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GCSE Maths · Practice Sheet 25

Sheet code: GCSE-MATHS-S25 · 20 questions

Name: ______________

Date: ______________

1.
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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2.
Quantitative Aptitude
A can finish a job in 14 days and B in 10 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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3.
Mathematics
Find the sum of the first 15 terms of an AP with first term 18 and common difference 3.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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4.
Quantitative Aptitude
Find the simple interest on £13,000 at 4% per annum for 6 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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5.
Mathematics
For the quadratic 3x² − 7x + 8 = 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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6.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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7.
Mathematics
Find the slope of the line through (6, -4) and (1, 8).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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8.
Quantitative Aptitude
Divide £2,106 between two people in the ratio 7:2. 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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9.
Quantitative Aptitude
The marked price of an item is £1,300. After a 25% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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10.
Quantitative Aptitude
Find the simple interest on £25,000 at 4% per annum for 4 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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11.
Mathematics
Evaluate log base 10 of 1,000.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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12.
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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13.
Quantitative Aptitude
What is 15% of 640?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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14.
Quantitative Aptitude
Pipe A fills a tank in 8 hours and pipe B in 11 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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15.
Quantitative Aptitude
The sum of the ages of two people is 28 years, and one is 4 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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16.
Quantitative Aptitude
Find the compound interest on £12,000 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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17.
Mathematics
In an arithmetic progression with first term 5 and common difference 6, find term number 20.
Formula:AP nth Term
$a_n = a + (n-1)d$
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18.
Quantitative Aptitude
A vehicle covers 216 km in 6 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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19.
Quantitative Aptitude
Pipe A fills a tank in 13 hours and pipe B in 12 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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20.
Quantitative Aptitude
An item is bought for £400 and sold for £460. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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