ACT · Practice Sheet 6

1. 1.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

   Formula:Probability (two dice)

   $P = \dfrac{\text{favourable}}{\text{total}}$

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2. 2.

   Physics

   A constant force of 92 N moves an object 36 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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3. 3.

   Mathematics

   If f(x) = 2x³ + 5x² + 4x, find f′(3).

   Formula:Derivative of a Polynomial

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

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4. 4.

   Quantitative Aptitude

   What is 15% of 680?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

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5. 5.

   Physics

   A constant force of 71 N moves an object 17 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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6. 6.

   Mathematics

   In an arithmetic progression with first term 4 and common difference 7, find term number 17.

   Formula:AP nth Term

   $a_n = a + (n-1)d$

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7. 7.

   Quantitative Aptitude

   A can finish a job in 4 days and B in 9 days. Working together, how long will they take?

   Formula:Time & Work (combined)

   $T = \dfrac{xy}{x+y}$

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8. 8.

   Quantitative Aptitude

   Divide $2,880 between two people in the ratio 5:5. How much does each receive?

   Formula:Sharing in a Ratio

   $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

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9. 9.

   Mathematics

   In an arithmetic progression with first term 19 and common difference 9, find term number 21.

   Formula:AP nth Term

   $a_n = a + (n-1)d$

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10. 10.

    Mathematics

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

    Formula:Slope of a Line

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

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11. 11.

    Physics

    Find the electrical power when 59 V drives a current of 5 A.

    Formula:Electrical Power

    $P = VI$

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12. 12.

    Physics

    An object starts at 17 m/s and accelerates at 10 m/s² for 2 s. Find its final velocity.

    Formula:Equation of Motion (v = u + at)

    $v = u + at$

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13. 13.

    Quantitative Aptitude

    A can finish a job in 11 days and B in 7 days. Working together, how long will they take?

    Formula:Time & Work (combined)

    $T = \dfrac{xy}{x+y}$

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14. 14.

    Quantitative Aptitude

    Pipe A fills a tank in 14 hours and pipe B in 13 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

    $T = \dfrac{xy}{x+y}$

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15. 15.

    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

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

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16. 16.

    Quantitative Aptitude

    Find the HCF and LCM of 6 and 13.

    Formula:LCM & HCF

    $\text{LCM}\times\text{HCF} = a\times b$

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17. 17.

    Mathematics

    Find the sum of the first 18 terms of an AP with first term 2 and common difference 6.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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18. 18.

    Physics

    An object starts at 8 m/s and accelerates at 9 m/s² for 9 s. Find its final velocity.

    Formula:Equation of Motion (v = u + at)

    $v = u + at$

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19. 19.

    Physics

    A constant force of 196 N moves an object 13 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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20. 20.

    Physics

    Find the momentum of a 13 kg body moving at 34 m/s.

    Formula:Linear Momentum

    $p = mv$

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