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11+ · Practice Sheet 7

Sheet code: ELEVEN-PLUS-S07 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
An item is bought for £300 and sold for £390. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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2.
Quantitative Aptitude
The sum of the ages of two people is 58 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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3.
Quantitative Aptitude
A invests £7,000 and B invests £3,000 for the same period. If the total profit is £32,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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4.
Quantitative Aptitude
Find the average of these 10 numbers: 80, 23, 72, 31, 66, 42, 89, 60, 57, 45.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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5.
Quantitative Aptitude
A vehicle covers 490 km in 7 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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6.
Mathematics
Find the sum of the first 6 terms of an AP with first term 5 and common difference 4.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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7.
Mathematics
Find term number 6 of a geometric progression with first term 1 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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8.
Mathematics
Evaluate log base 3 of 81.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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9.
Quantitative Aptitude
Divide £1,098 between two people in the ratio 5:4. 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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10.
Mathematics
Evaluate ∫ from 1 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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11.
Mathematics
Find the sum of the first 7 terms of a GP with first term 5 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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12.
Mathematics
Find the binomial coefficient C(5, 2) — the coefficient of x^2 in (1 + x)^5.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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13.
Quantitative Aptitude
A vehicle covers 648 km in 8 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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14.
Quantitative Aptitude
Find the simple interest on £30,000 at 4% per annum for 5 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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15.
Mathematics
In an arithmetic progression with first term 12 and common difference 7, find term number 10.
Formula:AP nth Term
$a_n = a + (n-1)d$
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16.
Quantitative Aptitude
An item is bought for £400 and sold for £460. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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17.
Quantitative Aptitude
Two varieties costing £40 and £60 per kg are mixed to give a mixture worth £50 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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18.
Mathematics
In an arithmetic progression with first term 18 and common difference 8, find term number 10.
Formula:AP nth Term
$a_n = a + (n-1)d$
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19.
Quantitative Aptitude
Two varieties costing £24 and £81 per kg are mixed to give a mixture worth £56 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.
Quantitative Aptitude
The marked price of an item is £1,000. After a 25% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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