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ACT · Practice Sheet 26

Sheet code: ACT-S26 · 20 questions

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

    The sum of the ages of two people is 62 years, and one is 4 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  2. 2.
    Quantitative Aptitude

    An item is bought for $900 and sold for $1,035. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  3. 3.
    Mathematics

    Evaluate ∫ from 0 to 3 of 1x^2 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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  4. 4.
    Quantitative Aptitude

    The sum of the ages of two people is 81 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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  5. 5.
    Physics

    A force of 858 N acts on an area of 30 m². Find the pressure.

    Formula:Pressure
    P=FAP = \dfrac{F}{A}
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  6. 6.
    Quantitative Aptitude

    An item is bought for $200 and sold for $300. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  7. 7.
    Physics

    Find the kinetic energy of a 3 kg object moving at 30 m/s.

    Formula:Kinetic Energy
    KE=12mv2KE = \tfrac{1}{2}mv^{2}
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  8. 8.
    Mathematics

    Evaluate log base 10 of 1,000,000.

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

    In an arithmetic progression with first term 6 and common difference 9, find term number 30.

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

    Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  11. 11.
    Quantitative Aptitude

    A vehicle covers 88 km in 2 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  12. 12.
    Mathematics

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

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  13. 13.
    Quantitative Aptitude

    What is 75% of 880?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  14. 14.
    Quantitative Aptitude

    A value changes from 900 to 540. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  15. 15.
    Physics

    Find the density of an object with mass 452 g and volume 25 cm³.

    Formula:Density
    ρ=mV\rho = \dfrac{m}{V}
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  16. 16.
    Quantitative Aptitude

    Two varieties costing $11 and $92 per kg are mixed to give a mixture worth $17 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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  17. 17.
    Quantitative Aptitude

    A invests $2,000 and B invests $5,000 for the same period. If the total profit is $38,000, 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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  18. 18.
    Mathematics

    Find the sum of the first 24 terms of an AP with first term 9 and common difference 2.

    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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  19. 19.
    Quantitative Aptitude

    What is 40% of 220?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  20. 20.
    Quantitative Aptitude

    Find the simple interest on $24,000 at 10% per annum for 3 year(s).

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