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A-Level Maths · Practice Sheet 19

Sheet code: A-LEVEL-MATHS-S19 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
A can finish a job in 6 days and B in 17 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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2.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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3.
Mathematics
Find the sum of the first 10 terms of an AP with first term 10 and common difference 2.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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4.
Mathematics
Find term number 7 of a geometric progression with first term 2 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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5.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 5?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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6.
Quantitative Aptitude
Find the average of these 10 numbers: 28, 43, 81, 50, 67, 70, 88, 84, 84, 50.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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7.
Mathematics
Find the binomial coefficient C(10, 4) — the coefficient of x^4 in (1 + x)^10.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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8.
Quantitative Aptitude
A value changes from 200 to 230. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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9.
Quantitative Aptitude
What is 20% of 1,000?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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10.
Quantitative Aptitude
A value changes from 400 to 560. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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11.
Quantitative Aptitude
Find the average of these 8 numbers: 66, 60, 38, 34, 25, 37, 68, 28.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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12.
Quantitative Aptitude
Find the compound interest on £11,000 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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13.
Quantitative Aptitude
A value changes from 300 to 150. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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14.
Mathematics
For the quadratic 1x² − 9x − 5 = 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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15.
Mathematics
Evaluate log base 5 of 625.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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16.
Mathematics
Evaluate ∫ from 1 to 4 of 1x^2 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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17.
Quantitative Aptitude
Find the simple interest on £37,000 at 10% per annum for 1 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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18.
Quantitative Aptitude
A invests £9,000 and B invests £4,000 for the same period. If the total profit is £11,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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19.
Quantitative Aptitude
A vehicle covers 220 km in 4 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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20.
Quantitative Aptitude
What is 15% of 580?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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