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A-Level Maths · Practice Sheet 16

Sheet code: A-LEVEL-MATHS-S16 · 20 questions

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

    The sum of the ages of two people is 48 years, and one is 12 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  2. 2.
    Quantitative Aptitude

    A value changes from 400 to 200. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  3. 3.
    Mathematics

    Find the sum of the first 3 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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  4. 4.
    Mathematics

    In an arithmetic progression with first term 2 and common difference 10, find term number 14.

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

    Find the sum of the first 9 terms of an AP with first term 18 and common difference 5.

    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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  6. 6.
    Mathematics

    Find term number 3 of a geometric progression with first term 3 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,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

    A invests £7,000 and B invests £9,000 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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  9. 9.
    Mathematics

    Find the distance between the points (7, -8) and (-8, 0).

    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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  10. 10.
    Quantitative Aptitude

    An item is bought for £800 and sold for £1,200. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  11. 11.
    Quantitative Aptitude

    Find the compound interest on £20,000 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.
    Mathematics

    Find the sum of the first 18 terms of an AP with first term 4 and common difference 10.

    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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  13. 13.
    Quantitative Aptitude

    The marked price of an item is £1,700. After a 50% 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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  14. 14.
    Mathematics

    Evaluate log base 10 of 10,000.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  15. 15.
    Quantitative Aptitude

    A invests £3,000 and B invests £7,000 for the same period. If the total profit is £24,000, 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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  16. 16.
    Quantitative Aptitude

    A vehicle covers 88 km in 2 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  17. 17.
    Mathematics

    Find the slope of the line through (5, 6) and (-4, -5).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  18. 18.
    Mathematics

    Find the distance between the points (5, -4) and (6, -8).

    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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  19. 19.
    Quantitative Aptitude

    Two varieties costing £27 and £77 per kg are mixed to give a mixture worth £32 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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  20. 20.
    Quantitative Aptitude

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