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SAT · Practice Sheet 40

Sheet code: SAT-S40 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Evaluate log base 3 of 27.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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2.
Mathematics
Find the sum of the first 18 terms of an AP with first term 20 and common difference 5.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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3.
Mathematics
Find the binomial coefficient C(6, 4) — the coefficient of x^4 in (1 + x)^6.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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4.
Mathematics
Find the distance between the points (6, 2) and (-6, 1).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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5.
Mathematics
If f(x) = 4x³ + 4x² + 6x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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6.
Mathematics
Find the sum of the first 7 terms of a GP with first term 1 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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7.
Mathematics
Find the sum of the first 13 terms of an AP with first term 8 and common difference 6.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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8.
Quantitative Aptitude
Find the HCF and LCM of 21 and 13.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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9.
Mathematics
Find the sum of the first 7 terms of an AP with first term 14 and common difference 7.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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10.
Quantitative Aptitude
A invests AED 6,000 and B invests AED 6,000 for the same period. If the total profit is AED 40,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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11.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 10?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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12.
Quantitative Aptitude
Two varieties costing AED 33 and AED 95 per kg are mixed to give a mixture worth AED 46 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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13.
Quantitative Aptitude
An item is bought for AED 600 and sold for AED 660. 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 AED 1,300. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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15.
Quantitative Aptitude
Pipe A fills a tank in 15 hours and pipe B in 7 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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16.
Quantitative Aptitude
The sum of the ages of two people is 81 years, and one is 5 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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17.
Quantitative Aptitude
The marked price of an item is AED 300. After a 40% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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18.
Mathematics
Find the sum of the first 6 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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19.
Mathematics
Evaluate log base 5 of 25.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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20.
Mathematics
For the quadratic 3x² − 3x + 4 = 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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