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TMUA · Practice Sheet 37

Sheet code: TMUA-S37 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    For the quadratic 3x² − 8x − 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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  2. 2.
    Quantitative Aptitude

    A value changes from 800 to 1,200. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  3. 3.
    Quantitative Aptitude

    An item is bought for £400 and sold for £500. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  4. 4.
    Mathematics

    For the quadratic 3x² − 7x + 1 = 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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  5. 5.
    Quantitative Aptitude

    Find the compound interest on £13,000 at 20% 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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  6. 6.
    Quantitative Aptitude

    Find the HCF and LCM of 10 and 29.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  7. 7.
    Mathematics

    Evaluate ∫ from 0 to 5 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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  8. 8.
    Quantitative Aptitude

    A invests £6,000 and B invests £7,000 for the same period. If the total profit is £22,000, 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.
    Quantitative Aptitude

    Pipe A fills a tank in 15 hours and pipe B in 11 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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  10. 10.
    Mathematics

    Find term number 3 of a geometric progression with first term 3 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  11. 11.
    Mathematics

    Evaluate ∫ from 0 to 5 of 1x^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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  12. 12.
    Quantitative Aptitude

    An item is bought for £600 and sold for £720. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
    View formula →
  13. 13.
    Mathematics

    Find term number 4 of a geometric progression with first term 6 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  14. 14.
    Mathematics

    For the quadratic 2x² + 2x − 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}
    View formula →
  15. 15.
    Quantitative Aptitude

    An item is bought for £900 and sold for £1,350. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
    View formula →
  16. 16.
    Quantitative Aptitude

    A can finish a job in 15 days and B in 19 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  17. 17.
    Quantitative Aptitude

    The sum of the ages of two people is 41 years, and one is 13 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  18. 18.
    Mathematics

    Find term number 3 of a geometric progression with first term 5 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  19. 19.
    Quantitative Aptitude

    What is 60% of 840?

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

    Find the simple interest on £7,000 at 5% per annum for 3 year(s).

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