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A-Level Maths · Practice Sheet 46

Sheet code: A-LEVEL-MATHS-S46 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
The marked price of an item is £1,300. After a 40% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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2.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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3.
Quantitative Aptitude
Two varieties costing £23 and £63 per kg are mixed to give a mixture worth £32 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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4.
Mathematics
If f(x) = 3x³ + 3x² + 3x, find f′(1).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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5.
Quantitative Aptitude
The marked price of an item is £1,100. After a 20% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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6.
Quantitative Aptitude
A value changes from 600 to 780. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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7.
Mathematics
If f(x) = 1x³ + 5x² + 5x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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8.
Quantitative Aptitude
Pipe A fills a tank in 8 hours and pipe B in 12 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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9.
Quantitative Aptitude
Find the average of these 5 numbers: 38, 61, 50, 83, 87.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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10.
Mathematics
Find the distance between the points (8, 6) and (4, -5).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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11.
Quantitative Aptitude
The sum of the ages of two people is 80 years, and one is 6 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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12.
Mathematics
In an arithmetic progression with first term 10 and common difference 2, find term number 21.
Formula:AP nth Term
$a_n = a + (n-1)d$
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13.
Mathematics
Find the sum of the first 6 terms of an AP with first term 6 and common difference 4.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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14.
Mathematics
Find term number 6 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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15.
Quantitative Aptitude
Find the HCF and LCM of 34 and 37.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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16.
Quantitative Aptitude
What is 75% of 420?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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17.
Quantitative Aptitude
A invests £8,000 and B invests £8,000 for the same period. If the total profit is £30,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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18.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 6?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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19.
Mathematics
Find the sum of the first 3 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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20.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 6?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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