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SAT · Practice Sheet 15

Sheet code: SAT-US-S15 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
If f(x) = 3x³ + 4x² + 7x, find f′(5).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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2.
Mathematics
In an arithmetic progression with first term 18 and common difference 5, find term number 7.
Formula:AP nth Term
$a_n = a + (n-1)d$
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3.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 6?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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4.
Mathematics
For the quadratic 1x² + 6x + 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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5.
Quantitative Aptitude
Find the simple interest on $3,000 at 5% per annum for 3 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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6.
Quantitative Aptitude
Find the compound interest on $4,000 at 20% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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7.
Quantitative Aptitude
A vehicle covers 432 km in 9 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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8.
Mathematics
If f(x) = 3x³ + 2x² + 6x, find f′(1).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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9.
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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10.
Mathematics
Find the distance between the points (-6, -2) and (7, 0).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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11.
Quantitative Aptitude
Find the compound interest on $7,000 at 10% per annum compounded annually for 2 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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12.
Quantitative Aptitude
A value changes from 200 to 230. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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13.
Mathematics
If f(x) = 1x³ + 3x² + 6x, find f′(4).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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14.
Quantitative Aptitude
Pipe A fills a tank in 10 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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15.
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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16.
Quantitative Aptitude
Two varieties costing $16 and $82 per kg are mixed to give a mixture worth $58 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.
Mathematics
Find the sum of the first 6 terms of an AP with first term 4 and common difference 6.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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18.
Quantitative Aptitude
The marked price of an item is $1,000. After a 5% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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19.
Quantitative Aptitude
Divide $1,218 between two people in the ratio 7:7. 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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20.
Mathematics
Find the sum of the first 6 terms of a GP with first term 3 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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