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11+ · Practice Sheet 33

Sheet code: ELEVEN-PLUS-S33 · 20 questions

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

    Find the compound interest on £13,000 at 20% 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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  2. 2.
    Quantitative Aptitude

    An item is bought for £600 and sold for £840. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  3. 3.
    Quantitative Aptitude

    Find the simple interest on £28,000 at 8% per annum for 5 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  4. 4.
    Quantitative Aptitude

    Find the compound interest on £17,000 at 10% 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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  5. 5.
    Mathematics

    Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  6. 6.
    Mathematics

    In an arithmetic progression with first term 15 and common difference 6, find term number 30.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  7. 7.
    Mathematics

    If f(x) = 1x³ + 5x² + 3x, 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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  8. 8.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 6?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  9. 9.
    Mathematics

    Evaluate ∫ from 2 to 4 of 4x^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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  10. 10.
    Mathematics

    Find term number 7 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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  11. 11.
    Quantitative Aptitude

    Find the average of these 8 numbers: 87, 48, 30, 26, 76, 82, 83, 55.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  12. 12.
    Mathematics

    Evaluate log base 2 of 4.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  13. 13.
    Quantitative Aptitude

    Find the HCF and LCM of 14 and 7.

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

    For the quadratic 3x² + 0x − 5 = 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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  15. 15.
    Mathematics

    In an arithmetic progression with first term 13 and common difference 9, find term number 17.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  16. 16.
    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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  17. 17.
    Quantitative Aptitude

    Two varieties costing £21 and £98 per kg are mixed to give a mixture worth £61 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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  18. 18.
    Quantitative Aptitude

    The sum of the ages of two people is 79 years, and one is 5 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  19. 19.
    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 3.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  20. 20.
    Quantitative Aptitude

    An item is bought for £400 and sold for £460. Find the profit percentage.

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