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TMUA · Practice Sheet 22

Sheet code: TMUA-S22 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
If f(x) = 5x³ + 6x² + 3x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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2.
Mathematics
Find the slope of the line through (5, 7) and (8, 5).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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3.
Mathematics
Evaluate ∫ from 2 to 5 of 1x^2 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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4.
Quantitative Aptitude
A invests £5,000 and B invests £5,000 for the same period. If the total profit is £13,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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5.
Quantitative Aptitude
Find the average of these 5 numbers: 90, 72, 55, 51, 30.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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6.
Quantitative Aptitude
The marked price of an item is £1,400. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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7.
Mathematics
In an arithmetic progression with first term 4 and common difference 2, find term number 15.
Formula:AP nth Term
$a_n = a + (n-1)d$
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8.
Quantitative Aptitude
Find the compound interest on £6,000 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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9.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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10.
Mathematics
For the quadratic 2x² − 1x − 6 = 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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11.
Mathematics
Find the sum of the first 4 terms of a GP with first term 5 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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12.
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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13.
Mathematics
Find term number 6 of a geometric progression with first term 1 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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14.
Quantitative Aptitude
Two varieties costing £15 and £74 per kg are mixed to give a mixture worth £50 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
Find the sum of the first 7 terms of a GP with first term 1 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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16.
Quantitative Aptitude
A value changes from 300 to 450. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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17.
Mathematics
If f(x) = 5x³ + 6x² + 6x, find f′(4).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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18.
Quantitative Aptitude
The marked price of an item is £900. After a 40% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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19.
Quantitative Aptitude
Pipe A fills a tank in 14 hours and pipe B in 15 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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20.
Quantitative Aptitude
Find the HCF and LCM of 25 and 23.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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