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A-Level Maths · Practice Sheet 47

Sheet code: A-LEVEL-MATHS-S47 · 20 questions

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

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

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  2. 2.
    Mathematics

    Find the distance between the points (6, -7) and (0, 4).

    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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  3. 3.
    Quantitative Aptitude

    What is 60% of 320?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  4. 4.
    Mathematics

    In an arithmetic progression with first term 10 and common difference 5, find term number 11.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  5. 5.
    Quantitative Aptitude

    A invests £7,000 and B invests £8,000 for the same period. If the total profit is £33,000, 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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  6. 6.
    Mathematics

    Find the sum of the first 3 terms of a GP with first term 2 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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  7. 7.
    Mathematics

    In an arithmetic progression with first term 19 and common difference 7, find term number 9.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  8. 8.
    Quantitative Aptitude

    The marked price of an item is £1,100. After a 25% 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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  9. 9.
    Mathematics

    Evaluate log base 3 of 9.

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

    Find term number 4 of a geometric progression with first term 6 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  11. 11.
    Quantitative Aptitude

    Pipe A fills a tank in 5 hours and pipe B in 12 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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  12. 12.
    Quantitative Aptitude

    A invests £6,000 and B invests £2,000 for the same period. If the total profit is £35,000, 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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  13. 13.
    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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  14. 14.
    Mathematics

    Find the binomial coefficient C(7, 4) — the coefficient of x^4 in (1 + x)^7.

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

    What is 25% of 980?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  16. 16.
    Mathematics

    Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  17. 17.
    Mathematics

    For the quadratic 4x² + 5x − 3 = 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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  18. 18.
    Mathematics

    If f(x) = 5x³ + 6x² + 3x, 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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  19. 19.
    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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  20. 20.
    Quantitative Aptitude

    Find the simple interest on £5,000 at 5% per annum for 1 year(s).

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