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ACT · Practice Sheet 13

Sheet code: ACT-S13 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
For the quadratic 2x² + 7x + 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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2.
Quantitative Aptitude
What is 10% of 380?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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3.
Mathematics
Find the slope of the line through (-8, -8) and (3, -8).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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4.
Mathematics
Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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5.
Quantitative Aptitude
Two varieties costing $31 and $66 per kg are mixed to give a mixture worth $36 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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6.
Quantitative Aptitude
A value changes from 700 to 525. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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7.
Quantitative Aptitude
A can finish a job in 15 days and B in 9 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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8.
Physics
Find the electrical power when 155 V drives a current of 5 A.
Formula:Electrical Power
$P = VI$
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9.
Quantitative Aptitude
What is 25% of 120?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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10.
Physics
A body moving at 10 m/s accelerates at 8 m/s² for 6 s. Find the distance travelled.
Formula:Equation of Motion (s = ut + ½at²)
$s = ut + \tfrac{1}{2}at^{2}$
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11.
Quantitative Aptitude
An item is bought for $600 and sold for $690. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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12.
Quantitative Aptitude
The marked price of an item is $200. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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13.
Physics
Find the kinetic energy of a 8 kg object moving at 4 m/s.
Formula:Kinetic Energy
$KE = \tfrac{1}{2}mv^{2}$
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14.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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15.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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16.
Mathematics
Find the binomial coefficient C(9, 2) — the coefficient of x^2 in (1 + x)^9.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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17.
Mathematics
Evaluate log base 3 of 27.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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18.
Physics
An object starts at 6 m/s and accelerates at 8 m/s² for 4 s. Find its final velocity.
Formula:Equation of Motion (v = u + at)
$v = u + at$
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19.
Mathematics
Find the sum of the first 13 terms of an AP with first term 8 and common difference 1.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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20.
Mathematics
Find term number 4 of a geometric progression with first term 2 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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