Engineering Entrance · Practice Sheet 3

1. 1.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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2. 2.

   Physics

   A constant force of 141 N moves an object 39 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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3. 3.

   Physics

   Find the density of an object with mass 129 g and volume 2 cm³.

   Formula:Density

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

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4. 4.

   Chemistry

   Find the pH of a solution with [H⁺] = 2×10⁻4 mol/L.

   Formula:pH of a Solution

   $pH = -\log_{10}[H^{+}]$

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5. 5.

   Chemistry

   A solution is made by dissolving 26 g of solute in 108 g of solvent. Find the mass percentage of the solute.

   Formula:Mass Percentage

   $\%\,\text{mass} = \dfrac{\text{solute}}{\text{solution}}\times 100$

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6. 6.

   Mathematics

   In an arithmetic progression with first term 18 and common difference 8, find term number 15.

   Formula:AP nth Term

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

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7. 7.

   Chemistry

   Find the molarity of a solution containing 2.5 mol of solute in 0.5 L of solution.

   Formula:Molarity

   $M = \dfrac{n}{V}$

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8. 8.

   Chemistry

   How many moles are present in 180 g of glucose (C₆H₁₂O₆) (molar mass = 180 g/mol)?

   Formula:Number of Moles

   $n = \dfrac{m}{M}$

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9. 9.

   Physics

   A force of 932 N acts on an area of 46 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Physics

    If 1,427 J of work is done in 27 s, find the power.

    Formula:Power

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

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11. 11.

    Physics

    A constant force of 121 N moves an object 9 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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12. 12.

    Mathematics

    Find term number 4 of a geometric progression with first term 5 and common ratio 2.

    Formula:GP nth Term

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

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13. 13.

    Physics

    A constant force of 86 N moves an object 3 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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14. 14.

    Physics

    Calculate the potential energy of a 32 kg object at a height of 42 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Physics

    Find the momentum of a 8 kg body moving at 17 m/s.

    Formula:Linear Momentum

    $p = mv$

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16. 16.

    Physics

    A body moving at 2 m/s accelerates at 1 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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17. 17.

    Chemistry

    A solution is made by dissolving 12 g of solute in 64 g of solvent. Find the mass percentage of the solute.

    Formula:Mass Percentage

    $\%\,\text{mass} = \dfrac{\text{solute}}{\text{solution}}\times 100$

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18. 18.

    Chemistry

    How many moles are present in 175.5 g of sodium chloride (NaCl) (molar mass = 58.5 g/mol)?

    Formula:Number of Moles

    $n = \dfrac{m}{M}$

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19. 19.

    Physics

    Calculate the potential energy of a 14 kg object at a height of 46 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Mathematics

    Evaluate log base 2 of 8.

    Formula:Logarithm Evaluation

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

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