GCSE Maths · Practice Sheet 14

1. 1.

   Quantitative Aptitude

   Find the compound interest on £13,000 at 20% per annum compounded annually for 2 years.

   Formula:Compound Interest

   $A = P\left(1+\dfrac{R}{100}\right)^{T}$

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2. 2.

   Quantitative Aptitude

   The marked price of an item is £500. After a 25% discount, find the selling price.

   Formula:Discount & Selling Price

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

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3. 3.

   Quantitative Aptitude

   Find the simple interest on £39,000 at 4% per annum for 4 year(s).

   Formula:Simple Interest

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

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4. 4.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 4.)

   Formula:Combinations

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

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5. 5.

   Quantitative Aptitude

   What is 60% of 280?

   Formula:Percentage of a Number

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

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6. 6.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 4.)

   Formula:Combinations

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

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7. 7.

   Quantitative Aptitude

   Pipe A fills a tank in 10 hours and pipe B in 5 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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8. 8.

   Quantitative Aptitude

   The sum of the ages of two people is 53 years, and one is 19 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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9. 9.

   Quantitative Aptitude

   Pipe A fills a tank in 5 hours and pipe B in 9 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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10. 10.

    Mathematics

    Evaluate ∫ from 2 to 4 of 4x^1 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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11. 11.

    Quantitative Aptitude

    The sum of the ages of two people is 95 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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12. 12.

    Quantitative Aptitude

    Find the HCF and LCM of 14 and 12.

    Formula:LCM & HCF

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

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13. 13.

    Mathematics

    Find the sum of the first 5 terms of an AP with first term 14 and common difference 2.

    Formula:AP Sum of n Terms

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

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14. 14.

    Mathematics

    Evaluate ∫ from 2 to 3 of 5x^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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15. 15.

    Quantitative Aptitude

    Find the average of these 8 numbers: 60, 46, 59, 48, 33, 52, 85, 69.

    Formula:Arithmetic Mean

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

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16. 16.

    Quantitative Aptitude

    An item is bought for £500 and sold for £700. Find the profit percentage.

    Formula:Profit Percentage

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

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17. 17.

    Mathematics

    Find term number 5 of a geometric progression with first term 4 and common ratio 3.

    Formula:GP nth Term

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

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18. 18.

    Quantitative Aptitude

    What is 50% of 1,000?

    Formula:Percentage of a Number

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

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19. 19.

    Mathematics

    For the quadratic 1x² + 7x + 2 = 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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20. 20.

    Quantitative Aptitude

    A can finish a job in 18 days and B in 10 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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