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GCSE Maths · Practice Sheet 36

Sheet code: GCSE-MATHS-S36 · 20 questions

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

    Two fair dice are rolled. What is the probability that the sum of the numbers is 10?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  2. 2.
    Quantitative Aptitude

    Find the average of these 10 numbers: 49, 76, 42, 81, 70, 45, 61, 72, 58, 71.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  3. 3.
    Quantitative Aptitude

    Two varieties costing £31 and £91 per kg are mixed to give a mixture worth £44 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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  4. 4.
    Mathematics

    Find the sum of the first 24 terms of an AP with first term 17 and common difference 10.

    Formula:AP Sum of n Terms
    Sn=n2 [2a+(n−1)d]S_n = \dfrac{n}{2}\,[2a+(n-1)d]
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  5. 5.
    Quantitative Aptitude

    Find the HCF and LCM of 30 and 8.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  6. 6.
    Mathematics

    For the quadratic 2x² − 6x − 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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  7. 7.
    Quantitative Aptitude

    Find the compound interest on £17,000 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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  8. 8.
    Quantitative Aptitude

    A can finish a job in 11 days and B in 13 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  9. 9.
    Mathematics

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

    Divide £1,365 between two people in the ratio 4:3. 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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  11. 11.
    Quantitative Aptitude

    An item is bought for £800 and sold for £960. 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

    Find the sum of the first 5 terms of a GP with first term 1 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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  13. 13.
    Mathematics

    Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  14. 14.
    Quantitative Aptitude

    Pipe A fills a tank in 8 hours and pipe B in 7 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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  15. 15.
    Mathematics

    In an arithmetic progression with first term 10 and common difference 3, find term number 26.

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

    Find the simple interest on £24,000 at 10% per annum for 3 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  17. 17.
    Mathematics

    For the quadratic 3x² + 2x + 9 = 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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  18. 18.
    Quantitative Aptitude

    The marked price of an item is £1,900. 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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  19. 19.
    Quantitative Aptitude

    What is 30% of 460?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  20. 20.
    Quantitative Aptitude

    A value changes from 900 to 630. Find the percentage decrease.

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