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A-Level Maths · Practice Sheet 36

Sheet code: A-LEVEL-MATHS-S36 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Pipe A fills a tank in 6 hours and pipe B in 10 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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2.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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3.
Mathematics
Find the sum of the first 5 terms of a GP with first term 1 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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4.
Mathematics
If f(x) = 2x³ + 1x² + 7x, find f′(4).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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5.
Quantitative Aptitude
Pipe A fills a tank in 10 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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6.
Quantitative Aptitude
An item is bought for £300 and sold for £360. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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7.
Mathematics
Find the slope of the line through (-6, -1) and (-5, -1).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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8.
Quantitative Aptitude
An item is bought for £600 and sold for £690. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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9.
Quantitative Aptitude
Two varieties costing £26 and £72 per kg are mixed to give a mixture worth £32 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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10.
Mathematics
In an arithmetic progression with first term 12 and common difference 9, find term number 20.
Formula:AP nth Term
$a_n = a + (n-1)d$
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11.
Quantitative Aptitude
Divide £3,770 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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12.
Quantitative Aptitude
An item is bought for £400 and sold for £560. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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13.
Quantitative Aptitude
What is 60% of 460?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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14.
Mathematics
In an arithmetic progression with first term 17 and common difference 8, find term number 7.
Formula:AP nth Term
$a_n = a + (n-1)d$
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15.
Quantitative Aptitude
Find the average of these 6 numbers: 58, 55, 79, 38, 40, 41.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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16.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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17.
Mathematics
Evaluate ∫ from 2 to 5 of 1x^1 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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18.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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19.
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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20.
Quantitative Aptitude
Find the compound interest on £11,000 at 10% per annum compounded annually for 2 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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