ACT · Practice Sheet 43

1. 1.

   Quantitative Aptitude

   Find the simple interest on $11,000 at 6% per annum for 2 year(s).

   Formula:Simple Interest

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

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2. 2.

   Physics

   A body moving at 13 m/s accelerates at 2 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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3. 3.

   Physics

   Find the electrical power when 135 V drives a current of 15 A.

   Formula:Electrical Power

   $P = VI$

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4. 4.

   Quantitative Aptitude

   Find the average of these 10 numbers: 29, 28, 39, 70, 58, 74, 50, 59, 28, 74.

   Formula:Arithmetic Mean

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

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5. 5.

   Quantitative Aptitude

   A vehicle covers 595 km in 7 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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6. 6.

   Mathematics

   Find term number 7 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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7. 7.

   Quantitative Aptitude

   An item is bought for $500 and sold for $650. Find the profit percentage.

   Formula:Profit Percentage

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

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8. 8.

   Mathematics

   In an arithmetic progression with first term 3 and common difference 9, find term number 13.

   Formula:AP nth Term

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

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9. 9.

   Physics

   A projectile is launched at 11 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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10. 10.

    Physics

    Find the electrical power when 19 V drives a current of 14 A.

    Formula:Electrical Power

    $P = VI$

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11. 11.

    Mathematics

    Find the sum of the first 15 terms of an AP with first term 15 and common difference 4.

    Formula:AP Sum of n Terms

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

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12. 12.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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13. 13.

    Quantitative Aptitude

    Find the HCF and LCM of 25 and 24.

    Formula:LCM & HCF

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

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14. 14.

    Mathematics

    Find the sum of the first 17 terms of an AP with first term 7 and common difference 1.

    Formula:AP Sum of n Terms

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

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15. 15.

    Mathematics

    Find the distance between the points (-3, 3) and (2, 2).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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16. 16.

    Quantitative Aptitude

    Find the HCF and LCM of 14 and 17.

    Formula:LCM & HCF

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

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17. 17.

    Physics

    A constant force of 182 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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18. 18.

    Quantitative Aptitude

    An item is bought for $300 and sold for $360. Find the profit percentage.

    Formula:Profit Percentage

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

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19. 19.

    Physics

    Find the kinetic energy of a 18 kg object moving at 10 m/s.

    Formula:Kinetic Energy

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

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20. 20.

    Quantitative Aptitude

    Find the average of these 8 numbers: 89, 89, 79, 63, 85, 20, 54, 44.

    Formula:Arithmetic Mean

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

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