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GCSE Maths · Practice Sheet 49

Sheet code: GCSE-MATHS-S49 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find term number 7 of a geometric progression with first term 4 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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2.
Quantitative Aptitude
A value changes from 200 to 140. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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3.
Mathematics
Evaluate log base 2 of 16.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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4.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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5.
Quantitative Aptitude
Pipe A fills a tank in 8 hours and pipe B in 3 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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6.
Quantitative Aptitude
A invests £9,000 and B invests £2,000 for the same period. If the total profit is £19,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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7.
Quantitative Aptitude
Find the HCF and LCM of 35 and 33.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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8.
Quantitative Aptitude
The sum of the ages of two people is 41 years, and one is 9 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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9.
Mathematics
Find the slope of the line through (6, 5) and (-1, 7).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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10.
Quantitative Aptitude
The marked price of an item is £1,800. After a 40% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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11.
Mathematics
Evaluate log base 2 of 16.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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12.
Quantitative Aptitude
Two varieties costing £34 and £85 per kg are mixed to give a mixture worth £59 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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13.
Quantitative Aptitude
The sum of the ages of two people is 70 years, and one is 20 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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14.
Quantitative Aptitude
Divide £1,944 between two people in the ratio 2:6. 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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15.
Mathematics
Find the binomial coefficient C(8, 3) — the coefficient of x^3 in (1 + x)^8.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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16.
Mathematics
Find the distance between the points (3, 8) and (3, -5).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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17.
Quantitative Aptitude
A invests £3,000 and B invests £6,000 for the same period. If the total profit is £34,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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18.
Quantitative Aptitude
A vehicle covers 336 km in 4 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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19.
Mathematics
Evaluate ∫ from 2 to 5 of 2x^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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20.
Quantitative Aptitude
Find the HCF and LCM of 8 and 36.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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