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11+ · Practice Sheet 32

Sheet code: ELEVEN-PLUS-S32 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    Find the distance between the points (6, 1) and (3, -6).

    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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  2. 2.
    Quantitative Aptitude

    Divide £2,398 between two people in the ratio 7:4. 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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  3. 3.
    Mathematics

    Find the binomial coefficient C(5, 4) — the coefficient of x^4 in (1 + x)^5.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  4. 4.
    Quantitative Aptitude

    Find the simple interest on £25,000 at 10% per annum for 4 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  5. 5.
    Mathematics

    Find the distance between the points (-5, 5) and (-7, 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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  6. 6.
    Quantitative Aptitude

    The marked price of an item is £400. 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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  7. 7.
    Quantitative Aptitude

    Find the average of these 6 numbers: 76, 26, 42, 68, 67, 76.

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

    What is 40% of 1,200?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  9. 9.
    Quantitative Aptitude

    A can finish a job in 20 days and B in 9 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  10. 10.
    Quantitative Aptitude

    The marked price of an item is £1,300. After a 30% discount, find the selling price.

    Formula:Discount & Selling Price
    SP=MP(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
    View formula →
  11. 11.
    Quantitative Aptitude

    A value changes from 400 to 500. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  12. 12.
    Mathematics

    For the quadratic 2x² + 4x − 7 = 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.
    Mathematics

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

    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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  14. 14.
    Quantitative Aptitude

    The sum of the ages of two people is 56 years, and one is 2 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  15. 15.
    Mathematics

    For the quadratic 3x² − 5x − 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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  16. 16.
    Mathematics

    In an arithmetic progression with first term 12 and common difference 4, find term number 24.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  17. 17.
    Mathematics

    Find the sum of the first 7 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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  18. 18.
    Quantitative Aptitude

    A can finish a job in 18 days and B in 4 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
    View formula →
  19. 19.
    Mathematics

    Find the slope of the line through (-8, 7) and (-2, 2).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  20. 20.
    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 2.)

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