ACT · Practice Sheet 46

1. 1.

   Physics

   Find the kinetic energy of a 18 kg object moving at 9 m/s.

   Formula:Kinetic Energy

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

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2. 2.

   Physics

   A projectile is launched at 47 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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3. 3.

   Physics

   Find the voltage across a 36 Ω resistor carrying a current of 11 A.

   Formula:Ohm's Law

   $V = IR$

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4. 4.

   Quantitative Aptitude

   A value changes from 600 to 750. Find the percentage increase.

   Formula:Percentage Change

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

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5. 5.

   Physics

   Find the density of an object with mass 86 g and volume 34 cm³.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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6. 6.

   Physics

   A body moving at 12 m/s accelerates at 6 m/s² for 9 s. Find the distance travelled.

   Formula:Equation of Motion (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^{2}$

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7. 7.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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8. 8.

   Physics

   If 729 J of work is done in 36 s, find the power.

   Formula:Power

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

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9. 9.

   Quantitative Aptitude

   The marked price of an item is $2,000. After a 40% discount, find the selling price.

   Formula:Discount & Selling Price

   $SP = MP\left(1-\dfrac{d}{100}\right)$

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10. 10.

    Mathematics

    If f(x) = 2x³ + 6x² + 6x, find f′(3).

    Formula:Derivative of a Polynomial

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

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11. 11.

    Mathematics

    For the quadratic 5x² − 2x + 1 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)

    $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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12. 12.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 4?

    Formula:Probability (two dice)

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

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13. 13.

    Physics

    Find the kinetic energy of a 2 kg object moving at 22 m/s.

    Formula:Kinetic Energy

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

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14. 14.

    Quantitative Aptitude

    An item is bought for $600 and sold for $660. Find the profit percentage.

    Formula:Profit Percentage

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

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15. 15.

    Mathematics

    Find term number 7 of a geometric progression with first term 1 and common ratio 3.

    Formula:GP nth Term

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

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16. 16.

    Mathematics

    Find the sum of the first 6 terms of a GP with first term 3 and common ratio 3.

    Formula:GP Sum of n Terms

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

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17. 17.

    Mathematics

    For the quadratic 3x² + 0x + 6 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)

    $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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18. 18.

    Quantitative Aptitude

    Find the average of these 10 numbers: 37, 78, 73, 89, 40, 57, 56, 42, 33, 82.

    Formula:Arithmetic Mean

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

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19. 19.

    Quantitative Aptitude

    Two varieties costing $13 and $79 per kg are mixed to give a mixture worth $31 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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20. 20.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 4.)

    Formula:Permutations

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

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