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SAT · Practice Sheet 6

Sheet code: SAT-US-S06 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Evaluate ∫ from 1 to 5 of 4x^1 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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2.
Quantitative Aptitude
An item is bought for $200 and sold for $300. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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3.
Mathematics
Find the sum of the first 5 terms of an AP with first term 8 and common difference 9.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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4.
Mathematics
For the quadratic 1x² + 5x + 5 = 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 compound interest on $14,000 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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6.
Mathematics
Find the sum of the first 18 terms of an AP with first term 10 and common difference 3.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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7.
Mathematics
If f(x) = 5x³ + 3x² + 9x, find f′(3).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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8.
Mathematics
Find the sum of the first 16 terms of an AP with first term 12 and common difference 5.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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9.
Quantitative Aptitude
An item is bought for $400 and sold for $440. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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10.
Quantitative Aptitude
Find the simple interest on $5,000 at 8% per annum for 6 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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11.
Quantitative Aptitude
What is 75% of 260?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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12.
Quantitative Aptitude
A vehicle covers 162 km in 3 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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13.
Quantitative Aptitude
Pipe A fills a tank in 6 hours and pipe B in 9 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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14.
Quantitative Aptitude
Find the compound interest on $20,000 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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15.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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16.
Quantitative Aptitude
Find the simple interest on $45,000 at 4% per annum for 2 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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17.
Mathematics
Evaluate log base 3 of 9.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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18.
Quantitative Aptitude
Find the average of these 10 numbers: 44, 45, 49, 67, 32, 71, 41, 28, 37, 67.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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19.
Mathematics
Find term number 6 of a geometric progression with first term 6 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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20.
Mathematics
Find the sum of the first 4 terms of a GP with first term 6 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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