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A-Level Maths · Practice Sheet 4

Sheet code: A-LEVEL-MATHS-S04 · 20 questions

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

    A value changes from 500 to 650. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  2. 2.
    Quantitative Aptitude

    Pipe A fills a tank in 10 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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  3. 3.
    Mathematics

    Evaluate ∫ from 0 to 5 of 3x^1 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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  4. 4.
    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 3.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  5. 5.
    Quantitative Aptitude

    Divide £1,340 between two people in the ratio 6:4. 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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  6. 6.
    Quantitative Aptitude

    Find the compound interest on £11,000 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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  7. 7.
    Quantitative Aptitude

    Find the simple interest on £16,000 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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  8. 8.
    Quantitative Aptitude

    A vehicle covers 205 km in 5 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  9. 9.
    Mathematics

    Evaluate ∫ from 1 to 4 of 1x^1 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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  10. 10.
    Quantitative Aptitude

    The sum of the ages of two people is 49 years, and one is 17 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  11. 11.
    Quantitative Aptitude

    Find the compound interest on £13,000 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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  12. 12.
    Quantitative Aptitude

    Pipe A fills a tank in 6 hours and pipe B in 10 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
    View formula →
  13. 13.
    Mathematics

    Find the binomial coefficient C(8, 4) — the coefficient of x^4 in (1 + x)^8.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  14. 14.
    Quantitative Aptitude

    A invests £7,000 and B invests £2,000 for the same period. If the total profit is £31,000, 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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  15. 15.
    Mathematics

    Evaluate log base 5 of 15,625.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  16. 16.
    Quantitative Aptitude

    Find the HCF and LCM of 29 and 35.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  17. 17.
    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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  18. 18.
    Quantitative Aptitude

    A value changes from 500 to 550. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  19. 19.
    Quantitative Aptitude

    An item is bought for £700 and sold for £875. Find the profit percentage.

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

    A vehicle covers 140 km in 4 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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