GCSE Maths · Practice Sheet 20

1. 1.

   Quantitative Aptitude

   Pipe A fills a tank in 9 hours and pipe B in 3 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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2. 2.

   Quantitative Aptitude

   Find the compound interest on £3,000 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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3. 3.

   Quantitative Aptitude

   The marked price of an item is £2,000. After a 10% discount, find the selling price.

   Formula:Discount & Selling Price

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

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4. 4.

   Mathematics

   For the quadratic 5x² + 5x + 0 = 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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5. 5.

   Quantitative Aptitude

   Find the compound interest on £14,000 at 10% per annum compounded annually for 2 years.

   Formula:Compound Interest

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

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6. 6.

   Quantitative Aptitude

   The sum of the ages of two people is 28 years, and one is 8 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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7. 7.

   Mathematics

   Evaluate log base 10 of 10,000.

   Formula:Logarithm Evaluation

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

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8. 8.

   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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9. 9.

   Quantitative Aptitude

   Find the simple interest on £27,000 at 6% per annum for 1 year(s).

   Formula:Simple Interest

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

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10. 10.

    Quantitative Aptitude

    Find the compound interest on £10,000 at 20% per annum compounded annually for 3 years.

    Formula:Compound Interest

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

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11. 11.

    Mathematics

    If f(x) = 1x³ + 4x² + 4x, find f′(2).

    Formula:Derivative of a Polynomial

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

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12. 12.

    Quantitative Aptitude

    A vehicle covers 365 km in 5 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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13. 13.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 3.)

    Formula:Permutations

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

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14. 14.

    Quantitative Aptitude

    Find the average of these 10 numbers: 79, 26, 34, 89, 71, 89, 38, 74, 33, 85.

    Formula:Arithmetic Mean

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

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15. 15.

    Mathematics

    Evaluate ∫ from 2 to 4 of 3x^3 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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16. 16.

    Quantitative Aptitude

    Find the HCF and LCM of 8 and 39.

    Formula:LCM & HCF

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

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17. 17.

    Mathematics

    Find the sum of the first 3 terms of a GP with first term 6 and common ratio 2.

    Formula:GP Sum of n Terms

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

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18. 18.

    Quantitative Aptitude

    Divide £1,308 between two people in the ratio 6:6. 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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19. 19.

    Quantitative Aptitude

    What is 20% of 340?

    Formula:Percentage of a Number

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

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20. 20.

    Quantitative Aptitude

    Find the compound interest on £10,000 at 20% per annum compounded annually for 3 years.

    Formula:Compound Interest

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

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