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11+ · Practice Sheet 50

Sheet code: ELEVEN-PLUS-S50 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find the distance between the points (4, -8) and (-5, 4).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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2.
Quantitative Aptitude
Find the HCF and LCM of 32 and 7.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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3.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 8?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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4.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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5.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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6.
Mathematics
Find the sum of the first 10 terms of an AP with first term 11 and common difference 7.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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7.
Quantitative Aptitude
An item is bought for £900 and sold for £1,170. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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8.
Mathematics
Find the binomial coefficient C(10, 4) — the coefficient of x^4 in (1 + x)^10.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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9.
Mathematics
Find term number 5 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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10.
Mathematics
Find the slope of the line through (-4, -5) and (-6, 2).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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11.
Quantitative Aptitude
Two varieties costing £37 and £74 per kg are mixed to give a mixture worth £42 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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12.
Mathematics
In an arithmetic progression with first term 18 and common difference 7, find term number 23.
Formula:AP nth Term
$a_n = a + (n-1)d$
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13.
Mathematics
Evaluate ∫ from 0 to 5 of 1x^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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14.
Quantitative Aptitude
Pipe A fills a tank in 6 hours and pipe B in 4 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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15.
Quantitative Aptitude
A invests £7,000 and B invests £8,000 for the same period. If the total profit is £31,000, 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
A value changes from 300 to 240. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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17.
Mathematics
Evaluate log base 10 of 1,000,000.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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18.
Quantitative Aptitude
Divide £845 between two people in the ratio 3:2. 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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19.
Quantitative Aptitude
The marked price of an item is £600. 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.
Quantitative Aptitude
A value changes from 700 to 735. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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