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SAT · Practice Sheet 11

Sheet code: SAT-US-S11 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    For the quadratic 5x² − 4x + 8 = 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

    Find the average of these 6 numbers: 66, 29, 54, 55, 40, 24.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  3. 3.
    Mathematics

    Find the slope of the line through (7, -1) and (1, -7).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  4. 4.
    Mathematics

    Find the distance between the points (3, -7) and (-4, -1).

    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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  5. 5.
    Mathematics

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

    In how many ways can 2 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 2.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  7. 7.
    Mathematics

    For the quadratic 4x² + 8x − 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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  8. 8.
    Mathematics

    Find the binomial coefficient C(7, 3) — the coefficient of x^3 in (1 + x)^7.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  9. 9.
    Mathematics

    In an arithmetic progression with first term 1 and common difference 4, find term number 10.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  10. 10.
    Quantitative Aptitude

    The sum of the ages of two people is 39 years, and one is 7 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  11. 11.
    Quantitative Aptitude

    The marked price of an item is $1,900. 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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  12. 12.
    Quantitative Aptitude

    Two varieties costing $31 and $79 per kg are mixed to give a mixture worth $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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  13. 13.
    Quantitative Aptitude

    The sum of the ages of two people is 88 years, and one is 20 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  14. 14.
    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  15. 15.
    Mathematics

    Find the sum of the first 3 terms of a GP with first term 3 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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  16. 16.
    Quantitative Aptitude

    A can finish a job in 13 days and B in 10 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

    An item is bought for $900 and sold for $1,125. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  18. 18.
    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 2.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  19. 19.
    Quantitative Aptitude

    A can finish a job in 5 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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  20. 20.
    Quantitative Aptitude

    The marked price of an item is $1,600. After a 30% 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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