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11+ · Practice Sheet 14

Sheet code: ELEVEN-PLUS-S14 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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2.
Quantitative Aptitude
Divide £1,936 between two people in the ratio 7:4. 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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3.
Mathematics
If f(x) = 1x³ + 6x² + 6x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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4.
Quantitative Aptitude
A vehicle covers 360 km in 5 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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5.
Quantitative Aptitude
An item is bought for £500 and sold for £700. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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6.
Mathematics
Evaluate log base 3 of 9.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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7.
Mathematics
Find the sum of the first 18 terms of an AP with first term 13 and common difference 9.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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8.
Quantitative Aptitude
The marked price of an item is £800. After a 40% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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9.
Quantitative Aptitude
Two varieties costing £40 and £80 per kg are mixed to give a mixture worth £72 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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10.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 8?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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11.
Quantitative Aptitude
The sum of the ages of two people is 44 years, and one is 2 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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12.
Quantitative Aptitude
Pipe A fills a tank in 12 hours and pipe B in 5 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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13.
Quantitative Aptitude
Divide £1,880 between two people in the ratio 7:3. 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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14.
Quantitative Aptitude
A can finish a job in 6 days and B in 10 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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15.
Quantitative Aptitude
Two varieties costing £26 and £66 per kg are mixed to give a mixture worth £57 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.
Quantitative Aptitude
An item is bought for £800 and sold for £1,200. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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17.
Quantitative Aptitude
Pipe A fills a tank in 8 hours and pipe B in 4 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.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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19.
Mathematics
Find the sum of the first 6 terms of a GP with first term 2 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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20.
Mathematics
Evaluate ∫ from 0 to 4 of 3x^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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