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A-Level Maths · Practice Sheet 48

Sheet code: A-LEVEL-MATHS-S48 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
The sum of the ages of two people is 80 years, and one is 20 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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2.
Quantitative Aptitude
Two varieties costing £10 and £96 per kg are mixed to give a mixture worth £16 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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3.
Mathematics
Find the sum of the first 23 terms of an AP with first term 12 and common difference 5.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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4.
Mathematics
If f(x) = 3x³ + 6x² + 3x, find f′(4).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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5.
Quantitative Aptitude
Pipe A fills a tank in 6 hours and pipe B in 9 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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6.
Quantitative Aptitude
Find the compound interest on £7,000 at 10% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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7.
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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8.
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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9.
Mathematics
For the quadratic 4x² − 7x + 8 = 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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10.
Mathematics
Find the sum of the first 25 terms of an AP with first term 3 and common difference 3.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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11.
Quantitative Aptitude
Find the average of these 10 numbers: 64, 51, 25, 41, 22, 77, 25, 30, 69, 43.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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12.
Mathematics
Find the distance between the points (8, -4) and (2, 0).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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13.
Mathematics
Find the slope of the line through (6, 6) and (2, -2).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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14.
Quantitative Aptitude
Two varieties costing £27 and £70 per kg are mixed to give a mixture worth £32 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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15.
Mathematics
For the quadratic 2x² − 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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16.
Mathematics
In an arithmetic progression with first term 14 and common difference 7, find term number 5.
Formula:AP nth Term
$a_n = a + (n-1)d$
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17.
Mathematics
Find term number 3 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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18.
Mathematics
Find the distance between the points (4, 3) and (4, 7).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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19.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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20.
Quantitative Aptitude
A vehicle covers 280 km in 8 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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