ACT · Practice Sheet 5

1. 1.

   Physics

   An object starts at 0 m/s and accelerates at 3 m/s² for 12 s. Find its final velocity.

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

   $v = u + at$

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2. 2.

   Mathematics

   In an arithmetic progression with first term 11 and common difference 9, find term number 24.

   Formula:AP nth Term

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

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3. 3.

   Quantitative Aptitude

   Two varieties costing $12 and $85 per kg are mixed to give a mixture worth $77 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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4. 4.

   Physics

   Find the kinetic energy of a 5 kg object moving at 14 m/s.

   Formula:Kinetic Energy

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

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5. 5.

   Physics

   Calculate the potential energy of a 45 kg object at a height of 40 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Mathematics

   Find the sum of the first 5 terms of a GP with first term 4 and common ratio 3.

   Formula:GP Sum of n Terms

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

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7. 7.

   Quantitative Aptitude

   A vehicle covers 168 km in 2 hours. Find its average speed.

   Formula:Speed, Distance & Time

   $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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8. 8.

   Physics

   An object starts at 8 m/s and accelerates at 1 m/s² for 6 s. Find its final velocity.

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

   $v = u + at$

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9. 9.

   Mathematics

   Find the sum of the first 8 terms of an AP with first term 8 and common difference 1.

   Formula:AP Sum of n Terms

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

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10. 10.

    Quantitative Aptitude

    Find the compound interest on $16,000 at 10% per annum compounded annually for 2 years.

    Formula:Compound Interest

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

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11. 11.

    Physics

    Find the density of an object with mass 310 g and volume 30 cm³.

    Formula:Density

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

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12. 12.

    Quantitative Aptitude

    What is 15% of 580?

    Formula:Percentage of a Number

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

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13. 13.

    Mathematics

    In an arithmetic progression with first term 2 and common difference 8, find term number 25.

    Formula:AP nth Term

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

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14. 14.

    Quantitative Aptitude

    A vehicle covers 287 km in 7 hours. Find its average speed.

    Formula:Speed, Distance & Time

    $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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15. 15.

    Quantitative Aptitude

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

    Formula:Profit Percentage

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

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16. 16.

    Mathematics

    If f(x) = 2x³ + 4x² + 6x, find f′(4).

    Formula:Derivative of a Polynomial

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

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17. 17.

    Physics

    Find the force required to accelerate a 46 kg mass at 16 m/s².

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

    $F = ma$

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18. 18.

    Mathematics

    Evaluate log base 10 of 10,000.

    Formula:Logarithm Evaluation

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

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19. 19.

    Mathematics

    Find the slope of the line through (-8, 6) and (5, -6).

    Formula:Slope of a Line

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

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20. 20.

    Quantitative Aptitude

    The sum of the ages of two people is 67 years, and one is 11 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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