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11+ · Practice Sheet 37

Sheet code: ELEVEN-PLUS-S37 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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2.
Quantitative Aptitude
What is 15% of 600?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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3.
Quantitative Aptitude
A value changes from 500 to 300. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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4.
Mathematics
Find the sum of the first 16 terms of an AP with first term 10 and common difference 1.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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5.
Mathematics
In an arithmetic progression with first term 20 and common difference 10, find term number 10.
Formula:AP nth Term
$a_n = a + (n-1)d$
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6.
Mathematics
Find the sum of the first 5 terms of a GP with first term 1 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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7.
Quantitative Aptitude
A vehicle covers 82 km in 2 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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8.
Mathematics
Find the distance between the points (-8, -5) and (-7, -3).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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9.
Mathematics
In an arithmetic progression with first term 20 and common difference 8, find term number 26.
Formula:AP nth Term
$a_n = a + (n-1)d$
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10.
Mathematics
Find the binomial coefficient C(7, 3) — the coefficient of x^3 in (1 + x)^7.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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11.
Quantitative Aptitude
Divide £2,784 between two people in the ratio 6:6. 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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12.
Mathematics
Find the sum of the first 3 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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13.
Mathematics
Evaluate log base 2 of 32.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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14.
Quantitative Aptitude
Two varieties costing £37 and £69 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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15.
Quantitative Aptitude
Find the average of these 8 numbers: 23, 43, 78, 24, 54, 21, 28, 88.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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16.
Mathematics
Evaluate ∫ from 0 to 5 of 3x^1 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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17.
Quantitative Aptitude
What is 15% of 420?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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18.
Mathematics
For the quadratic 4x² − 3x + 0 = 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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19.
Mathematics
Find the distance between the points (1, 4) and (-5, -8).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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20.
Quantitative Aptitude
A can finish a job in 17 days and B in 5 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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