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11+ · Practice Sheet 46

Sheet code: ELEVEN-PLUS-S46 · 20 questions

Name: ______________

Date: ______________

1.
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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2.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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3.
Mathematics
Find the sum of the first 7 terms of a GP with first term 4 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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4.
Mathematics
Find the binomial coefficient C(6, 4) — the coefficient of x^4 in (1 + x)^6.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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5.
Quantitative Aptitude
Two varieties costing £31 and £79 per kg are mixed to give a mixture worth £54 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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6.
Quantitative Aptitude
A invests £10,000 and B invests £10,000 for the same period. If the total profit is £37,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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7.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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8.
Mathematics
In an arithmetic progression with first term 8 and common difference 3, find term number 6.
Formula:AP nth Term
$a_n = a + (n-1)d$
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9.
Quantitative Aptitude
A vehicle covers 207 km in 3 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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10.
Quantitative Aptitude
Find the average of these 6 numbers: 63, 30, 61, 25, 40, 38.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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11.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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12.
Quantitative Aptitude
Divide £980 between two people in the ratio 2:3. 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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13.
Mathematics
Evaluate log base 3 of 27.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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14.
Mathematics
Find the distance between the points (4, 0) and (5, 2).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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15.
Quantitative Aptitude
A invests £9,000 and B invests £3,000 for the same period. If the total profit is £30,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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16.
Quantitative Aptitude
The marked price of an item is £500. After a 25% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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17.
Mathematics
If f(x) = 5x³ + 4x² + 8x, find f′(3).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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18.
Quantitative Aptitude
What is 20% of 480?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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19.
Quantitative Aptitude
Two varieties costing £24 and £91 per kg are mixed to give a mixture worth £85 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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20.
Mathematics
In an arithmetic progression with first term 13 and common difference 2, find term number 24.
Formula:AP nth Term
$a_n = a + (n-1)d$
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