GCSE Maths · Practice Sheet 29

1. 1.

   Quantitative Aptitude

   Find the HCF and LCM of 13 and 12.

   Formula:LCM & HCF

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

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2. 2.

   Mathematics

   If f(x) = 5x³ + 5x² + 4x, find f′(3).

   Formula:Derivative of a Polynomial

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

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3. 3.

   Quantitative Aptitude

   A can finish a job in 13 days and B in 15 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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4. 4.

   Quantitative Aptitude

   Find the compound interest on £3,000 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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5. 5.

   Mathematics

   For the quadratic 3x² − 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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6. 6.

   Quantitative Aptitude

   Find the HCF and LCM of 18 and 12.

   Formula:LCM & HCF

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

   View formula →
7. 7.

   Mathematics

   For the quadratic 3x² − 5x + 6 = 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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8. 8.

   Quantitative Aptitude

   The marked price of an item is £1,600. After a 10% discount, find the selling price.

   Formula:Discount & Selling Price

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

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9. 9.

   Mathematics

   Find the slope of the line through (5, -7) and (-7, 6).

   Formula:Slope of a Line

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

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10. 10.

    Mathematics

    If f(x) = 3x³ + 4x² + 5x, find f′(5).

    Formula:Derivative of a Polynomial

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

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11. 11.

    Quantitative Aptitude

    What is 20% of 420?

    Formula:Percentage of a Number

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

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12. 12.

    Quantitative Aptitude

    A value changes from 800 to 680. Find the percentage decrease.

    Formula:Percentage Change

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

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13. 13.

    Quantitative Aptitude

    A invests £3,000 and B invests £2,000 for the same period. If the total profit is £13,000, find A's share.

    Formula:Partnership (profit share)

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

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14. 14.

    Quantitative Aptitude

    Pipe A fills a tank in 10 hours and pipe B in 11 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

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15. 15.

    Mathematics

    For the quadratic 1x² − 9x − 9 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)

    $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

    View formula →
16. 16.

    Quantitative Aptitude

    What is 15% of 760?

    Formula:Percentage of a Number

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

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17. 17.

    Quantitative Aptitude

    Find the average of these 8 numbers: 80, 70, 39, 48, 72, 69, 62, 84.

    Formula:Arithmetic Mean

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

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18. 18.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)

    Formula:Permutations

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

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19. 19.

    Mathematics

    Find the slope of the line through (-6, 1) and (0, -1).

    Formula:Slope of a Line

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

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20. 20.

    Quantitative Aptitude

    Find the average of these 6 numbers: 35, 32, 81, 46, 21, 35.

    Formula:Arithmetic Mean

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

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