GCSE Maths · Practice Sheet 23

1. 1.

   Mathematics

   Evaluate log base 3 of 27.

   Formula:Logarithm Evaluation

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

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2. 2.

   Quantitative Aptitude

   Find the average of these 6 numbers: 52, 20, 80, 80, 35, 84.

   Formula:Arithmetic Mean

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

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3. 3.

   Quantitative Aptitude

   Pipe A fills a tank in 11 hours and pipe B in 8 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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4. 4.

   Mathematics

   Evaluate log base 2 of 16.

   Formula:Logarithm Evaluation

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

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5. 5.

   Mathematics

   Find the binomial coefficient C(6, 3) — the coefficient of x^3 in (1 + x)^6.

   Formula:Binomial Coefficient

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

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6. 6.

   Quantitative Aptitude

   Pipe A fills a tank in 12 hours and pipe B in 13 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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7. 7.

   Quantitative Aptitude

   A value changes from 500 to 375. Find the percentage decrease.

   Formula:Percentage Change

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

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8. 8.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 2.)

   Formula:Combinations

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

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9. 9.

   Quantitative Aptitude

   What is 75% of 1,180?

   Formula:Percentage of a Number

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

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10. 10.

    Mathematics

    Find the slope of the line through (-6, 1) and (2, 8).

    Formula:Slope of a Line

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

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11. 11.

    Quantitative Aptitude

    The sum of the ages of two people is 62 years, and one is 10 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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12. 12.

    Quantitative Aptitude

    Two varieties costing £25 and £72 per kg are mixed to give a mixture worth £66 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

    An item is bought for £300 and sold for £390. Find the profit percentage.

    Formula:Profit Percentage

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

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14. 14.

    Mathematics

    Find the distance between the points (4, 4) and (6, -8).

    Formula:Distance Between Two Points

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

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15. 15.

    Mathematics

    In an arithmetic progression with first term 14 and common difference 4, find term number 25.

    Formula:AP nth Term

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

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16. 16.

    Mathematics

    Find the binomial coefficient C(9, 2) — the coefficient of x^2 in (1 + x)^9.

    Formula:Binomial Coefficient

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

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17. 17.

    Quantitative Aptitude

    The marked price of an item is £500. After a 30% discount, find the selling price.

    Formula:Discount & Selling Price

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

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18. 18.

    Mathematics

    Find the sum of the first 15 terms of an AP with first term 8 and common difference 4.

    Formula:AP Sum of n Terms

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

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19. 19.

    Quantitative Aptitude

    Find the compound interest on £10,000 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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20. 20.

    Mathematics

    Find term number 4 of a geometric progression with first term 1 and common ratio 2.

    Formula:GP nth Term

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

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