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ACT · Practice Sheet 45

Sheet code: ACT-S45 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
An item is bought for $400 and sold for $520. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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2.
Mathematics
Find the sum of the first 7 terms of a GP with first term 2 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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3.
Mathematics
Find the binomial coefficient C(10, 2) — the coefficient of x^2 in (1 + x)^10.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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4.
Mathematics
Evaluate ∫ from 0 to 4 of 1x^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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5.
Quantitative Aptitude
A invests $4,000 and B invests $7,000 for the same period. If the total profit is $19,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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6.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 5?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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7.
Physics
Find the momentum of a 26 kg body moving at 40 m/s.
Formula:Linear Momentum
$p = mv$
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8.
Quantitative Aptitude
A invests $2,000 and B invests $10,000 for the same period. If the total profit is $5,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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9.
Mathematics
For the quadratic 5x² − 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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10.
Mathematics
Find term number 3 of a geometric progression with first term 6 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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11.
Quantitative Aptitude
What is 60% of 580?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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12.
Physics
A force of 93 N acts on an area of 7 m². Find the pressure.
Formula:Pressure
$P = \dfrac{F}{A}$
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13.
Mathematics
For the quadratic 5x² + 1x − 5 = 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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14.
Quantitative Aptitude
A value changes from 300 to 225. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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15.
Physics
Find the force required to accelerate a 14 kg mass at 6 m/s².
Formula:Newton's Second Law (F = ma)
$F = ma$
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16.
Mathematics
Find the distance between the points (0, 0) and (5, -4).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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17.
Physics
A constant force of 72 N moves an object 27 m in the direction of the force. Calculate the work done.
Formula:Work Done
$W = F\,d$
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18.
Mathematics
For the quadratic 1x² + 3x + 0 = 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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19.
Quantitative Aptitude
What is 15% of 700?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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20.
Quantitative Aptitude
The sum of the ages of two people is 86 years, and one is 20 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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