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A-Level Maths · Practice Sheet 30

Sheet code: A-LEVEL-MATHS-S30 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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2.
Mathematics
For the quadratic 1x² − 5x + 4 = 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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3.
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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4.
Mathematics
Find the sum of the first 11 terms of an AP with first term 19 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
An item is bought for £700 and sold for £910. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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6.
Quantitative Aptitude
Two varieties costing £24 and £69 per kg are mixed to give a mixture worth £40 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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7.
Quantitative Aptitude
What is 20% of 220?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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8.
Quantitative Aptitude
Pipe A fills a tank in 9 hours and pipe B in 11 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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9.
Quantitative Aptitude
Divide £1,148 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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10.
Mathematics
Find the sum of the first 8 terms of an AP with first term 10 and common difference 9.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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11.
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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12.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
View formula →
13.
Mathematics
For the quadratic 3x² + 0x − 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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14.
Quantitative Aptitude
Pipe A fills a tank in 6 hours and pipe B in 7 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.
Mathematics
Find the slope of the line through (4, 5) and (-3, -8).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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16.
Quantitative Aptitude
The sum of the ages of two people is 86 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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17.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 10?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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18.
Quantitative Aptitude
The marked price of an item is £1,800. After a 50% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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19.
Quantitative Aptitude
Find the average of these 8 numbers: 22, 22, 87, 23, 82, 31, 34, 68.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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20.
Quantitative Aptitude
A can finish a job in 12 days and B in 9 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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