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GCSE Maths · Practice Sheet 10

Sheet code: GCSE-MATHS-S10 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Two varieties costing £14 and £82 per kg are mixed to give a mixture worth £70 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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2.
Mathematics
Evaluate ∫ from 2 to 5 of 3x^2 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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3.
Quantitative Aptitude
An item is bought for £700 and sold for £805. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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4.
Mathematics
For the quadratic 4x² + 1x + 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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5.
Mathematics
Find the sum of the first 5 terms of a GP with first term 6 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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6.
Mathematics
Find the slope of the line through (2, 0) and (0, 7).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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7.
Quantitative Aptitude
Find the average of these 8 numbers: 38, 68, 39, 51, 59, 25, 74, 70.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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8.
Quantitative Aptitude
Find the simple interest on £24,000 at 6% per annum for 5 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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9.
Mathematics
Find the distance between the points (-4, -5) and (-8, -5).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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10.
Mathematics
Find the slope of the line through (1, 4) and (-1, -1).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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11.
Quantitative Aptitude
The sum of the ages of two people is 73 years, and one is 11 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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12.
Quantitative Aptitude
A vehicle covers 207 km in 3 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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13.
Mathematics
Find the sum of the first 7 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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14.
Quantitative Aptitude
Pipe A fills a tank in 15 hours and pipe B in 16 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.
Mathematics
Evaluate log base 10 of 100.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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16.
Quantitative Aptitude
Find the average of these 6 numbers: 83, 30, 80, 85, 39, 49.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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17.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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18.
Quantitative Aptitude
Find the compound interest on £6,000 at 10% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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19.
Mathematics
If f(x) = 3x³ + 1x² + 8x, find f′(1).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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20.
Quantitative Aptitude
Pipe A fills a tank in 11 hours and pipe B in 9 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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