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SAT · Practice Sheet 37

Sheet code: SAT-US-S37 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
For the quadratic 5x² + 2x + 3 = 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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2.
Quantitative Aptitude
Find the HCF and LCM of 17 and 36.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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3.
Quantitative Aptitude
A invests $2,000 and B invests $7,000 for the same period. If the total profit is $32,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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4.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 7?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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5.
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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6.
Mathematics
For the quadratic 3x² + 4x − 1 = 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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7.
Mathematics
Find the distance between the points (-2, 4) and (-6, 7).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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8.
Quantitative Aptitude
A can finish a job in 9 days and B in 6 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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9.
Quantitative Aptitude
A value changes from 600 to 750. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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10.
Mathematics
In an arithmetic progression with first term 15 and common difference 7, find term number 12.
Formula:AP nth Term
$a_n = a + (n-1)d$
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11.
Mathematics
Find the sum of the first 4 terms of a GP with first term 1 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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12.
Quantitative Aptitude
A invests $7,000 and B invests $3,000 for the same period. If the total profit is $14,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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13.
Quantitative Aptitude
An item is bought for $600 and sold for $720. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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14.
Quantitative Aptitude
The marked price of an item is $500. After a 40% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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15.
Quantitative Aptitude
What is 50% of 540?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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16.
Mathematics
Evaluate ∫ from 1 to 5 of 5x^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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17.
Mathematics
Evaluate log base 3 of 243.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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18.
Quantitative Aptitude
Divide $536 between two people in the ratio 3:5. 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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19.
Quantitative Aptitude
Find the simple interest on $6,000 at 5% per annum for 6 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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20.
Quantitative Aptitude
Pipe A fills a tank in 7 hours and pipe B in 5 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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