GCSE Maths · Practice Sheet 17

1. 1.

   Quantitative Aptitude

   The marked price of an item is £1,100. After a 5% 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

   Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

   Formula:Probability (two dice)

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

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3. 3.

   Mathematics

   Find the sum of the first 18 terms of an AP with first term 6 and common difference 9.

   Formula:AP Sum of n Terms

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

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4. 4.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 5?

   Formula:Probability (two dice)

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

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5. 5.

   Quantitative Aptitude

   Two varieties costing £37 and £71 per kg are mixed to give a mixture worth £51 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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6. 6.

   Mathematics

   Evaluate log base 3 of 27.

   Formula:Logarithm Evaluation

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

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7. 7.

   Quantitative Aptitude

   Find the simple interest on £41,000 at 6% per annum for 5 year(s).

   Formula:Simple Interest

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

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8. 8.

   Mathematics

   Find the sum of the first 6 terms of a GP with first term 4 and common ratio 3.

   Formula:GP Sum of n Terms

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

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9. 9.

   Quantitative Aptitude

   Find the HCF and LCM of 33 and 34.

   Formula:LCM & HCF

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

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10. 10.

    Mathematics

    Find term number 4 of a geometric progression with first term 2 and common ratio 2.

    Formula:GP nth Term

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

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11. 11.

    Mathematics

    Find the distance between the points (-7, -5) and (-8, -1).

    Formula:Distance Between Two Points

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

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12. 12.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 5?

    Formula:Probability (two dice)

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

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13. 13.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 3.)

    Formula:Permutations

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

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14. 14.

    Mathematics

    For the quadratic 4x² + 5x + 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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15. 15.

    Mathematics

    Find the slope of the line through (-6, 4) and (4, -2).

    Formula:Slope of a Line

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

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16. 16.

    Quantitative Aptitude

    A invests £3,000 and B invests £5,000 for the same period. If the total profit is £17,000, find A's share.

    Formula:Partnership (profit share)

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

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17. 17.

    Quantitative Aptitude

    Find the HCF and LCM of 28 and 9.

    Formula:LCM & HCF

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

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18. 18.

    Mathematics

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

    Formula:GP Sum of n Terms

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

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19. 19.

    Quantitative Aptitude

    A can finish a job in 15 days and B in 16 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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20. 20.

    Mathematics

    Evaluate log base 2 of 4.

    Formula:Logarithm Evaluation

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

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