GCSE Maths · Practice Sheet 2

1. 1.

   Quantitative Aptitude

   Divide £324 between two people in the ratio 2:4. 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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2. 2.

   Quantitative Aptitude

   A can finish a job in 19 days and B in 10 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

   A value changes from 200 to 100. Find the percentage decrease.

   Formula:Percentage Change

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

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4. 4.

   Quantitative Aptitude

   Find the average of these 8 numbers: 81, 44, 73, 78, 21, 49, 75, 24.

   Formula:Arithmetic Mean

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

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5. 5.

   Mathematics

   Find term number 7 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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6. 6.

   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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7. 7.

   Quantitative Aptitude

   Two varieties costing £24 and £71 per kg are mixed to give a mixture worth £63 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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8. 8.

   Quantitative Aptitude

   The marked price of an item is £700. After a 25% discount, find the selling price.

   Formula:Discount & Selling Price

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

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9. 9.

   Quantitative Aptitude

   Find the simple interest on £48,000 at 8% per annum for 5 year(s).

   Formula:Simple Interest

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

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10. 10.

    Quantitative Aptitude

    What is 60% of 980?

    Formula:Percentage of a Number

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

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11. 11.

    Mathematics

    If f(x) = 3x³ + 2x² + 5x, find f′(3).

    Formula:Derivative of a Polynomial

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

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12. 12.

    Mathematics

    Find the sum of the first 8 terms of an AP with first term 3 and common difference 1.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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13. 13.

    Quantitative Aptitude

    What is 50% of 480?

    Formula:Percentage of a Number

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

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14. 14.

    Mathematics

    Find the distance between the points (-6, -4) and (6, 1).

    Formula:Distance Between Two Points

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

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15. 15.

    Quantitative Aptitude

    Pipe A fills a tank in 15 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. 16.

    Mathematics

    Find the slope of the line through (2, -3) and (-6, 0).

    Formula:Slope of a Line

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

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17. 17.

    Quantitative Aptitude

    Find the HCF and LCM of 19 and 25.

    Formula:LCM & HCF

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

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18. 18.

    Mathematics

    Find term number 6 of a geometric progression with first term 1 and common ratio 3.

    Formula:GP nth Term

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

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19. 19.

    Mathematics

    Find the sum of the first 3 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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20. 20.

    Quantitative Aptitude

    Pipe A fills a tank in 11 hours and pipe B in 7 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

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