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SAT · Practice Sheet 46

Sheet code: SAT-S46 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find the sum of the first 3 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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2.
Quantitative Aptitude
Pipe A fills a tank in 4 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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3.
Mathematics
Find term number 7 of a geometric progression with first term 1 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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4.
Quantitative Aptitude
Two varieties costing AED 29 and AED 62 per kg are mixed to give a mixture worth AED 45 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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5.
Quantitative Aptitude
A value changes from 900 to 1,350. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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6.
Quantitative Aptitude
Find the compound interest on AED 13,000 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
An item is bought for AED 500 and sold for AED 550. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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8.
Mathematics
If f(x) = 1x³ + 5x² + 3x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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9.
Mathematics
In an arithmetic progression with first term 15 and common difference 2, find term number 13.
Formula:AP nth Term
$a_n = a + (n-1)d$
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10.
Quantitative Aptitude
Find the average of these 6 numbers: 34, 22, 49, 55, 62, 57.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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11.
Mathematics
Evaluate log base 10 of 1,000,000.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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12.
Mathematics
Evaluate ∫ from 1 to 3 of 3x^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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13.
Mathematics
Find the binomial coefficient C(5, 2) — the coefficient of x^2 in (1 + x)^5.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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14.
Mathematics
In an arithmetic progression with first term 20 and common difference 6, find term number 21.
Formula:AP nth Term
$a_n = a + (n-1)d$
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15.
Quantitative Aptitude
A can finish a job in 6 days and B in 5 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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16.
Mathematics
For the quadratic 2x² + 5x + 8 = 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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17.
Mathematics
Find the sum of the first 23 terms of an AP with first term 18 and common difference 1.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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18.
Mathematics
Find the distance between the points (6, -2) and (-2, -2).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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19.
Quantitative Aptitude
Pipe A fills a tank in 10 hours and pipe B in 14 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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20.
Quantitative Aptitude
A vehicle covers 420 km in 5 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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