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GCSE Maths · Practice Sheet 9

Sheet code: GCSE-MATHS-S09 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Find the average of these 8 numbers: 46, 58, 77, 42, 26, 36, 25, 55.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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2.
Quantitative Aptitude
Divide £748 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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3.
Mathematics
For the quadratic 1x² + 9x + 6 = 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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4.
Quantitative Aptitude
Divide £2,808 between two people in the ratio 6:6. 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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5.
Quantitative Aptitude
A can finish a job in 7 days and B in 12 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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6.
Mathematics
Find the binomial coefficient C(9, 2) — the coefficient of x^2 in (1 + x)^9.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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7.
Mathematics
Evaluate log base 10 of 1,000,000.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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8.
Quantitative Aptitude
What is 40% of 700?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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9.
Mathematics
If f(x) = 4x³ + 2x² + 8x, find f′(3).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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10.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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11.
Quantitative Aptitude
The sum of the ages of two people is 82 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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12.
Quantitative Aptitude
A invests £5,000 and B invests £4,000 for the same period. If the total profit is £22,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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13.
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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14.
Mathematics
Find the sum of the first 3 terms of a GP with first term 4 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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15.
Mathematics
If f(x) = 4x³ + 1x² + 1x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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16.
Quantitative Aptitude
An item is bought for £800 and sold for £880. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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17.
Quantitative Aptitude
Two varieties costing £33 and £93 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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18.
Quantitative Aptitude
Divide £2,601 between two people in the ratio 2:7. 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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19.
Mathematics
Find the distance between the points (-6, -8) and (0, -3).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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20.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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