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GCSE Maths · Practice Sheet 15

Sheet code: GCSE-MATHS-S15 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
An item is bought for £400 and sold for £520. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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2.
Mathematics
Find the distance between the points (8, -5) and (-1, 2).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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3.
Mathematics
Find the slope of the line through (2, -2) and (3, 3).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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4.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 5?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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5.
Quantitative Aptitude
Find the average of these 8 numbers: 41, 49, 67, 33, 74, 62, 48, 56.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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6.
Quantitative Aptitude
Find the compound interest on £14,000 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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7.
Quantitative Aptitude
A invests £4,000 and B invests £10,000 for the same period. If the total profit is £16,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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8.
Mathematics
If f(x) = 2x³ + 2x² + 6x, find f′(3).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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9.
Mathematics
In an arithmetic progression with first term 10 and common difference 2, find term number 19.
Formula:AP nth Term
$a_n = a + (n-1)d$
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10.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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11.
Quantitative Aptitude
Two varieties costing £11 and £99 per kg are mixed to give a mixture worth £79 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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12.
Mathematics
Evaluate ∫ from 1 to 4 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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13.
Mathematics
Find the sum of the first 5 terms of a GP with first term 5 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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14.
Mathematics
If f(x) = 2x³ + 5x² + 5x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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15.
Quantitative Aptitude
What is 25% of 1,000?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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16.
Mathematics
In an arithmetic progression with first term 6 and common difference 5, find term number 9.
Formula:AP nth Term
$a_n = a + (n-1)d$
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17.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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18.
Quantitative Aptitude
The marked price of an item is £1,200. After a 20% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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19.
Quantitative Aptitude
Find the simple interest on £37,000 at 8% per annum for 4 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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20.
Quantitative Aptitude
The marked price of an item is £400. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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