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GCSE Maths · Practice Sheet 40

Sheet code: GCSE-MATHS-S40 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
A can finish a job in 8 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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2.
Mathematics
Find the sum of the first 20 terms of an AP with first term 20 and common difference 8.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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3.
Quantitative Aptitude
Find the compound interest on £9,000 at 20% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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4.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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5.
Mathematics
Evaluate ∫ from 0 to 4 of 1x^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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6.
Mathematics
Find the sum of the first 14 terms of an AP with first term 8 and common difference 5.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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7.
Quantitative Aptitude
A can finish a job in 10 days and B in 11 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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8.
Mathematics
Find the sum of the first 20 terms of an AP with first term 16 and common difference 4.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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9.
Mathematics
Evaluate log base 5 of 25.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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10.
Quantitative Aptitude
A invests £10,000 and B invests £9,000 for the same period. If the total profit is £39,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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11.
Mathematics
For the quadratic 1x² − 7x − 7 = 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.
Mathematics
Find the distance between the points (7, -1) and (-8, -4).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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13.
Quantitative Aptitude
What is 60% of 420?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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14.
Quantitative Aptitude
Find the compound interest on £8,000 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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15.
Quantitative Aptitude
The sum of the ages of two people is 65 years, and one is 13 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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16.
Quantitative Aptitude
The marked price of an item is £500. After a 50% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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17.
Mathematics
Find the slope of the line through (0, 3) and (-1, 5).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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18.
Mathematics
Evaluate ∫ from 2 to 3 of 2x^3 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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19.
Quantitative Aptitude
An item is bought for £500 and sold for £600. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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20.
Mathematics
Find the distance between the points (-2, 1) and (-1, -5).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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