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SAT · Practice Sheet 11

Sheet code: SAT-S11 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    Find the sum of the first 14 terms of an AP with first term 19 and common difference 6.

    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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  2. 2.
    Mathematics

    Find term number 7 of a geometric progression with first term 4 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  3. 3.
    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 3.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  4. 4.
    Quantitative Aptitude

    A can finish a job in 18 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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  5. 5.
    Mathematics

    For the quadratic 4x² + 7x + 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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  6. 6.
    Quantitative Aptitude

    Two varieties costing AED 27 and AED 100 per kg are mixed to give a mixture worth AED 87 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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  7. 7.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 6?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  8. 8.
    Quantitative Aptitude

    The sum of the ages of two people is 49 years, and one is 17 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  9. 9.
    Mathematics

    Find the distance between the points (2, -7) and (-6, 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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  10. 10.
    Quantitative Aptitude

    Find the HCF and LCM of 31 and 28.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  11. 11.
    Mathematics

    Evaluate log base 2 of 4.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  12. 12.
    Quantitative Aptitude

    The marked price of an item is AED 1,800. After a 50% 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

    Find the distance between the points (5, 0) and (1, 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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  14. 14.
    Mathematics

    Evaluate ∫ from 2 to 5 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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  15. 15.
    Mathematics

    Find the distance between the points (-3, -1) 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.
    Mathematics

    If f(x) = 2x³ + 5x² + 7x, 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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  17. 17.
    Mathematics

    Find the sum of the first 9 terms of an AP with first term 14 and common difference 5.

    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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  18. 18.
    Quantitative Aptitude

    An item is bought for AED 900 and sold for AED 1,170. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  19. 19.
    Mathematics

    Find the sum of the first 22 terms of an AP with first term 10 and common difference 3.

    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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  20. 20.
    Quantitative Aptitude

    The sum of the ages of two people is 75 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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