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A-Level Maths · Practice Sheet 43

Sheet code: A-LEVEL-MATHS-S43 · 20 questions

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

    In how many ways can 3 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 3.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  2. 2.
    Mathematics

    Find term number 7 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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  3. 3.
    Mathematics

    Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  4. 4.
    Quantitative Aptitude

    A value changes from 600 to 540. Find the percentage decrease.

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

    Pipe A fills a tank in 5 hours and pipe B in 4 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.
    Quantitative Aptitude

    Find the average of these 5 numbers: 40, 83, 42, 30, 87.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  7. 7.
    Quantitative Aptitude

    Two varieties costing £34 and £98 per kg are mixed to give a mixture worth £69 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)
    q1q2=p2−mm−p1\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}
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  8. 8.
    Quantitative Aptitude

    Find the compound interest on £6,000 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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  9. 9.
    Mathematics

    If f(x) = 2x³ + 5x² + 7x, find f′(3).

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  10. 10.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 10?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  11. 11.
    Quantitative Aptitude

    Two varieties costing £28 and £61 per kg are mixed to give a mixture worth £41 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)
    q1q2=p2−mm−p1\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}
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  12. 12.
    Quantitative Aptitude

    Find the HCF and LCM of 38 and 20.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  13. 13.
    Quantitative Aptitude

    Find the average of these 5 numbers: 49, 57, 25, 70, 74.

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

    Find the simple interest on £36,000 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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  15. 15.
    Mathematics

    For the quadratic 4x² − 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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  16. 16.
    Mathematics

    Find the distance between the points (-5, -7) and (-2, -3).

    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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  17. 17.
    Quantitative Aptitude

    Find the compound interest on £9,000 at 20% per annum compounded annually for 3 years.

    Formula:Compound Interest
    A=P(1+R100)TA = P\left(1+\dfrac{R}{100}\right)^{T}
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  18. 18.
    Quantitative Aptitude

    An item is bought for £400 and sold for £500. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  19. 19.
    Quantitative Aptitude

    A vehicle covers 469 km in 7 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  20. 20.
    Quantitative Aptitude

    Pipe A fills a tank in 13 hours and pipe B in 4 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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