GCSE Maths · Practice Sheet 39

1. 1.

   Quantitative Aptitude

   The marked price of an item is £1,600. After a 25% discount, find the selling price.

   Formula:Discount & Selling Price

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

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2. 2.

   Quantitative Aptitude

   A vehicle covers 96 km in 2 hours. Find its average speed.

   Formula:Speed, Distance & Time

   $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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3. 3.

   Quantitative Aptitude

   Find the simple interest on £41,000 at 8% per annum for 2 year(s).

   Formula:Simple Interest

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

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4. 4.

   Mathematics

   Find the slope of the line through (-2, 1) and (-3, 4).

   Formula:Slope of a Line

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

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5. 5.

   Quantitative Aptitude

   Find the HCF and LCM of 18 and 35.

   Formula:LCM & HCF

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

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6. 6.

   Quantitative Aptitude

   A invests £7,000 and B invests £8,000 for the same period. If the total profit is £37,000, find A's share.

   Formula:Partnership (profit share)

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

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7. 7.

   Quantitative Aptitude

   The sum of the ages of two people is 77 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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8. 8.

   Mathematics

   If f(x) = 5x³ + 3x² + 7x, find f′(3).

   Formula:Derivative of a Polynomial

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

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9. 9.

   Mathematics

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

   Formula:GP Sum of n Terms

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

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10. 10.

    Mathematics

    Find the slope of the line through (7, -8) and (5, 2).

    Formula:Slope of a Line

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

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11. 11.

    Quantitative Aptitude

    Find the average of these 8 numbers: 42, 79, 77, 90, 77, 62, 59, 37.

    Formula:Arithmetic Mean

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

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12. 12.

    Quantitative Aptitude

    A can finish a job in 13 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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13. 13.

    Mathematics

    Evaluate log base 2 of 32.

    Formula:Logarithm Evaluation

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

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14. 14.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 1 and common ratio 2.

    Formula:GP Sum of n Terms

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

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15. 15.

    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 2.)

    Formula:Combinations

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

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16. 16.

    Quantitative Aptitude

    Find the average of these 5 numbers: 49, 88, 51, 68, 43.

    Formula:Arithmetic Mean

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

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17. 17.

    Mathematics

    For the quadratic 3x² − 7x − 4 = 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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18. 18.

    Mathematics

    Find the sum of the first 22 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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19. 19.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 4?

    Formula:Probability (two dice)

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

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20. 20.

    Quantitative Aptitude

    The sum of the ages of two people is 50 years, and one is 14 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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