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A-Level Maths · Practice Sheet 40

Sheet code: A-LEVEL-MATHS-S40 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

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

    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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  2. 2.
    Mathematics

    Find the sum of the first 5 terms of a GP with first term 6 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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  3. 3.
    Mathematics

    If f(x) = 1x³ + 6x² + 1x, find f′(4).

    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

    Two fair dice are rolled. What is the probability that the sum of the numbers is 6?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  5. 5.
    Quantitative Aptitude

    Find the simple interest on £48,000 at 6% per annum for 5 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  6. 6.
    Mathematics

    Find the sum of the first 7 terms of an AP with first term 2 and common difference 8.

    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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  7. 7.
    Quantitative Aptitude

    Find the average of these 8 numbers: 48, 31, 30, 70, 50, 75, 86, 23.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  8. 8.
    Quantitative Aptitude

    A invests £6,000 and B invests £10,000 for the same period. If the total profit is £34,000, 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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  9. 9.
    Quantitative Aptitude

    Find the average of these 10 numbers: 26, 45, 45, 79, 60, 35, 76, 25, 21, 34.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  10. 10.
    Quantitative Aptitude

    Find the simple interest on £23,000 at 4% per annum for 6 year(s).

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

    What is 60% of 600?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  12. 12.
    Mathematics

    For the quadratic 3x² − 4x + 6 = 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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  13. 13.
    Quantitative Aptitude

    The sum of the ages of two people is 90 years, and one is 14 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

    Evaluate ∫ from 0 to 5 of 5x^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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  15. 15.
    Mathematics

    In an arithmetic progression with first term 19 and common difference 5, find term number 25.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  16. 16.
    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 3.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  17. 17.
    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 3.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  18. 18.
    Quantitative Aptitude

    Pipe A fills a tank in 8 hours and pipe B in 13 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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  19. 19.
    Quantitative Aptitude

    A value changes from 300 to 375. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  20. 20.
    Quantitative Aptitude

    An item is bought for £900 and sold for £1,080. Find the profit percentage.

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