ACT · Practice Sheet 9

1. 1.

   Physics

   A projectile is launched at 17 m/s at 60° to the horizontal. Find its range (g = 9.8 m/s²).

   Formula:Projectile Range

   $R = \dfrac{u^{2}\sin 2\theta}{g}$

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2. 2.

   Physics

   Find the electrical power when 34 V drives a current of 3 A.

   Formula:Electrical Power

   $P = VI$

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3. 3.

   Mathematics

   If f(x) = 3x³ + 5x² + 5x, 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

   In how many ways can 4 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 4.)

   Formula:Combinations

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

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5. 5.

   Quantitative Aptitude

   In how many ways can 3 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 3.)

   Formula:Permutations

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

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6. 6.

   Quantitative Aptitude

   What is 60% of 400?

   Formula:Percentage of a Number

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

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7. 7.

   Quantitative Aptitude

   An item is bought for $400 and sold for $600. Find the profit percentage.

   Formula:Profit Percentage

   $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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8. 8.

   Mathematics

   Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.

   Formula:Binomial Coefficient

   $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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9. 9.

   Quantitative Aptitude

   A value changes from 600 to 450. Find the percentage decrease.

   Formula:Percentage Change

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

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10. 10.

    Physics

    A constant force of 52 N moves an object 8 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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11. 11.

    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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12. 12.

    Physics

    If 3,525 J of work is done in 38 s, find the power.

    Formula:Power

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

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13. 13.

    Quantitative Aptitude

    Find the average of these 10 numbers: 82, 41, 57, 43, 81, 87, 74, 34, 75, 43.

    Formula:Arithmetic Mean

    $\bar{x} = \dfrac{\sum x}{n}$

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14. 14.

    Mathematics

    Find term number 6 of a geometric progression with first term 5 and common ratio 3.

    Formula:GP nth Term

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

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15. 15.

    Physics

    A force of 963 N acts on an area of 44 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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16. 16.

    Quantitative Aptitude

    Divide $793 between two people in the ratio 6:7. 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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17. 17.

    Physics

    Find the kinetic energy of a 5 kg object moving at 25 m/s.

    Formula:Kinetic Energy

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

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18. 18.

    Physics

    A projectile is launched at 20 m/s at 60° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range

    $R = \dfrac{u^{2}\sin 2\theta}{g}$

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19. 19.

    Physics

    Find the force required to accelerate a 38 kg mass at 8 m/s².

    Formula:Newton's Second Law (F = ma)

    $F = ma$

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20. 20.

    Quantitative Aptitude

    A can finish a job in 12 days and B in 8 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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