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11+ · Practice Sheet 38

Sheet code: ELEVEN-PLUS-S38 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
In an arithmetic progression with first term 15 and common difference 1, find term number 18.
Formula:AP nth Term
$a_n = a + (n-1)d$
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2.
Quantitative Aptitude
Divide £1,840 between two people in the ratio 5:5. 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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3.
Quantitative Aptitude
What is 75% of 460?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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4.
Quantitative Aptitude
A invests £5,000 and B invests £2,000 for the same period. If the total profit is £28,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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5.
Quantitative Aptitude
A can finish a job in 14 days and B in 16 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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6.
Quantitative Aptitude
Two varieties costing £28 and £76 per kg are mixed to give a mixture worth £49 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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7.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 4?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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8.
Quantitative Aptitude
Find the compound interest on £4,000 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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9.
Quantitative Aptitude
An item is bought for £200 and sold for £230. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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10.
Quantitative Aptitude
A invests £7,000 and B invests £2,000 for the same period. If the total profit is £38,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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11.
Mathematics
Evaluate log base 10 of 1,000.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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12.
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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13.
Quantitative Aptitude
A value changes from 700 to 560. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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14.
Mathematics
In an arithmetic progression with first term 20 and common difference 10, find term number 24.
Formula:AP nth Term
$a_n = a + (n-1)d$
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15.
Quantitative Aptitude
A can finish a job in 12 days and B in 20 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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16.
Quantitative Aptitude
A invests £9,000 and B invests £5,000 for the same period. If the total profit is £19,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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17.
Quantitative Aptitude
The sum of the ages of two people is 76 years, and one is 2 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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18.
Mathematics
For the quadratic 3x² + 4x + 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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19.
Quantitative Aptitude
Divide £1,274 between two people in the ratio 6:7. 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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20.
Mathematics
Evaluate ∫ from 2 to 5 of 3x^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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