GCSE Maths · Practice Sheet 4

1. 1.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 2.)

   Formula:Permutations

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

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2. 2.

   Quantitative Aptitude

   Find the average of these 5 numbers: 88, 89, 47, 86, 49.

   Formula:Arithmetic Mean

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

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3. 3.

   Quantitative Aptitude

   Find the simple interest on £16,000 at 12% per annum for 1 year(s).

   Formula:Simple Interest

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

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4. 4.

   Quantitative Aptitude

   The marked price of an item is £300. After a 25% discount, find the selling price.

   Formula:Discount & Selling Price

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

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5. 5.

   Mathematics

   In an arithmetic progression with first term 13 and common difference 1, find term number 16.

   Formula:AP nth Term

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

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6. 6.

   Quantitative Aptitude

   Divide £464 between two people in the ratio 5:3. 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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7. 7.

   Mathematics

   Find the sum of the first 6 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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8. 8.

   Quantitative Aptitude

   What is 50% of 620?

   Formula:Percentage of a Number

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

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9. 9.

   Mathematics

   If f(x) = 2x³ + 2x² + 3x, find f′(1).

   Formula:Derivative of a Polynomial

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

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10. 10.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

    Formula:Probability (two dice)

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

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11. 11.

    Mathematics

    For the quadratic 3x² − 9x + 5 = 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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12. 12.

    Quantitative Aptitude

    Two varieties costing £37 and £97 per kg are mixed to give a mixture worth £81 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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13. 13.

    Quantitative Aptitude

    What is 10% of 100?

    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 (-3, -5) and (3, 8).

    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

    The sum of the ages of two people is 37 years, and one is 9 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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16. 16.

    Mathematics

    Find the sum of the first 4 terms of a GP with first term 4 and common ratio 2.

    Formula:GP Sum of n Terms

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

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17. 17.

    Quantitative Aptitude

    The sum of the ages of two people is 74 years, and one is 20 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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18. 18.

    Quantitative Aptitude

    A can finish a job in 5 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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19. 19.

    Mathematics

    Find the sum of the first 5 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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20. 20.

    Mathematics

    Evaluate ∫ from 1 to 3 of 1x^2 dx.

    Formula:Definite Integral of a Power

    $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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