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SAT · Practice Sheet 4

Sheet code: SAT-US-S04 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    Find the slope of the line through (-8, 5) and (3, -2).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  2. 2.
    Mathematics

    Find the distance between the points (5, -4) 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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  3. 3.
    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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  4. 4.
    Mathematics

    Find the sum of the first 3 terms of a GP with first term 4 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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  5. 5.
    Quantitative Aptitude

    Find the simple interest on $7,000 at 5% per annum for 6 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  6. 6.
    Quantitative Aptitude

    Find the average of these 8 numbers: 86, 55, 50, 45, 40, 23, 23, 43.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  7. 7.
    Quantitative Aptitude

    An item is bought for $700 and sold for $840. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  8. 8.
    Quantitative Aptitude

    Find the compound interest on $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

    Find the simple interest on $2,000 at 6% per annum for 3 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  10. 10.
    Quantitative Aptitude

    Two varieties costing $39 and $79 per kg are mixed to give a mixture worth $49 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 can finish a job in 11 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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  12. 12.
    Mathematics

    For the quadratic 3x² + 6x + 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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  13. 13.
    Mathematics

    Find the slope of the line through (-7, 1) and (-2, 7).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  14. 14.
    Mathematics

    If f(x) = 4x³ + 3x² + 9x, find f′(5).

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  15. 15.
    Mathematics

    Find the distance between the points (-3, 0) and (4, -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 simple interest on $9,000 at 4% per annum for 3 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  17. 17.
    Mathematics

    Find the binomial coefficient C(8, 4) — the coefficient of x^4 in (1 + x)^8.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  18. 18.
    Quantitative Aptitude

    Find the HCF and LCM of 15 and 27.

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

    Pipe A fills a tank in 14 hours and pipe B in 12 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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  20. 20.
    Quantitative Aptitude

    The marked price of an item is $1,500. 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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