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11+ · Practice Sheet 39

Sheet code: ELEVEN-PLUS-S39 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
What is 75% of 1,060?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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2.
Mathematics
Evaluate ∫ from 2 to 4 of 2x^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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3.
Quantitative Aptitude
Pipe A fills a tank in 7 hours and pipe B in 8 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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4.
Quantitative Aptitude
A invests £2,000 and B invests £2,000 for the same period. If the total profit is £10,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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5.
Mathematics
Evaluate log base 5 of 125.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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6.
Quantitative Aptitude
The sum of the ages of two people is 46 years, and one is 10 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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7.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 9?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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8.
Quantitative Aptitude
Find the HCF and LCM of 23 and 13.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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9.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 6?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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10.
Mathematics
For the quadratic 2x² + 2x − 3 = 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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11.
Quantitative Aptitude
Divide £712 between two people in the ratio 5:3. 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.
Quantitative Aptitude
Find the simple interest on £40,000 at 10% per annum for 4 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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13.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 6?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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14.
Quantitative Aptitude
A can finish a job in 6 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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15.
Mathematics
Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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16.
Quantitative Aptitude
A vehicle covers 612 km in 9 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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17.
Quantitative Aptitude
What is 40% of 320?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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18.
Mathematics
Find the slope of the line through (7, -6) and (5, -8).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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19.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 9?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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20.
Mathematics
For the quadratic 5x² − 5x + 4 = 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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