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A-Level Maths · Practice Sheet 6

Sheet code: A-LEVEL-MATHS-S06 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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2.
Quantitative Aptitude
An item is bought for £900 and sold for £1,350. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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3.
Quantitative Aptitude
The marked price of an item is £1,000. After a 40% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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4.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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5.
Quantitative Aptitude
Divide £2,106 between two people in the ratio 5:4. How much does each receive?
Formula:Sharing in a Ratio
$\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$
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6.
Mathematics
If f(x) = 5x³ + 4x² + 5x, find f′(1).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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7.
Quantitative Aptitude
Find the HCF and LCM of 7 and 10.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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8.
Mathematics
Find the sum of the first 10 terms of an AP with first term 17 and common difference 5.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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9.
Quantitative Aptitude
A invests £4,000 and B invests £6,000 for the same period. If the total profit is £8,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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10.
Quantitative Aptitude
Pipe A fills a tank in 10 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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11.
Quantitative Aptitude
A vehicle covers 400 km in 8 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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12.
Mathematics
Evaluate log base 5 of 625.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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13.
Mathematics
Find the sum of the first 6 terms of a GP with first term 5 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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14.
Quantitative Aptitude
A value changes from 900 to 1,125. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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15.
Mathematics
Evaluate ∫ from 2 to 4 of 4x^1 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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16.
Quantitative Aptitude
The marked price of an item is £1,800. After a 30% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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17.
Quantitative Aptitude
An item is bought for £200 and sold for £250. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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18.
Mathematics
Find the sum of the first 7 terms of a GP with first term 3 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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19.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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20.
Mathematics
In an arithmetic progression with first term 4 and common difference 9, find term number 5.
Formula:AP nth Term
$a_n = a + (n-1)d$
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