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A-Level Maths · Practice Sheet 33

Sheet code: A-LEVEL-MATHS-S33 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
For the quadratic 2x² + 9x − 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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2.
Mathematics
Find the sum of the first 12 terms of an AP with first term 10 and common difference 4.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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3.
Mathematics
Find term number 7 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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4.
Quantitative Aptitude
Find the HCF and LCM of 14 and 19.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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5.
Mathematics
Find the slope of the line through (-7, -4) and (4, -4).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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6.
Quantitative Aptitude
Pipe A fills a tank in 8 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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7.
Mathematics
In an arithmetic progression with first term 4 and common difference 2, find term number 22.
Formula:AP nth Term
$a_n = a + (n-1)d$
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8.
Mathematics
If f(x) = 5x³ + 4x² + 4x, find f′(1).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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9.
Mathematics
Evaluate ∫ from 0 to 5 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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10.
Quantitative Aptitude
A vehicle covers 756 km in 9 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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11.
Mathematics
Find the slope of the line through (-8, 7) and (8, -8).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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12.
Mathematics
Evaluate ∫ from 2 to 3 of 3x^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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13.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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14.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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15.
Quantitative Aptitude
Find the compound interest on £14,000 at 10% per annum compounded annually for 2 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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16.
Quantitative Aptitude
Divide £340 between two people in the ratio 3:2. 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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17.
Quantitative Aptitude
Find the simple interest on £6,000 at 5% per annum for 2 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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18.
Quantitative Aptitude
Find the compound interest on £11,000 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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19.
Quantitative Aptitude
Divide £1,504 between two people in the ratio 4:4. 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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20.
Mathematics
Find the sum of the first 13 terms of an AP with first term 18 and common difference 1.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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