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11+ · Practice Sheet 40

Sheet code: ELEVEN-PLUS-S40 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
For the quadratic 1x² − 9x + 9 = 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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2.
Mathematics
Find the distance between the points (-5, 1) and (6, -1).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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3.
Quantitative Aptitude
Two varieties costing £11 and £62 per kg are mixed to give a mixture worth £47 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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4.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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5.
Quantitative Aptitude
The marked price of an item is £1,800. After a 5% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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6.
Quantitative Aptitude
A invests £6,000 and B invests £3,000 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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7.
Quantitative Aptitude
The marked price of an item is £900. After a 50% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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8.
Mathematics
Evaluate ∫ from 0 to 5 of 3x^3 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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9.
Quantitative Aptitude
An item is bought for £700 and sold for £805. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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10.
Quantitative Aptitude
The marked price of an item is £200. After a 20% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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11.
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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12.
Quantitative Aptitude
Pipe A fills a tank in 4 hours and pipe B in 15 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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13.
Quantitative Aptitude
A invests £3,000 and B invests £7,000 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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14.
Mathematics
Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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15.
Mathematics
Find term number 5 of a geometric progression with first term 4 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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16.
Mathematics
Find the binomial coefficient C(8, 4) — the coefficient of x^4 in (1 + x)^8.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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17.
Quantitative Aptitude
A vehicle covers 68 km in 2 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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18.
Quantitative Aptitude
Find the average of these 8 numbers: 33, 85, 66, 76, 76, 28, 36, 60.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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19.
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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20.
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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