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SAT · Practice Sheet 17

Sheet code: SAT-US-S17 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find the sum of the first 5 terms of a GP with first term 5 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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2.
Mathematics
Evaluate log base 10 of 100,000.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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3.
Mathematics
Find term number 4 of a geometric progression with first term 3 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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4.
Mathematics
For the quadratic 1x² + 3x − 2 = 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 $16,000 at 20% per annum compounded annually for 2 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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6.
Mathematics
Evaluate ∫ from 0 to 3 of 5x^2 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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7.
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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8.
Quantitative Aptitude
An item is bought for $500 and sold for $650. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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9.
Quantitative Aptitude
The marked price of an item is $200. After a 25% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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10.
Quantitative Aptitude
Find the simple interest on $47,000 at 4% per annum for 1 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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11.
Quantitative Aptitude
Find the HCF and LCM of 37 and 27.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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12.
Mathematics
Find the sum of the first 6 terms of a GP with first term 5 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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13.
Quantitative Aptitude
A can finish a job in 18 days and B in 17 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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14.
Mathematics
Find term number 6 of a geometric progression with first term 2 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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15.
Quantitative Aptitude
A value changes from 500 to 700. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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16.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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17.
Quantitative Aptitude
A can finish a job in 15 days and B in 10 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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18.
Mathematics
Find the sum of the first 21 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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19.
Quantitative Aptitude
A can finish a job in 15 days and B in 7 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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20.
Mathematics
Evaluate ∫ from 2 to 4 of 4x^2 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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