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11+ · Practice Sheet 17

Sheet code: ELEVEN-PLUS-S17 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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2.
Quantitative Aptitude
Pipe A fills a tank in 10 hours and pipe B in 11 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
The sum of the ages of two people is 54 years, and one is 12 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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4.
Quantitative Aptitude
Find the compound interest on £12,000 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.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 6?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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6.
Mathematics
Evaluate ∫ from 2 to 4 of 4x^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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7.
Quantitative Aptitude
What is 50% of 1,000?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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8.
Quantitative Aptitude
An item is bought for £900 and sold for £1,260. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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9.
Mathematics
Find the sum of the first 3 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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10.
Mathematics
Find the slope of the line through (-2, 2) and (1, 6).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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11.
Quantitative Aptitude
Two varieties costing £17 and £92 per kg are mixed to give a mixture worth £66 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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12.
Mathematics
Find term number 6 of a geometric progression with first term 4 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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13.
Mathematics
Evaluate ∫ from 2 to 3 of 2x^1 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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14.
Mathematics
Find the binomial coefficient C(10, 2) — the coefficient of x^2 in (1 + x)^10.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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15.
Mathematics
Find the sum of the first 20 terms of an AP with first term 8 and common difference 2.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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16.
Quantitative Aptitude
A invests £7,000 and B invests £8,000 for the same period. If the total profit is £28,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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17.
Quantitative Aptitude
The sum of the ages of two people is 58 years, and one is 10 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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18.
Quantitative Aptitude
Divide £2,376 between two people in the ratio 5:7. 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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19.
Quantitative Aptitude
A value changes from 200 to 120. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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20.
Mathematics
Find the sum of the first 10 terms of an AP with first term 6 and common difference 6.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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