GCSE Maths · Practice Sheet 33

1. 1.

   Quantitative Aptitude

   The sum of the ages of two people is 56 years, and one is 8 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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2. 2.

   Quantitative Aptitude

   A can finish a job in 15 days and B in 19 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

   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.

   Mathematics

   Find term number 6 of a geometric progression with first term 6 and common ratio 2.

   Formula:GP nth Term

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

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5. 5.

   Quantitative Aptitude

   Find the HCF and LCM of 39 and 14.

   Formula:LCM & HCF

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

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6. 6.

   Mathematics

   In an arithmetic progression with first term 6 and common difference 7, find term number 19.

   Formula:AP nth Term

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

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7. 7.

   Quantitative Aptitude

   Find the average of these 8 numbers: 84, 27, 89, 56, 58, 53, 72, 79.

   Formula:Arithmetic Mean

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

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8. 8.

   Quantitative Aptitude

   Two varieties costing £24 and £78 per kg are mixed to give a mixture worth £45 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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9. 9.

   Quantitative Aptitude

   A invests £4,000 and B invests £10,000 for the same period. If the total profit is £25,000, find A's share.

   Formula:Partnership (profit share)

   $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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10. 10.

    Quantitative Aptitude

    Pipe A fills a tank in 15 hours and pipe B in 16 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

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11. 11.

    Mathematics

    Find the distance between the points (-2, -4) and (6, 3).

    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 term number 6 of a geometric progression with first term 2 and common ratio 2.

    Formula:GP nth Term

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

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13. 13.

    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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14. 14.

    Mathematics

    In an arithmetic progression with first term 5 and common difference 7, find term number 6.

    Formula:AP nth Term

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

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15. 15.

    Mathematics

    If f(x) = 1x³ + 3x² + 3x, find f′(1).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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16. 16.

    Mathematics

    Find the distance between the points (-5, 7) and (-2, -4).

    Formula:Distance Between Two Points

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

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17. 17.

    Mathematics

    Evaluate log base 10 of 1,000.

    Formula:Logarithm Evaluation

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

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18. 18.

    Quantitative Aptitude

    What is 30% of 900?

    Formula:Percentage of a Number

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

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19. 19.

    Mathematics

    Find the distance between the points (-1, 6) and (5, 1).

    Formula:Distance Between Two Points

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

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20. 20.

    Quantitative Aptitude

    Find the average of these 8 numbers: 71, 50, 68, 89, 27, 46, 54, 82.

    Formula:Arithmetic Mean

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

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