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GCSE Maths · Practice Sheet 8

Sheet code: GCSE-MATHS-S08 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Pipe A fills a tank in 12 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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2.
Quantitative Aptitude
What is 50% of 660?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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3.
Quantitative Aptitude
A invests £8,000 and B invests £6,000 for the same period. If the total profit is £8,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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4.
Mathematics
Evaluate log base 10 of 100.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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5.
Quantitative Aptitude
Two varieties costing £27 and £94 per kg are mixed to give a mixture worth £45 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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6.
Mathematics
Find the sum of the first 7 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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7.
Mathematics
If f(x) = 4x³ + 6x² + 2x, find f′(1).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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8.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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9.
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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10.
Mathematics
Evaluate log base 3 of 729.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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11.
Mathematics
For the quadratic 3x² − 9x + 0 = 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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12.
Quantitative Aptitude
A vehicle covers 104 km in 2 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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13.
Quantitative Aptitude
Find the simple interest on £26,000 at 10% per annum for 6 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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14.
Mathematics
Find term number 3 of a geometric progression with first term 2 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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15.
Quantitative Aptitude
Find the compound interest on £3,000 at 20% per annum compounded annually for 2 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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16.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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17.
Mathematics
Find the sum of the first 6 terms of an AP with first term 18 and common difference 10.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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18.
Mathematics
In an arithmetic progression with first term 20 and common difference 3, find term number 30.
Formula:AP nth Term
$a_n = a + (n-1)d$
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19.
Quantitative Aptitude
Find the average of these 8 numbers: 78, 72, 33, 64, 25, 75, 40, 90.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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20.
Quantitative Aptitude
What is 20% of 140?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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