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SAT · Practice Sheet 26

Sheet code: SAT-S26 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    Evaluate ∫ from 2 to 4 of 1x^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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  2. 2.
    Quantitative Aptitude

    A invests AED 9,000 and B invests AED 4,000 for the same period. If the total profit is AED 31,000, 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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  3. 3.
    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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  4. 4.
    Mathematics

    Find term number 5 of a geometric progression with first term 2 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  5. 5.
    Mathematics

    Evaluate ∫ from 2 to 4 of 3x^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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  6. 6.
    Quantitative Aptitude

    What is 75% of 740?

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

    Find the sum of the first 3 terms of a GP with first term 1 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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  8. 8.
    Mathematics

    Evaluate log base 10 of 1,000.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  9. 9.
    Mathematics

    Find the distance between the points (3, -4) and (0, -2).

    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.
    Quantitative Aptitude

    Two varieties costing AED 38 and AED 78 per kg are mixed to give a mixture worth AED 53 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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  11. 11.
    Quantitative Aptitude

    A value changes from 400 to 360. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  12. 12.
    Quantitative Aptitude

    A invests AED 2,000 and B invests AED 9,000 for the same period. If the total profit is AED 39,000, 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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  13. 13.
    Mathematics

    In an arithmetic progression with first term 16 and common difference 8, find term number 23.

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

    The sum of the ages of two people is 40 years, and one is 10 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  15. 15.
    Quantitative Aptitude

    A value changes from 200 to 100. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  16. 16.
    Mathematics

    In an arithmetic progression with first term 6 and common difference 10, find term number 10.

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

    Find the HCF and LCM of 18 and 33.

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

    If f(x) = 2x³ + 3x² + 6x, 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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  19. 19.
    Quantitative Aptitude

    Find the HCF and LCM of 16 and 33.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  20. 20.
    Quantitative Aptitude

    Find the simple interest on AED 2,000 at 8% per annum for 3 year(s).

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