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GCSE Maths · Practice Sheet 16

Sheet code: GCSE-MATHS-S16 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    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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  2. 2.
    Mathematics

    Find the sum of the first 19 terms of an AP with first term 4 and common difference 1.

    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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  3. 3.
    Mathematics

    If f(x) = 3x³ + 4x² + 6x, 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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  4. 4.
    Quantitative Aptitude

    Find the HCF and LCM of 17 and 23.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  5. 5.
    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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  6. 6.
    Mathematics

    For the quadratic 5x² + 4x + 0 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)
    α+β=−ba,  αβ=ca\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}
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  7. 7.
    Mathematics

    Find the binomial coefficient C(7, 2) — the coefficient of x^2 in (1 + x)^7.

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

    A value changes from 900 to 1,035. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  9. 9.
    Quantitative Aptitude

    A can finish a job in 7 days and B in 16 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  10. 10.
    Mathematics

    Evaluate ∫ from 0 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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  11. 11.
    Quantitative Aptitude

    The sum of the ages of two people is 47 years, and one is 3 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  12. 12.
    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 2.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  13. 13.
    Quantitative Aptitude

    Find the average of these 5 numbers: 84, 73, 59, 69, 42.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  14. 14.
    Mathematics

    Find the binomial coefficient C(8, 3) — the coefficient of x^3 in (1 + x)^8.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  15. 15.
    Quantitative Aptitude

    A value changes from 400 to 460. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  16. 16.
    Quantitative Aptitude

    The marked price of an item is £300. After a 40% 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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  17. 17.
    Quantitative Aptitude

    Find the simple interest on £21,000 at 8% per annum for 1 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  18. 18.
    Mathematics

    Evaluate log base 5 of 3,125.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  19. 19.
    Quantitative Aptitude

    Pipe A fills a tank in 10 hours and pipe B in 15 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.
    Quantitative Aptitude

    A invests £6,000 and B invests £4,000 for the same period. If the total profit is £7,000, find A's share.

    Formula:Partnership (profit share)
    ShareA=Profit×AA+B\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}
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