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GCSE Maths · Practice Sheet 19

Sheet code: GCSE-MATHS-S19 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Quantitative Aptitude

    Pipe A fills a tank in 15 hours and pipe B in 14 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
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  2. 2.
    Quantitative Aptitude

    What is 40% of 740?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  3. 3.
    Quantitative Aptitude

    An item is bought for £700 and sold for £770. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  4. 4.
    Quantitative Aptitude

    Find the HCF and LCM of 12 and 22.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  5. 5.
    Quantitative Aptitude

    An item is bought for £700 and sold for £805. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  6. 6.
    Mathematics

    Evaluate ∫ from 1 to 5 of 5x^3 dx.

    Formula:Definite Integral of a Power
    ∫pqaxn dx=an+1[xn+1]pq\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}
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  7. 7.
    Mathematics

    Find the binomial coefficient C(10, 4) — the coefficient of x^4 in (1 + x)^10.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  8. 8.
    Mathematics

    If f(x) = 5x³ + 5x² + 7x, find f′(1).

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  9. 9.
    Quantitative Aptitude

    An item is bought for £700 and sold for £805. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
    View formula →
  10. 10.
    Mathematics

    Find the distance between the points (1, -2) and (0, -8).

    Formula:Distance Between Two Points
    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
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  11. 11.
    Quantitative Aptitude

    Find the simple interest on £43,000 at 4% per annum for 1 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  12. 12.
    Quantitative Aptitude

    Find the average of these 6 numbers: 55, 61, 20, 57, 74, 79.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  13. 13.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 9?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  14. 14.
    Quantitative Aptitude

    The marked price of an item is £1,300. After a 15% discount, find the selling price.

    Formula:Discount & Selling Price
    SP=MP(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
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  15. 15.
    Quantitative Aptitude

    Find the simple interest on £25,000 at 5% per annum for 2 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  16. 16.
    Mathematics

    Find the binomial coefficient C(7, 4) — the coefficient of x^4 in (1 + x)^7.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\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(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
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  18. 18.
    Mathematics

    Find the sum of the first 21 terms of an AP with first term 12 and common difference 2.

    Formula:AP Sum of n Terms
    Sn=n2 [2a+(n−1)d]S_n = \dfrac{n}{2}\,[2a+(n-1)d]
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  19. 19.
    Quantitative Aptitude

    An item is bought for £400 and sold for £520. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
    View formula →
  20. 20.
    Quantitative Aptitude

    A can finish a job in 6 days and B in 15 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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