ACT · Practice Sheet 1

1. 1.

   Mathematics

   Evaluate log base 2 of 4.

   Formula:Logarithm Evaluation

   $\log_{b}(b^{k}) = k$

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2. 2.

   Mathematics

   If f(x) = 2x³ + 3x² + 2x, find f′(4).

   Formula:Derivative of a Polynomial

   $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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3. 3.

   Quantitative Aptitude

   In how many ways can 3 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 3.)

   Formula:Permutations

   $^{n}P_{r} = \dfrac{n!}{(n-r)!}$

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4. 4.

   Quantitative Aptitude

   Find the simple interest on $28,000 at 10% per annum for 3 year(s).

   Formula:Simple Interest

   $SI = \dfrac{P\times R\times T}{100}$

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5. 5.

   Quantitative Aptitude

   Find the compound interest on $18,000 at 20% per annum compounded annually for 2 years.

   Formula:Compound Interest

   $A = P\left(1+\dfrac{R}{100}\right)^{T}$

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6. 6.

   Physics

   Find the kinetic energy of a 19 kg object moving at 24 m/s.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2}mv^{2}$

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7. 7.

   Quantitative Aptitude

   A invests $2,000 and B invests $7,000 for the same period. If the total profit is $32,000, find A's share.

   Formula:Partnership (profit share)

   $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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8. 8.

   Quantitative Aptitude

   A value changes from 500 to 250. Find the percentage decrease.

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$

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9. 9.

   Mathematics

   Find term number 6 of a geometric progression with first term 4 and common ratio 3.

   Formula:GP nth Term

   $a_n = a\,r^{\,n-1}$

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10. 10.

    Physics

    Find the voltage across a 34 Ω resistor carrying a current of 11 A.

    Formula:Ohm's Law

    $V = IR$

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11. 11.

    Mathematics

    If f(x) = 5x³ + 4x² + 7x, find f′(2).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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12. 12.

    Physics

    If 1,770 J of work is done in 8 s, find the power.

    Formula:Power

    $P = \dfrac{W}{t}$

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13. 13.

    Mathematics

    Find the slope of the line through (-2, 4) and (0, -1).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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14. 14.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 3.)

    Formula:Permutations

    $^{n}P_{r} = \dfrac{n!}{(n-r)!}$

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15. 15.

    Quantitative Aptitude

    Two varieties costing $39 and $62 per kg are mixed to give a mixture worth $44 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)

    $\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$

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16. 16.

    Mathematics

    Find term number 7 of a geometric progression with first term 6 and common ratio 2.

    Formula:GP nth Term

    $a_n = a\,r^{\,n-1}$

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17. 17.

    Quantitative Aptitude

    Find the simple interest on $36,000 at 8% per annum for 2 year(s).

    Formula:Simple Interest

    $SI = \dfrac{P\times R\times T}{100}$

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18. 18.

    Mathematics

    Find the slope of the line through (-6, -7) and (-5, 7).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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19. 19.

    Quantitative Aptitude

    A value changes from 500 to 650. Find the percentage increase.

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$

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20. 20.

    Quantitative Aptitude

    Find the simple interest on $15,000 at 5% per annum for 6 year(s).

    Formula:Simple Interest

    $SI = \dfrac{P\times R\times T}{100}$

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