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GCSE Maths · Practice Sheet 7

Sheet code: GCSE-MATHS-S07 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Find the average of these 5 numbers: 72, 88, 37, 65, 76.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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2.
Mathematics
Evaluate ∫ from 1 to 3 of 4x^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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3.
Quantitative Aptitude
An item is bought for £700 and sold for £910. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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4.
Quantitative Aptitude
A can finish a job in 16 days and B in 8 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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5.
Quantitative Aptitude
Find the compound interest on £15,000 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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6.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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7.
Quantitative Aptitude
A can finish a job in 9 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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8.
Quantitative Aptitude
Find the HCF and LCM of 9 and 38.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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9.
Quantitative Aptitude
The sum of the ages of two people is 80 years, and one is 10 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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10.
Mathematics
Evaluate log base 5 of 625.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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11.
Quantitative Aptitude
A vehicle covers 280 km in 4 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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12.
Mathematics
In an arithmetic progression with first term 9 and common difference 5, find term number 8.
Formula:AP nth Term
$a_n = a + (n-1)d$
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13.
Mathematics
For the quadratic 1x² + 4x − 5 = 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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14.
Quantitative Aptitude
Pipe A fills a tank in 10 hours and pipe B in 5 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
In how many ways can 4 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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16.
Mathematics
Find the binomial coefficient C(6, 2) — the coefficient of x^2 in (1 + x)^6.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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17.
Mathematics
Find the slope of the line through (1, 0) and (0, 4).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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18.
Mathematics
Find the sum of the first 6 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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19.
Mathematics
Find the binomial coefficient C(6, 3) — the coefficient of x^3 in (1 + x)^6.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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20.
Quantitative Aptitude
A invests £4,000 and B invests £4,000 for the same period. If the total profit is £25,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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