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GCSE Maths · Practice Sheet 45

Sheet code: GCSE-MATHS-S45 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
For the quadratic 1x² + 5x + 8 = 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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2.
Quantitative Aptitude
Find the compound interest on £17,000 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.
Quantitative Aptitude
Divide £2,296 between two people in the ratio 4:4. How much does each receive?
Formula:Sharing in a Ratio
$\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$
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4.
Quantitative Aptitude
A vehicle covers 288 km in 4 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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5.
Quantitative Aptitude
What is 40% of 300?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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6.
Mathematics
In an arithmetic progression with first term 20 and common difference 8, find term number 22.
Formula:AP nth Term
$a_n = a + (n-1)d$
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7.
Quantitative Aptitude
Find the average of these 8 numbers: 87, 32, 32, 71, 20, 47, 88, 88.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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8.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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9.
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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10.
Quantitative Aptitude
A vehicle covers 146 km in 2 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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11.
Mathematics
Find the sum of the first 5 terms of a GP with first term 6 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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12.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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13.
Quantitative Aptitude
Divide £594 between two people in the ratio 7:4. How much does each receive?
Formula:Sharing in a Ratio
$\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$
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14.
Mathematics
Find the sum of the first 24 terms of an AP with first term 20 and common difference 5.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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15.
Mathematics
Find the slope of the line through (-5, 8) and (8, 8).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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16.
Quantitative Aptitude
A can finish a job in 8 days and B in 17 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 sum of the ages of two people is 58 years, and one is 16 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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18.
Mathematics
Find term number 6 of a geometric progression with first term 5 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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19.
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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20.
Mathematics
If f(x) = 2x³ + 6x² + 1x, find f′(1).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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