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SAT · Practice Sheet 12

Sheet code: SAT-US-S12 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find the sum of the first 12 terms of an AP with first term 20 and common difference 9.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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2.
Quantitative Aptitude
An item is bought for $500 and sold for $600. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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3.
Quantitative Aptitude
The marked price of an item is $1,200. After a 30% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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4.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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5.
Mathematics
Evaluate ∫ from 0 to 3 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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6.
Mathematics
Find the distance between the points (-3, 0) and (6, -3).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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7.
Quantitative Aptitude
Find the simple interest on $40,000 at 8% per annum for 4 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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8.
Quantitative Aptitude
Find the average of these 10 numbers: 45, 26, 25, 55, 61, 58, 35, 88, 41, 28.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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9.
Mathematics
If f(x) = 5x³ + 6x² + 7x, find f′(5).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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10.
Quantitative Aptitude
Two varieties costing $17 and $62 per kg are mixed to give a mixture worth $42 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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11.
Quantitative Aptitude
The sum of the ages of two people is 23 years, and one is 3 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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12.
Quantitative Aptitude
Divide $2,150 between two people in the ratio 3:7. 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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13.
Quantitative Aptitude
A value changes from 800 to 600. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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14.
Mathematics
Find the sum of the first 5 terms of an AP with first term 2 and common difference 9.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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15.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 8?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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16.
Quantitative Aptitude
What is 40% of 1,180?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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17.
Quantitative Aptitude
Find the average of these 6 numbers: 89, 47, 87, 69, 86, 48.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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18.
Quantitative Aptitude
Two varieties costing $36 and $63 per kg are mixed to give a mixture worth $43 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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19.
Quantitative Aptitude
A value changes from 700 to 665. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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20.
Mathematics
Evaluate ∫ from 0 to 3 of 2x^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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