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SAT · Practice Sheet 50

Sheet code: SAT-S50 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    Find term number 5 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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  2. 2.
    Quantitative Aptitude

    A vehicle covers 210 km in 5 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  3. 3.
    Mathematics

    Find the sum of the first 5 terms of a GP with first term 2 and common ratio 3.

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
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  4. 4.
    Mathematics

    If f(x) = 4x³ + 5x² + 9x, 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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  5. 5.
    Quantitative Aptitude

    A value changes from 600 to 300. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  6. 6.
    Mathematics

    Find the sum of the first 6 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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  7. 7.
    Quantitative Aptitude

    Two varieties costing AED 12 and AED 93 per kg are mixed to give a mixture worth AED 81 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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  8. 8.
    Quantitative Aptitude

    A invests AED 5,000 and B invests AED 8,000 for the same period. If the total profit is AED 8,000, 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.
    Mathematics

    Find the distance between the points (8, -1) and (2, -4).

    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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  10. 10.
    Mathematics

    For the quadratic 3x² − 8x + 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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  11. 11.
    Quantitative Aptitude

    An item is bought for AED 600 and sold for AED 900. 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.
    Quantitative Aptitude

    The marked price of an item is AED 800. After a 40% 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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  13. 13.
    Mathematics

    In an arithmetic progression with first term 10 and common difference 10, find term number 24.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  14. 14.
    Quantitative Aptitude

    Find the HCF and LCM of 17 and 26.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  15. 15.
    Mathematics

    Find the distance between the points (-7, 3) and (-2, -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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  16. 16.
    Quantitative Aptitude

    Find the HCF and LCM of 10 and 13.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  17. 17.
    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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  18. 18.
    Quantitative Aptitude

    Find the HCF and LCM of 22 and 39.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  19. 19.
    Quantitative Aptitude

    The marked price of an item is AED 700. After a 20% 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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  20. 20.
    Quantitative Aptitude

    The sum of the ages of two people is 47 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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