A-Level Maths · Practice Sheet 14

1. 1.

   Quantitative Aptitude

   Find the HCF and LCM of 19 and 26.

   Formula:LCM & HCF

   $\text{LCM}\times\text{HCF} = a\times b$

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2. 2.

   Mathematics

   Find the slope of the line through (-2, 2) and (-1, 5).

   Formula:Slope of a Line

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

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3. 3.

   Quantitative Aptitude

   Find the average of these 10 numbers: 70, 32, 68, 21, 74, 46, 83, 55, 79, 42.

   Formula:Arithmetic Mean

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

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4. 4.

   Mathematics

   Find the sum of the first 5 terms of a GP with first term 2 and common ratio 2.

   Formula:GP Sum of n Terms

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

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5. 5.

   Mathematics

   Evaluate log base 5 of 125.

   Formula:Logarithm Evaluation

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

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6. 6.

   Mathematics

   For the quadratic 5x² + 3x − 9 = 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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7. 7.

   Mathematics

   Find the distance between the points (-4, 0) and (1, -1).

   Formula:Distance Between Two Points

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

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8. 8.

   Quantitative Aptitude

   What is 20% of 1,160?

   Formula:Percentage of a Number

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

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9. 9.

   Mathematics

   Find term number 7 of a geometric progression with first term 6 and common ratio 3.

   Formula:GP nth Term

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

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10. 10.

    Quantitative Aptitude

    Find the compound interest on £14,000 at 20% per annum compounded annually for 2 years.

    Formula:Compound Interest

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

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11. 11.

    Quantitative Aptitude

    Two varieties costing £29 and £60 per kg are mixed to give a mixture worth £48 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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12. 12.

    Quantitative Aptitude

    The sum of the ages of two people is 53 years, and one is 17 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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13. 13.

    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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14. 14.

    Quantitative Aptitude

    What is 75% of 700?

    Formula:Percentage of a Number

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

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15. 15.

    Mathematics

    Find the slope of the line through (4, -5) and (0, -1).

    Formula:Slope of a Line

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

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16. 16.

    Quantitative Aptitude

    Find the compound interest on £19,000 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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17. 17.

    Mathematics

    Find the distance between the points (7, -1) and (4, -8).

    Formula:Distance Between Two Points

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

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18. 18.

    Quantitative Aptitude

    Find the compound interest on £17,000 at 20% per annum compounded annually for 2 years.

    Formula:Compound Interest

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

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19. 19.

    Mathematics

    Evaluate log base 3 of 243.

    Formula:Logarithm Evaluation

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

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20. 20.

    Quantitative Aptitude

    Find the HCF and LCM of 18 and 36.

    Formula:LCM & HCF

    $\text{LCM}\times\text{HCF} = a\times b$

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