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A-Level Maths · Practice Sheet 37

Sheet code: A-LEVEL-MATHS-S37 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Find the average of these 8 numbers: 25, 51, 69, 65, 80, 59, 57, 31.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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2.
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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3.
Quantitative Aptitude
The sum of the ages of two people is 75 years, and one is 13 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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4.
Quantitative Aptitude
What is 10% of 340?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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5.
Quantitative Aptitude
The marked price of an item is £1,300. After a 50% 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 vehicle covers 616 km in 8 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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7.
Mathematics
Find term number 6 of a geometric progression with first term 4 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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8.
Quantitative Aptitude
A invests £2,000 and B invests £5,000 for the same period. If the total profit is £37,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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9.
Quantitative Aptitude
Pipe A fills a tank in 13 hours and pipe B in 4 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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10.
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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11.
Mathematics
Evaluate log base 10 of 10,000.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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12.
Quantitative Aptitude
What is 50% of 740?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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13.
Quantitative Aptitude
Pipe A fills a tank in 8 hours and pipe B in 3 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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14.
Quantitative Aptitude
A value changes from 500 to 450. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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15.
Quantitative Aptitude
Find the compound interest on £15,000 at 20% per annum compounded annually for 2 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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16.
Quantitative Aptitude
The marked price of an item is £900. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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17.
Mathematics
For the quadratic 4x² − 7x − 7 = 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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18.
Mathematics
In an arithmetic progression with first term 15 and common difference 2, find term number 9.
Formula:AP nth Term
$a_n = a + (n-1)d$
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19.
Mathematics
Evaluate log base 2 of 64.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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20.
Quantitative Aptitude
Find the simple interest on £17,000 at 5% per annum for 3 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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