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11+ · Practice Sheet 10

Sheet code: ELEVEN-PLUS-S10 · 20 questions

Name: ______________

Date: ______________

1.
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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2.
Mathematics
For the quadratic 2x² + 1x − 1 = 0, find the sum and product of its roots.
Formula:Vieta's Formulas (roots)
$\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$
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3.
Mathematics
Evaluate log base 10 of 1,000,000.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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4.
Quantitative Aptitude
What is 50% of 1,160?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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5.
Mathematics
Evaluate log base 2 of 8.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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6.
Quantitative Aptitude
What is 40% of 500?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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7.
Quantitative Aptitude
The sum of the ages of two people is 36 years, and one is 4 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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8.
Quantitative Aptitude
Find the HCF and LCM of 17 and 8.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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9.
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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10.
Mathematics
Find the sum of the first 3 terms of a GP with first term 6 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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11.
Quantitative Aptitude
A invests £8,000 and B invests £9,000 for the same period. If the total profit is £23,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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12.
Quantitative Aptitude
Find the simple interest on £16,000 at 4% per annum for 1 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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13.
Quantitative Aptitude
A can finish a job in 12 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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14.
Quantitative Aptitude
The sum of the ages of two people is 100 years, and one is 20 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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15.
Quantitative Aptitude
Find the compound interest on £20,000 at 20% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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16.
Quantitative Aptitude
A can finish a job in 5 days and B in 9 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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17.
Quantitative Aptitude
Two varieties costing £32 and £68 per kg are mixed to give a mixture worth £40 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
Find the sum of the first 5 terms of a GP with first term 6 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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19.
Quantitative Aptitude
The marked price of an item is £700. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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20.
Mathematics
In an arithmetic progression with first term 16 and common difference 7, find term number 5.
Formula:AP nth Term
$a_n = a + (n-1)d$
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