A-Level Maths · Practice Sheet 23

1. 1.

   Quantitative Aptitude

   Two varieties costing £13 and £67 per kg are mixed to give a mixture worth £60 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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2. 2.

   Quantitative Aptitude

   Find the average of these 8 numbers: 67, 20, 38, 41, 23, 76, 63, 83.

   Formula:Arithmetic Mean

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

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3. 3.

   Quantitative Aptitude

   In how many ways can 3 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 3.)

   Formula:Permutations

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

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4. 4.

   Quantitative Aptitude

   Divide £2,530 between two people in the ratio 4:6. 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. 5.

   Quantitative Aptitude

   Find the average of these 6 numbers: 48, 62, 22, 84, 20, 51.

   Formula:Arithmetic Mean

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

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6. 6.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 9?

   Formula:Probability (two dice)

   $P = \dfrac{\text{favourable}}{\text{total}}$

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7. 7.

   Mathematics

   Find the sum of the first 6 terms of a GP with first term 3 and common ratio 2.

   Formula:GP Sum of n Terms

   $S_n = a\,\dfrac{r^{n}-1}{r-1}$

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8. 8.

   Quantitative Aptitude

   Divide £3,692 between two people in the ratio 6:7. 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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9. 9.

   Quantitative Aptitude

   Find the compound interest on £3,000 at 10% per annum compounded annually for 2 years.

   Formula:Compound Interest

   $A = P\left(1+\dfrac{R}{100}\right)^{T}$

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10. 10.

    Mathematics

    Find the slope of the line through (-7, -2) and (-3, -7).

    Formula:Slope of a Line

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

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11. 11.

    Mathematics

    Find the distance between the points (7, 6) and (4, -8).

    Formula:Distance Between Two Points

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

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12. 12.

    Mathematics

    Find the slope of the line through (-1, -8) and (0, -8).

    Formula:Slope of a Line

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

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13. 13.

    Quantitative Aptitude

    Divide £1,952 between two people in the ratio 4:4. 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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14. 14.

    Quantitative Aptitude

    A can finish a job in 4 days and B in 13 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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15. 15.

    Quantitative Aptitude

    Find the average of these 8 numbers: 69, 61, 53, 21, 32, 42, 65, 60.

    Formula:Arithmetic Mean

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

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16. 16.

    Quantitative Aptitude

    Two varieties costing £11 and £85 per kg are mixed to give a mixture worth £20 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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17. 17.

    Quantitative Aptitude

    What is 10% of 660?

    Formula:Percentage of a Number

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

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18. 18.

    Quantitative Aptitude

    Find the average of these 5 numbers: 57, 52, 35, 62, 32.

    Formula:Arithmetic Mean

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

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19. 19.

    Quantitative Aptitude

    Find the compound interest on £13,000 at 10% per annum compounded annually for 3 years.

    Formula:Compound Interest

    $A = P\left(1+\dfrac{R}{100}\right)^{T}$

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20. 20.

    Mathematics

    Find term number 3 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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