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SAT · Practice Sheet 1

Sheet code: SAT-US-S01 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 5?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  2. 2.
    Quantitative Aptitude

    The sum of the ages of two people is 91 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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  3. 3.
    Mathematics

    Find term number 7 of a geometric progression with first term 6 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  4. 4.
    Mathematics

    In an arithmetic progression with first term 12 and common difference 8, find term number 29.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  5. 5.
    Mathematics

    Find the sum of the first 22 terms of an AP with first term 7 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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  6. 6.
    Quantitative Aptitude

    Find the average of these 6 numbers: 59, 71, 23, 84, 88, 41.

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

    Pipe A fills a tank in 11 hours and pipe B in 8 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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  8. 8.
    Quantitative Aptitude

    A value changes from 800 to 1,200. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  9. 9.
    Mathematics

    Find the sum of the first 7 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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  10. 10.
    Mathematics

    Find the sum of the first 6 terms of an AP with first term 15 and common difference 4.

    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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  11. 11.
    Mathematics

    Find the slope of the line through (-5, 3) and (4, 5).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  12. 12.
    Mathematics

    Find the sum of the first 24 terms of an AP with first term 16 and common difference 9.

    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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  13. 13.
    Quantitative Aptitude

    Pipe A fills a tank in 3 hours and pipe B in 8 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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  14. 14.
    Mathematics

    If f(x) = 5x³ + 4x² + 1x, find f′(2).

    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.
    Quantitative Aptitude

    Find the simple interest on $28,000 at 12% per annum for 5 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  16. 16.
    Quantitative Aptitude

    An item is bought for $500 and sold for $600. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  17. 17.
    Quantitative Aptitude

    The sum of the ages of two people is 34 years, and one is 14 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  18. 18.
    Quantitative Aptitude

    Find the HCF and LCM of 18 and 18.

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

    Find the simple interest on $20,000 at 12% per annum for 4 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  20. 20.
    Mathematics

    Evaluate ∫ from 1 to 3 of 5x^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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