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A-Level Maths · Practice Sheet 28

Sheet code: A-LEVEL-MATHS-S28 · 20 questions

Name: ______________

Date: ______________

1.
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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2.
Quantitative Aptitude
The marked price of an item is £1,800. After a 20% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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3.
Quantitative Aptitude
Find the HCF and LCM of 39 and 26.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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4.
Quantitative Aptitude
A vehicle covers 84 km in 2 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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5.
Mathematics
Find the binomial coefficient C(8, 4) — the coefficient of x^4 in (1 + x)^8.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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6.
Mathematics
If f(x) = 5x³ + 2x² + 3x, find f′(3).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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7.
Mathematics
Find term number 3 of a geometric progression with first term 3 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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8.
Quantitative Aptitude
A invests £6,000 and B invests £5,000 for the same period. If the total profit is £22,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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9.
Mathematics
If f(x) = 1x³ + 6x² + 9x, find f′(4).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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10.
Quantitative Aptitude
Find the HCF and LCM of 7 and 39.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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11.
Quantitative Aptitude
A can finish a job in 9 days and B in 11 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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12.
Mathematics
Find the sum of the first 19 terms of an AP with first term 12 and common difference 4.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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13.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 8?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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14.
Mathematics
Evaluate ∫ from 0 to 4 of 5x^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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15.
Quantitative Aptitude
The sum of the ages of two people is 52 years, and one is 14 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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16.
Quantitative Aptitude
The marked price of an item is £2,000. 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
Divide £1,640 between two people in the ratio 7:3. 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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18.
Mathematics
Evaluate ∫ from 2 to 3 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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19.
Quantitative Aptitude
An item is bought for £600 and sold for £750. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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20.
Quantitative Aptitude
Pipe A fills a tank in 5 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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