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SAT · Practice Sheet 30

Sheet code: SAT-S30 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    If f(x) = 3x³ + 1x² + 9x, find f′(4).

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  2. 2.
    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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  3. 3.
    Quantitative Aptitude

    Pipe A fills a tank in 4 hours and pipe B in 5 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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  4. 4.
    Mathematics

    For the quadratic 4x² + 3x + 0 = 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.
    Mathematics

    If f(x) = 4x³ + 6x² + 5x, find f′(3).

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  6. 6.
    Quantitative Aptitude

    What is 30% of 360?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  7. 7.
    Mathematics

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

    Find the compound interest on AED 19,000 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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  9. 9.
    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 2.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  10. 10.
    Mathematics

    Find the distance between the points (-6, 6) and (1, 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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  11. 11.
    Quantitative Aptitude

    A can finish a job in 9 days and B in 14 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  12. 12.
    Quantitative Aptitude

    Find the simple interest on AED 10,000 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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  13. 13.
    Mathematics

    For the quadratic 1x² + 2x + 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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  14. 14.
    Mathematics

    Find term number 6 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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  15. 15.
    Quantitative Aptitude

    A can finish a job in 15 days and B in 17 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  16. 16.
    Quantitative Aptitude

    An item is bought for AED 200 and sold for AED 250. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  17. 17.
    Quantitative Aptitude

    Two varieties costing AED 39 and AED 100 per kg are mixed to give a mixture worth AED 48 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

    A invests AED 4,000 and B invests AED 8,000 for the same period. If the total profit is AED 7,000, 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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  19. 19.
    Quantitative Aptitude

    Divide AED 2,160 between two people in the ratio 7:5. 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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  20. 20.
    Quantitative Aptitude

    A can finish a job in 12 days and B in 5 days. Working together, how long will they take?

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