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A-Level Maths · Practice Sheet 42

Sheet code: A-LEVEL-MATHS-S42 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
What is 30% of 1,060?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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2.
Quantitative Aptitude
Find the simple interest on £26,000 at 10% per annum for 6 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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3.
Quantitative Aptitude
Two varieties costing £16 and £88 per kg are mixed to give a mixture worth £76 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
Find the sum of the first 25 terms of an AP with first term 9 and common difference 9.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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5.
Mathematics
Find term number 7 of a geometric progression with first term 3 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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6.
Mathematics
In an arithmetic progression with first term 20 and common difference 10, find term number 8.
Formula:AP nth Term
$a_n = a + (n-1)d$
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7.
Quantitative Aptitude
Divide £888 between two people in the ratio 2:2. 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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8.
Quantitative Aptitude
The marked price of an item is £400. After a 50% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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9.
Mathematics
Evaluate ∫ from 0 to 3 of 3x^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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10.
Quantitative Aptitude
An item is bought for £800 and sold for £1,000. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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11.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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12.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 7?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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13.
Quantitative Aptitude
An item is bought for £500 and sold for £750. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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14.
Quantitative Aptitude
A invests £3,000 and B invests £6,000 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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15.
Quantitative Aptitude
Find the simple interest on £36,000 at 6% per annum for 2 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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16.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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17.
Quantitative Aptitude
A can finish a job in 8 days and B in 18 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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18.
Mathematics
Find the binomial coefficient C(7, 2) — the coefficient of x^2 in (1 + x)^7.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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19.
Quantitative Aptitude
A value changes from 600 to 480. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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20.
Mathematics
Find term number 4 of a geometric progression with first term 5 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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