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11+ · Practice Sheet 5

Sheet code: ELEVEN-PLUS-S05 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Divide £2,230 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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2.
Quantitative Aptitude
A can finish a job in 8 days and B in 7 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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3.
Mathematics
Find the binomial coefficient C(9, 3) — the coefficient of x^3 in (1 + x)^9.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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4.
Quantitative Aptitude
Find the compound interest on £18,000 at 10% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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5.
Quantitative Aptitude
Find the HCF and LCM of 16 and 27.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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6.
Quantitative Aptitude
A invests £6,000 and B invests £4,000 for the same period. If the total profit is £24,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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7.
Mathematics
Find the binomial coefficient C(9, 3) — the coefficient of x^3 in (1 + x)^9.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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8.
Quantitative Aptitude
A can finish a job in 6 days and B in 14 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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9.
Quantitative Aptitude
Two varieties costing £22 and £69 per kg are mixed to give a mixture worth £49 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
Find the HCF and LCM of 18 and 15.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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11.
Mathematics
Find the sum of the first 12 terms of an AP with first term 14 and common difference 8.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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12.
Mathematics
Find the sum of the first 6 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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13.
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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14.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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15.
Mathematics
Evaluate ∫ from 2 to 3 of 2x^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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16.
Quantitative Aptitude
An item is bought for £500 and sold for £650. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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17.
Mathematics
Find the slope of the line through (1, -4) and (8, -8).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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18.
Quantitative Aptitude
Two varieties costing £18 and £91 per kg are mixed to give a mixture worth £69 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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19.
Mathematics
Evaluate ∫ from 2 to 4 of 1x^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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20.
Mathematics
In an arithmetic progression with first term 20 and common difference 5, find term number 9.
Formula:AP nth Term
$a_n = a + (n-1)d$
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