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11+ · Practice Sheet 27

Sheet code: ELEVEN-PLUS-S27 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find the sum of the first 5 terms of a GP with first term 5 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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2.
Quantitative Aptitude
What is 20% of 780?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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3.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 7?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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4.
Quantitative Aptitude
Pipe A fills a tank in 4 hours and pipe B in 9 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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5.
Quantitative Aptitude
Find the HCF and LCM of 15 and 37.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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6.
Mathematics
Find the sum of the first 24 terms of an AP with first term 4 and common difference 10.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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7.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 10?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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8.
Mathematics
Evaluate log base 5 of 125.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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9.
Quantitative Aptitude
Two varieties costing £40 and £60 per kg are mixed to give a mixture worth £46 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.
Mathematics
Find the sum of the first 11 terms of an AP with first term 13 and common difference 4.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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11.
Quantitative Aptitude
Find the simple interest on £22,000 at 10% per annum for 4 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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12.
Mathematics
Find the binomial coefficient C(6, 2) — the coefficient of x^2 in (1 + x)^6.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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13.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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14.
Mathematics
Find term number 7 of a geometric progression with first term 6 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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15.
Quantitative Aptitude
The sum of the ages of two people is 34 years, and one is 12 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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16.
Quantitative Aptitude
Pipe A fills a tank in 3 hours and pipe B in 10 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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17.
Mathematics
In an arithmetic progression with first term 13 and common difference 4, find term number 20.
Formula:AP nth Term
$a_n = a + (n-1)d$
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18.
Quantitative Aptitude
A invests £2,000 and B invests £8,000 for the same period. If the total profit is £16,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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19.
Mathematics
Find the sum of the first 3 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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20.
Quantitative Aptitude
Find the compound interest on £10,000 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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