(1).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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8.
Quantitative Aptitude
A invests $9,000 and B invests $10,000 for the same period. If the total profit is $33,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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9.
Quantitative Aptitude
An item is bought for $300 and sold for $375. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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10.
Mathematics
Find the sum of the first 7 terms of an AP with first term 3 and common difference 3.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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11.
Quantitative Aptitude
The marked price of an item is $200. After a 5% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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12.
Mathematics
Find the sum of the first 25 terms of an AP with first term 2 and common difference 6.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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13.
Mathematics
Evaluate log base 3 of 243.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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14.
Quantitative Aptitude
A vehicle covers 696 km in 8 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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15.
Quantitative Aptitude
What is 60% of 460?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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16.
Quantitative Aptitude
Two varieties costing $17 and $80 per kg are mixed to give a mixture worth $66 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.
Quantitative Aptitude
The marked price of an item is $700. After a 10% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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18.
Mathematics
If f(x) = 2x³ + 2x² + 9x, find f′(4).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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19.
Mathematics
For the quadratic 2x² + 8x + 0 = 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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20.
Mathematics
Find the binomial coefficient C(7, 2) — the coefficient of x^2 in (1 + x)^7.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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