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11+ · Practice Sheet 19

Sheet code: ELEVEN-PLUS-S19 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
If f(x) = 4x³ + 4x² + 4x, find f′(4).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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2.
Mathematics
Find the sum of the first 7 terms of a GP with first term 3 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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3.
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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4.
Quantitative Aptitude
Pipe A fills a tank in 8 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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5.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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6.
Mathematics
If f(x) = 5x³ + 2x² + 4x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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7.
Quantitative Aptitude
A invests £5,000 and B invests £4,000 for the same period. If the total profit is £7,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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8.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 5?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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9.
Mathematics
Find the sum of the first 7 terms of a GP with first term 4 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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10.
Quantitative Aptitude
Pipe A fills a tank in 15 hours and pipe B in 4 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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11.
Quantitative Aptitude
A vehicle covers 146 km in 2 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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12.
Quantitative Aptitude
A invests £9,000 and B invests £5,000 for the same period. If the total profit is £40,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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13.
Mathematics
Find the binomial coefficient C(10, 2) — the coefficient of x^2 in (1 + x)^10.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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14.
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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15.
Quantitative Aptitude
Divide £630 between two people in the ratio 5:4. 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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16.
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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17.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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18.
Quantitative Aptitude
Find the simple interest on £37,000 at 6% per annum for 6 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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19.
Quantitative Aptitude
Divide £2,510 between two people in the ratio 6:4. 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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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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