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A-Level Maths · Practice Sheet 1

Sheet code: A-LEVEL-MATHS-S01 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find the sum of the first 23 terms of an AP with first term 1 and common difference 5.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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2.
Quantitative Aptitude
A can finish a job in 12 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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3.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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4.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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5.
Quantitative Aptitude
Find the average of these 8 numbers: 65, 51, 64, 88, 88, 72, 75, 48.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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6.
Mathematics
Find the distance between the points (3, -8) and (6, -7).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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7.
Quantitative Aptitude
A vehicle covers 344 km in 8 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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8.
Quantitative Aptitude
A invests £9,000 and B invests £9,000 for the same period. If the total profit is £17,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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9.
Mathematics
Evaluate ∫ from 0 to 3 of 1x^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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10.
Quantitative Aptitude
The marked price of an item is £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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11.
Mathematics
For the quadratic 2x² + 9x − 7 = 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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12.
Quantitative Aptitude
A invests £10,000 and B invests £7,000 for the same period. If the total profit is £25,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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13.
Quantitative Aptitude
Find the simple interest on £6,000 at 4% per annum for 2 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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14.
Quantitative Aptitude
Pipe A fills a tank in 14 hours and pipe B in 8 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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15.
Quantitative Aptitude
Two varieties costing £38 and £61 per kg are mixed to give a mixture worth £51 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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16.
Mathematics
For the quadratic 5x² − 4x − 3 = 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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17.
Mathematics
Find the sum of the first 18 terms of an AP with first term 15 and common difference 8.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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18.
Quantitative Aptitude
An item is bought for £200 and sold for £280. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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19.
Quantitative Aptitude
Find the simple interest on £31,000 at 6% per annum for 2 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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20.
Quantitative Aptitude
Divide £924 between two people in the ratio 4:7. 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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