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GCSE Maths · Practice Sheet 48

Sheet code: GCSE-MATHS-S48 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

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

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  2. 2.
    Mathematics

    Evaluate log base 5 of 3,125.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  3. 3.
    Quantitative Aptitude

    Find the average of these 8 numbers: 55, 84, 82, 26, 77, 83, 40, 63.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  4. 4.
    Mathematics

    Evaluate log base 10 of 100.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  5. 5.
    Quantitative Aptitude

    Pipe A fills a tank in 4 hours and pipe B in 8 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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  6. 6.
    Mathematics

    Find the binomial coefficient C(6, 2) — the coefficient of x^2 in (1 + x)^6.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  7. 7.
    Mathematics

    Find term number 6 of a geometric progression with first term 6 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  8. 8.
    Quantitative Aptitude

    A can finish a job in 17 days and B in 6 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  9. 9.
    Quantitative Aptitude

    Find the compound interest on £3,000 at 10% per annum compounded annually for 2 years.

    Formula:Compound Interest
    A=P(1+R100)TA = P\left(1+\dfrac{R}{100}\right)^{T}
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  10. 10.
    Quantitative Aptitude

    Find the simple interest on £33,000 at 6% per annum for 3 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  11. 11.
    Quantitative Aptitude

    A can finish a job in 13 days and B in 8 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  12. 12.
    Mathematics

    In an arithmetic progression with first term 13 and common difference 6, find term number 7.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  13. 13.
    Quantitative Aptitude

    Find the compound interest on £18,000 at 20% per annum compounded annually for 2 years.

    Formula:Compound Interest
    A=P(1+R100)TA = P\left(1+\dfrac{R}{100}\right)^{T}
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  14. 14.
    Quantitative Aptitude

    Divide £2,200 between two people in the ratio 5:5. How much does each receive?

    Formula:Sharing in a Ratio
    Share=Total×partsum of parts\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}
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  15. 15.
    Mathematics

    Find the slope of the line through (-2, 8) and (7, 8).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  16. 16.
    Quantitative Aptitude

    A value changes from 400 to 420. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  17. 17.
    Mathematics

    Find the sum of the first 7 terms of a GP with first term 2 and common ratio 2.

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
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  18. 18.
    Quantitative Aptitude

    Find the average of these 8 numbers: 83, 64, 80, 27, 20, 61, 78, 69.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  19. 19.
    Quantitative Aptitude

    Pipe A fills a tank in 5 hours and pipe B in 6 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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  20. 20.
    Mathematics

    Evaluate ∫ from 2 to 4 of 1x^2 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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