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GCSE Maths · Practice Sheet 28

Sheet code: GCSE-MATHS-S28 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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2.
Quantitative Aptitude
Find the compound interest on £6,000 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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3.
Mathematics
If f(x) = 2x³ + 5x² + 5x, find f′(5).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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4.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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5.
Quantitative Aptitude
Find the compound interest on £4,000 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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6.
Mathematics
Evaluate ∫ from 1 to 3 of 3x^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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7.
Mathematics
If f(x) = 5x³ + 5x² + 8x, find f′(3).
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 3 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
View formula →
9.
Quantitative Aptitude
The marked price of an item is £1,600. After a 10% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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10.
Quantitative Aptitude
A vehicle covers 588 km in 7 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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11.
Quantitative Aptitude
The sum of the ages of two people is 34 years, and one is 2 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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12.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 9?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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13.
Mathematics
Find the slope of the line through (-4, -6) and (-3, 3).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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14.
Quantitative Aptitude
A vehicle covers 322 km in 7 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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15.
Quantitative Aptitude
Find the HCF and LCM of 25 and 30.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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16.
Quantitative Aptitude
A can finish a job in 8 days and B in 15 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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17.
Quantitative Aptitude
The marked price of an item is £900. After a 20% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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18.
Mathematics
Find the sum of the first 3 terms of a GP with first term 1 and common ratio 3.
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(9, 4) — the coefficient of x^4 in (1 + x)^9.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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20.
Quantitative Aptitude
Two varieties costing £36 and £75 per kg are mixed to give a mixture worth £65 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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