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A-Level Maths · Practice Sheet 38

Sheet code: A-LEVEL-MATHS-S38 · 20 questions

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

    A vehicle covers 297 km in 9 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  2. 2.
    Quantitative Aptitude

    A can finish a job in 5 days and B in 9 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  3. 3.
    Quantitative Aptitude

    Find the compound interest on £15,000 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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  4. 4.
    Quantitative Aptitude

    A value changes from 500 to 625. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  5. 5.
    Mathematics

    Find term number 5 of a geometric progression with first term 1 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  6. 6.
    Mathematics

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

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  7. 7.
    Quantitative Aptitude

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

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  8. 8.
    Quantitative Aptitude

    Find the HCF and LCM of 30 and 34.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  9. 9.
    Mathematics

    Evaluate log base 5 of 625.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  10. 10.
    Mathematics

    Find the sum of the first 4 terms of a GP with first term 5 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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  11. 11.
    Mathematics

    Evaluate log base 3 of 9.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  12. 12.
    Quantitative Aptitude

    A value changes from 400 to 480. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  13. 13.
    Quantitative Aptitude

    The sum of the ages of two people is 43 years, and one is 7 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  14. 14.
    Mathematics

    Find the sum of the first 13 terms of an AP with first term 9 and common difference 3.

    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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  15. 15.
    Mathematics

    Find the sum of the first 5 terms of a GP with first term 4 and common ratio 3.

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
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  16. 16.
    Quantitative Aptitude

    Find the simple interest on £8,000 at 12% per annum for 6 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  17. 17.
    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 4.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  18. 18.
    Mathematics

    For the quadratic 4x² + 7x − 4 = 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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  19. 19.
    Mathematics

    Find the slope of the line through (0, 6) and (3, -8).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  20. 20.
    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 2.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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