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GCSE Maths · Practice Sheet 42

Sheet code: GCSE-MATHS-S42 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Find the HCF and LCM of 9 and 13.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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2.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 5?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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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
Divide £2,684 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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5.
Quantitative Aptitude
Two varieties costing £23 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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6.
Mathematics
If f(x) = 3x³ + 5x² + 3x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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7.
Mathematics
Find the sum of the first 7 terms of a GP with first term 2 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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8.
Quantitative Aptitude
Find the average of these 6 numbers: 66, 74, 27, 26, 26, 80.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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9.
Mathematics
If f(x) = 1x³ + 2x² + 4x, find f′(1).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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10.
Quantitative Aptitude
A can finish a job in 12 days and B in 6 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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11.
Quantitative Aptitude
A invests £6,000 and B invests £10,000 for the same period. If the total profit is £36,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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12.
Quantitative Aptitude
An item is bought for £500 and sold for £575. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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13.
Mathematics
For the quadratic 1x² + 0x + 1 = 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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14.
Quantitative Aptitude
An item is bought for £300 and sold for £330. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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15.
Quantitative Aptitude
Pipe A fills a tank in 6 hours and pipe B in 9 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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16.
Quantitative Aptitude
The marked price of an item is £1,300. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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17.
Mathematics
Find the binomial coefficient C(8, 4) — the coefficient of x^4 in (1 + x)^8.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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18.
Quantitative Aptitude
Two varieties costing £24 and £64 per kg are mixed to give a mixture worth £54 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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19.
Quantitative Aptitude
A invests £10,000 and B invests £4,000 for the same period. If the total profit is £32,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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20.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 4?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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