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11+ · Practice Sheet 30

Sheet code: ELEVEN-PLUS-S30 · 20 questions

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

    Two varieties costing £22 and £98 per kg are mixed to give a mixture worth £82 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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  2. 2.
    Mathematics

    Evaluate ∫ from 2 to 3 of 5x^3 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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  3. 3.
    Quantitative Aptitude

    The sum of the ages of two people is 50 years, and one is 20 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  4. 4.
    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 2.)

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

    Pipe A fills a tank in 11 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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  6. 6.
    Quantitative Aptitude

    Divide £2,930 between two people in the ratio 5:5. 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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  7. 7.
    Quantitative Aptitude

    Find the compound interest on £4,000 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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  8. 8.
    Mathematics

    Evaluate ∫ from 1 to 4 of 4x^3 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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  9. 9.
    Quantitative Aptitude

    A invests £10,000 and B invests £8,000 for the same period. If the total profit is £15,000, 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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  10. 10.
    Quantitative Aptitude

    What is 75% of 180?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  11. 11.
    Mathematics

    Evaluate log base 2 of 8.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  12. 12.
    Mathematics

    Find the distance between the points (-6, 3) and (-5, -2).

    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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  13. 13.
    Mathematics

    Find the slope of the line through (8, 2) and (-4, -4).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  14. 14.
    Quantitative Aptitude

    An item is bought for £800 and sold for £1,000. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  15. 15.
    Quantitative Aptitude

    A value changes from 900 to 1,170. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  16. 16.
    Mathematics

    For the quadratic 4x² + 0x + 4 = 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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  17. 17.
    Mathematics

    In an arithmetic progression with first term 12 and common difference 7, find term number 16.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  18. 18.
    Quantitative Aptitude

    Find the compound interest on £10,000 at 10% 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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  19. 19.
    Quantitative Aptitude

    Find the average of these 5 numbers: 89, 50, 41, 78, 74.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  20. 20.
    Mathematics

    In an arithmetic progression with first term 1 and common difference 2, find term number 16.

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