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11+ · Practice Sheet 9

Sheet code: ELEVEN-PLUS-S09 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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2.
Quantitative Aptitude
Pipe A fills a tank in 13 hours and pipe B in 10 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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3.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 4?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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4.
Quantitative Aptitude
Two varieties costing £24 and £76 per kg are mixed to give a mixture worth £37 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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5.
Quantitative Aptitude
Find the simple interest on £31,000 at 4% per annum for 6 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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6.
Quantitative Aptitude
A vehicle covers 648 km in 9 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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7.
Quantitative Aptitude
What is 75% of 720?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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8.
Mathematics
Find the distance between the points (-1, 7) and (-1, -7).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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9.
Mathematics
Find the sum of the first 4 terms of a GP with first term 4 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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10.
Mathematics
In an arithmetic progression with first term 17 and common difference 9, find term number 16.
Formula:AP nth Term
$a_n = a + (n-1)d$
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11.
Mathematics
Evaluate ∫ from 2 to 5 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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12.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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13.
Quantitative Aptitude
Find the simple interest on £10,000 at 4% per annum for 4 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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14.
Mathematics
For the quadratic 1x² − 6x − 3 = 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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15.
Quantitative Aptitude
The sum of the ages of two people is 36 years, and one is 4 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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16.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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17.
Quantitative Aptitude
Pipe A fills a tank in 9 hours and pipe B in 7 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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18.
Mathematics
Find the distance between the points (4, 5) and (-2, -6).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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19.
Quantitative Aptitude
What is 25% of 120?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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20.
Quantitative Aptitude
Find the average of these 10 numbers: 20, 83, 87, 72, 62, 71, 42, 36, 62, 25.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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