A-Level Maths · Practice Sheet 2

1. 1.

   Quantitative Aptitude

   Find the average of these 6 numbers: 28, 63, 25, 68, 59, 61.

   Formula:Arithmetic Mean

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

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2. 2.

   Mathematics

   For the quadratic 4x² − 3x + 8 = 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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3. 3.

   Mathematics

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

   Formula:GP nth Term

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

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4. 4.

   Quantitative Aptitude

   The marked price of an item is £800. After a 20% discount, find the selling price.

   Formula:Discount & Selling Price

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

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5. 5.

   Quantitative Aptitude

   A can finish a job in 9 days and B in 11 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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6. 6.

   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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7. 7.

   Quantitative Aptitude

   A vehicle covers 84 km in 2 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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8. 8.

   Mathematics

   Find the distance between the points (8, 3) and (7, 1).

   Formula:Distance Between Two Points

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

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9. 9.

   Quantitative Aptitude

   Find the simple interest on £21,000 at 6% per annum for 6 year(s).

   Formula:Simple Interest

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

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10. 10.

    Mathematics

    Find the sum of the first 7 terms of a GP with first term 5 and common ratio 3.

    Formula:GP Sum of n Terms

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

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11. 11.

    Mathematics

    For the quadratic 3x² − 6x + 8 = 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 →
12. 12.

    Quantitative Aptitude

    The marked price of an item is £200. After a 30% discount, find the selling price.

    Formula:Discount & Selling Price

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

    View formula →
13. 13.

    Quantitative Aptitude

    An item is bought for £700 and sold for £875. Find the profit percentage.

    Formula:Profit Percentage

    $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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14. 14.

    Quantitative Aptitude

    The marked price of an item is £1,300. After a 30% discount, find the selling price.

    Formula:Discount & Selling Price

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

    View formula →
15. 15.

    Quantitative Aptitude

    Divide £815 between two people in the ratio 2:3. 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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16. 16.

    Mathematics

    Find the distance between the points (-5, -1) and (0, -7).

    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 3 of 729.

    Formula:Logarithm Evaluation

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

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18. 18.

    Quantitative Aptitude

    The marked price of an item is £2,000. After a 20% discount, find the selling price.

    Formula:Discount & Selling Price

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

    View formula →
19. 19.

    Quantitative Aptitude

    A can finish a job in 18 days and B in 20 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

    View formula →
20. 20.

    Quantitative Aptitude

    Find the average of these 5 numbers: 75, 60, 73, 75, 41.

    Formula:Arithmetic Mean

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

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