A-Level Maths · Practice Sheet 24

1. 1.

   Quantitative Aptitude

   A value changes from 500 to 475. Find the percentage decrease.

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$

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2. 2.

   Quantitative Aptitude

   A can finish a job in 18 days and B in 11 days. Working together, how long will they take?

   Formula:Time & Work (combined)

   $T = \dfrac{xy}{x+y}$

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3. 3.

   Quantitative Aptitude

   Find the simple interest on £37,000 at 8% per annum for 3 year(s).

   Formula:Simple Interest

   $SI = \dfrac{P\times R\times T}{100}$

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4. 4.

   Mathematics

   For the quadratic 3x² + 8x − 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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5. 5.

   Quantitative Aptitude

   What is 75% of 840?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

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6. 6.

   Quantitative Aptitude

   Find the simple interest on £27,000 at 8% per annum for 4 year(s).

   Formula:Simple Interest

   $SI = \dfrac{P\times R\times T}{100}$

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7. 7.

   Mathematics

   In an arithmetic progression with first term 20 and common difference 4, find term number 24.

   Formula:AP nth Term

   $a_n = a + (n-1)d$

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8. 8.

   Mathematics

   Find the slope of the line through (4, -3) and (6, 0).

   Formula:Slope of a Line

   $m = \dfrac{y_2-y_1}{x_2-x_1}$

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9. 9.

   Quantitative Aptitude

   Pipe A fills a tank in 10 hours and pipe B in 5 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

   $T = \dfrac{xy}{x+y}$

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10. 10.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 4.)

    Formula:Permutations

    $^{n}P_{r} = \dfrac{n!}{(n-r)!}$

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11. 11.

    Quantitative Aptitude

    Find the average of these 5 numbers: 44, 34, 25, 54, 43.

    Formula:Arithmetic Mean

    $\bar{x} = \dfrac{\sum x}{n}$

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12. 12.

    Mathematics

    In an arithmetic progression with first term 6 and common difference 7, find term number 13.

    Formula:AP nth Term

    $a_n = a + (n-1)d$

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13. 13.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 4.)

    Formula:Combinations

    $^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$

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14. 14.

    Quantitative Aptitude

    Two varieties costing £36 and £64 per kg are mixed to give a mixture worth £44 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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15. 15.

    Quantitative Aptitude

    Pipe A fills a tank in 12 hours and pipe B in 15 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. 16.

    Mathematics

    Evaluate ∫ from 2 to 3 of 1x^3 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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17. 17.

    Mathematics

    Find the distance between the points (6, 6) and (6, -8).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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18. 18.

    Mathematics

    Evaluate log base 2 of 32.

    Formula:Logarithm Evaluation

    $\log_{b}(b^{k}) = k$

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19. 19.

    Quantitative Aptitude

    An item is bought for £800 and sold for £1,120. Find the profit percentage.

    Formula:Profit Percentage

    $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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20. 20.

    Quantitative Aptitude

    The marked price of an item is £200. After a 25% discount, find the selling price.

    Formula:Discount & Selling Price

    $SP = MP\left(1-\dfrac{d}{100}\right)$

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