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11+ · Practice Sheet 18

Sheet code: ELEVEN-PLUS-S18 · 20 questions

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

    Divide £714 between two people in the ratio 4:2. 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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  2. 2.
    Quantitative Aptitude

    A can finish a job in 20 days and B in 22 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  3. 3.
    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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  4. 4.
    Quantitative Aptitude

    What is 20% of 1,120?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  5. 5.
    Mathematics

    Find the distance between the points (3, -6) and (0, 3).

    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

    Two fair dice are rolled. What is the probability that the sum of the numbers is 9?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  7. 7.
    Mathematics

    Find the slope of the line through (4, 1) and (-1, 8).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  8. 8.
    Quantitative Aptitude

    A value changes from 700 to 980. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  9. 9.
    Quantitative Aptitude

    A can finish a job in 19 days and B in 4 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.
    Mathematics

    Evaluate ∫ from 0 to 3 of 2x^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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  11. 11.
    Quantitative Aptitude

    An item is bought for £500 and sold for £750. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  12. 12.
    Mathematics

    For the quadratic 2x² − 1x − 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.
    Quantitative Aptitude

    Find the simple interest on £4,000 at 5% per annum for 2 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  14. 14.
    Mathematics

    Evaluate ∫ from 2 to 5 of 2x^2 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

    Find the distance between the points (-8, 1) and (0, -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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  16. 16.
    Quantitative Aptitude

    Find the average of these 10 numbers: 56, 43, 55, 39, 68, 73, 71, 49, 72, 74.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  17. 17.
    Mathematics

    Find the distance between the points (8, -1) and (6, 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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  18. 18.
    Quantitative Aptitude

    Divide £1,230 between two people in the ratio 2:4. 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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  19. 19.
    Quantitative Aptitude

    A can finish a job in 7 days and B in 11 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  20. 20.
    Mathematics

    Find term number 6 of a geometric progression with first term 1 and common ratio 3.

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