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11+ · Practice Sheet 34

Sheet code: ELEVEN-PLUS-S34 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Evaluate ∫ from 2 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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2.
Mathematics
Find term number 5 of a geometric progression with first term 6 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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3.
Quantitative Aptitude
Find the average of these 10 numbers: 24, 51, 33, 60, 30, 58, 69, 77, 89, 88.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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4.
Quantitative Aptitude
Find the compound interest on £17,000 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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5.
Mathematics
For the quadratic 4x² + 9x + 9 = 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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6.
Mathematics
Find the sum of the first 4 terms of a GP with first term 5 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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7.
Mathematics
If f(x) = 4x³ + 2x² + 8x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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8.
Quantitative Aptitude
A can finish a job in 17 days and B in 11 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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9.
Mathematics
Evaluate ∫ from 0 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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10.
Mathematics
Find the slope of the line through (6, 6) and (-1, -5).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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11.
Quantitative Aptitude
A value changes from 700 to 1,050. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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12.
Quantitative Aptitude
Two varieties costing £38 and £78 per kg are mixed to give a mixture worth £47 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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13.
Quantitative Aptitude
A value changes from 600 to 720. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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14.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 9?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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15.
Quantitative Aptitude
Two varieties costing £35 and £71 per kg are mixed to give a mixture worth £44 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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16.
Mathematics
If f(x) = 3x³ + 4x² + 8x, find f′(1).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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17.
Mathematics
For the quadratic 2x² + 6x + 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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18.
Quantitative Aptitude
Pipe A fills a tank in 7 hours and pipe B in 8 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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19.
Mathematics
Evaluate ∫ from 2 to 3 of 4x^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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20.
Quantitative Aptitude
The sum of the ages of two people is 61 years, and one is 7 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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