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11+ · Practice Sheet 28

Sheet code: ELEVEN-PLUS-S28 · 20 questions

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

    The marked price of an item is £1,000. 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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  2. 2.
    Quantitative Aptitude

    A invests £9,000 and B invests £2,000 for the same period. If the total profit is £21,000, 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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  3. 3.
    Mathematics

    For the quadratic 4x² − 2x + 2 = 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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  4. 4.
    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 2.)

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

    Find term number 4 of a geometric progression with first term 4 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  6. 6.
    Mathematics

    Find the sum of the first 4 terms of a GP with first term 3 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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  7. 7.
    Quantitative Aptitude

    A value changes from 200 to 100. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  8. 8.
    Quantitative Aptitude

    A invests £3,000 and B invests £6,000 for the same period. If the total profit is £23,000, 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, 4) and (3, 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

    Find the simple interest on £26,000 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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  11. 11.
    Mathematics

    Find term number 3 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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  12. 12.
    Mathematics

    Find the binomial coefficient C(9, 2) — the coefficient of x^2 in (1 + x)^9.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  13. 13.
    Quantitative Aptitude

    Find the HCF and LCM of 12 and 19.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  14. 14.
    Mathematics

    Evaluate ∫ from 0 to 5 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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  15. 15.
    Mathematics

    Evaluate log base 3 of 729.

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

    What is 20% of 120?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  17. 17.
    Mathematics

    If f(x) = 5x³ + 5x² + 6x, find f′(1).

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  18. 18.
    Quantitative Aptitude

    A value changes from 800 to 600. Find the percentage decrease.

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

    Find the average of these 10 numbers: 69, 74, 84, 31, 63, 38, 60, 87, 58, 62.

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

    Evaluate ∫ from 0 to 4 of 2x^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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