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11+ · Practice Sheet 15

Sheet code: ELEVEN-PLUS-S15 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
What is 60% of 80?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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2.
Mathematics
Find the slope of the line through (-4, -5) and (2, -5).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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3.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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4.
Quantitative Aptitude
A value changes from 500 to 400. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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5.
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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6.
Mathematics
In an arithmetic progression with first term 7 and common difference 4, find term number 22.
Formula:AP nth Term
$a_n = a + (n-1)d$
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7.
Mathematics
Find the distance between the points (-4, 7) and (0, -3).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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8.
Quantitative Aptitude
A can finish a job in 11 days and B in 14 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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9.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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10.
Mathematics
Find the sum of the first 6 terms of an AP with first term 17 and common difference 4.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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11.
Mathematics
If f(x) = 2x³ + 4x² + 3x, find f′(1).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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12.
Mathematics
Find term number 3 of a geometric progression with first term 3 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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13.
Quantitative Aptitude
Divide £2,064 between two people in the ratio 5:7. 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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14.
Quantitative Aptitude
Two varieties costing £25 and £62 per kg are mixed to give a mixture worth £53 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.
Mathematics
Find the sum of the first 4 terms of a GP with first term 3 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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16.
Quantitative Aptitude
A can finish a job in 15 days and B in 8 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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17.
Quantitative Aptitude
Divide £2,882 between two people in the ratio 7:4. 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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18.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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19.
Mathematics
For the quadratic 4x² + 5x − 5 = 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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20.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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