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A-Level Maths · Practice Sheet 41

Sheet code: A-LEVEL-MATHS-S41 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Find the average of these 10 numbers: 78, 32, 35, 33, 88, 35, 89, 68, 39, 27.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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2.
Mathematics
Find the sum of the first 17 terms of an AP with first term 6 and common difference 2.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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3.
Quantitative Aptitude
A value changes from 900 to 630. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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4.
Mathematics
Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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5.
Mathematics
Find the slope of the line through (-4, 6) and (8, -5).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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6.
Quantitative Aptitude
The sum of the ages of two people is 69 years, and one is 13 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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7.
Mathematics
In an arithmetic progression with first term 10 and common difference 6, find term number 21.
Formula:AP nth Term
$a_n = a + (n-1)d$
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8.
Mathematics
Find the sum of the first 15 terms of an AP with first term 15 and common difference 1.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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9.
Quantitative Aptitude
What is 10% of 880?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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10.
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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11.
Quantitative Aptitude
Pipe A fills a tank in 11 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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12.
Mathematics
Find term number 4 of a geometric progression with first term 6 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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13.
Mathematics
For the quadratic 5x² + 4x + 2 = 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
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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15.
Quantitative Aptitude
A invests £2,000 and B invests £9,000 for the same period. If the total profit is £8,000, 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
Divide £805 between two people in the ratio 2:3. 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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17.
Quantitative Aptitude
A invests £8,000 and B invests £8,000 for the same period. If the total profit is £31,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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18.
Quantitative Aptitude
The sum of the ages of two people is 57 years, and one is 17 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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19.
Mathematics
If f(x) = 3x³ + 1x² + 5x, find f′(5).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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20.
Quantitative Aptitude
An item is bought for £500 and sold for £700. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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