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GCSE Maths · Practice Sheet 24

Sheet code: GCSE-MATHS-S24 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Divide £2,464 between two people in the ratio 4:7. 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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2.
Mathematics
Find term number 7 of a geometric progression with first term 5 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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3.
Mathematics
If f(x) = 1x³ + 3x² + 1x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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4.
Quantitative Aptitude
Pipe A fills a tank in 14 hours and pipe B in 8 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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5.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 6?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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6.
Mathematics
Find the binomial coefficient C(6, 4) — the coefficient of x^4 in (1 + x)^6.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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7.
Quantitative Aptitude
The sum of the ages of two people is 90 years, and one is 18 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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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
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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9.
Quantitative Aptitude
Divide £828 between two people in the ratio 2:4. 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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10.
Mathematics
Find the slope of the line through (-7, -4) and (-1, 7).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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11.
Mathematics
Evaluate ∫ from 1 to 3 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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12.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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13.
Mathematics
In an arithmetic progression with first term 18 and common difference 8, find term number 18.
Formula:AP nth Term
$a_n = a + (n-1)d$
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14.
Mathematics
Find the distance between the points (1, -3) and (0, -8).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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15.
Mathematics
Evaluate log base 3 of 243.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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16.
Quantitative Aptitude
What is 40% of 880?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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17.
Quantitative Aptitude
A can finish a job in 17 days and B in 14 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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18.
Quantitative Aptitude
A invests £3,000 and B invests £5,000 for the same period. If the total profit is £27,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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19.
Mathematics
Find the distance between the points (-4, -2) and (-2, -4).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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20.
Mathematics
Find the sum of the first 21 terms of an AP with first term 12 and common difference 5.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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