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A-Level Maths · Practice Sheet 25

Sheet code: A-LEVEL-MATHS-S25 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Find the compound interest on £3,000 at 20% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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2.
Mathematics
Evaluate ∫ from 0 to 5 of 3x^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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3.
Quantitative Aptitude
A value changes from 600 to 360. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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4.
Mathematics
Find the sum of the first 13 terms of an AP with first term 18 and common difference 4.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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5.
Quantitative Aptitude
A value changes from 700 to 980. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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6.
Quantitative Aptitude
Pipe A fills a tank in 3 hours and pipe B in 13 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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7.
Quantitative Aptitude
The marked price of an item is £400. After a 5% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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8.
Mathematics
Find the binomial coefficient C(5, 3) — the coefficient of x^3 in (1 + x)^5.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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9.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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10.
Quantitative Aptitude
The marked price of an item is £1,700. After a 50% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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11.
Mathematics
Evaluate ∫ from 2 to 4 of 3x^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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12.
Quantitative Aptitude
Two varieties costing £16 and £100 per kg are mixed to give a mixture worth £47 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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13.
Mathematics
Evaluate ∫ from 0 to 4 of 3x^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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14.
Quantitative Aptitude
Two varieties costing £30 and £92 per kg are mixed to give a mixture worth £36 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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15.
Quantitative Aptitude
A invests £8,000 and B invests £6,000 for the same period. If the total profit is £10,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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16.
Quantitative Aptitude
A value changes from 500 to 525. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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17.
Quantitative Aptitude
A vehicle covers 600 km in 8 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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18.
Quantitative Aptitude
The marked price of an item is £200. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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19.
Quantitative Aptitude
A invests £4,000 and B invests £8,000 for the same period. If the total profit is £16,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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20.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 9?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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