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A-Level Maths · Practice Sheet 13

Sheet code: A-LEVEL-MATHS-S13 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find the sum of the first 6 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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2.
Mathematics
If f(x) = 2x³ + 3x² + 6x, find f′(3).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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3.
Quantitative Aptitude
Find the average of these 10 numbers: 40, 56, 43, 22, 57, 52, 48, 31, 68, 55.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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4.
Mathematics
Find the binomial coefficient C(5, 2) — the coefficient of x^2 in (1 + x)^5.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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5.
Quantitative Aptitude
The marked price of an item is £1,500. 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
Pipe A fills a tank in 8 hours and pipe B in 7 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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7.
Quantitative Aptitude
Find the simple interest on £39,000 at 5% per annum for 2 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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8.
Quantitative Aptitude
An item is bought for £200 and sold for £280. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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9.
Mathematics
In an arithmetic progression with first term 4 and common difference 4, find term number 28.
Formula:AP nth Term
$a_n = a + (n-1)d$
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10.
Mathematics
Find term number 5 of a geometric progression with first term 4 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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11.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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12.
Mathematics
Evaluate log base 5 of 125.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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13.
Mathematics
Find the sum of the first 7 terms of a GP with first term 4 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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14.
Quantitative Aptitude
A can finish a job in 13 days and B in 5 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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15.
Quantitative Aptitude
The marked price of an item is £200. After a 30% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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16.
Mathematics
Find the sum of the first 5 terms of a GP with first term 2 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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17.
Mathematics
If f(x) = 3x³ + 4x² + 6x, find f′(4).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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18.
Quantitative Aptitude
Divide £3,318 between two people in the ratio 7:7. 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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19.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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20.
Mathematics
Find the sum of the first 16 terms of an AP with first term 14 and common difference 4.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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