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11+ · Practice Sheet 21

Sheet code: ELEVEN-PLUS-S21 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find the sum of the first 5 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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2.
Mathematics
If f(x) = 5x³ + 2x² + 1x, find f′(3).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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3.
Quantitative Aptitude
The sum of the ages of two people is 81 years, and one is 3 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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4.
Quantitative Aptitude
Find the HCF and LCM of 22 and 9.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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5.
Mathematics
In an arithmetic progression with first term 4 and common difference 1, find term number 8.
Formula:AP nth Term
$a_n = a + (n-1)d$
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6.
Mathematics
Find the distance between the points (-7, -3) and (-8, -5).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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7.
Quantitative Aptitude
Divide £648 between two people in the ratio 3:5. 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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8.
Quantitative Aptitude
A vehicle covers 395 km in 5 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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9.
Quantitative Aptitude
Find the compound interest on £3,000 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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10.
Mathematics
Find term number 4 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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11.
Mathematics
Evaluate log base 3 of 81.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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12.
Mathematics
If f(x) = 1x³ + 6x² + 7x, find f′(4).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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13.
Quantitative Aptitude
A invests £3,000 and B invests £2,000 for the same period. If the total profit is £15,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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14.
Quantitative Aptitude
Find the compound interest on £14,000 at 10% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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15.
Quantitative Aptitude
What is 20% of 860?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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16.
Quantitative Aptitude
The marked price of an item is £500. After a 5% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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17.
Mathematics
In an arithmetic progression with first term 6 and common difference 9, find term number 27.
Formula:AP nth Term
$a_n = a + (n-1)d$
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18.
Quantitative Aptitude
Find the simple interest on £13,000 at 4% per annum for 1 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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19.
Quantitative Aptitude
Two varieties costing £38 and £84 per kg are mixed to give a mixture worth £60 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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20.
Mathematics
Evaluate ∫ from 1 to 5 of 1x^2 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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