Engineering Entrance · Practice Sheet 38

1. 1.

   Chemistry

   A solution is made by dissolving 10 g of solute in 200 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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2. 2.

   Mathematics

   For the quadratic 1x² + 0x + 3 = 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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3. 3.

   Mathematics

   Evaluate log base 2 of 8.

   Formula:Logarithm Evaluation

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

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4. 4.

   Physics

   Find the density of an object with mass 131 g and volume 25 cm³.

   Formula:Density

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

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5. 5.

   Mathematics

   Find the sum of the first 6 terms of a GP with first term 1 and common ratio 3.

   Formula:GP Sum of n Terms

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

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6. 6.

   Physics

   Find the electrical power when 135 V drives a current of 3 A.

   Formula:Electrical Power

   $P = VI$

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7. 7.

   Physics

   Find the kinetic energy of a 13 kg object moving at 15 m/s.

   Formula:Kinetic Energy

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

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8. 8.

   Chemistry

   Find the molarity of a solution containing 2.5 mol of solute in 2 L of solution.

   Formula:Molarity

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

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9. 9.

   Mathematics

   Find term number 7 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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10. 10.

    Physics

    Calculate the potential energy of a 29 kg object at a height of 37 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Physics

    Find the voltage across a 4 Ω resistor carrying a current of 16 A.

    Formula:Ohm's Law

    $V = IR$

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12. 12.

    Physics

    A force of 716 N acts on an area of 18 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    Physics

    A body moving at 4 m/s accelerates at 1 m/s² for 6 s. Find the distance travelled.

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

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

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14. 14.

    Mathematics

    If f(x) = 1x³ + 2x² + 3x, find f′(3).

    Formula:Derivative of a Polynomial

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

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15. 15.

    Mathematics

    Find the sum of the first 5 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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16. 16.

    Physics

    A body moving at 10 m/s accelerates at 3 m/s² for 8 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

    Find the pressure of 3 mol of an ideal gas at 379 K in a 6 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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18. 18.

    Physics

    A force of 737 N acts on an area of 44 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Mathematics

    Find the slope of the line through (-7, 7) and (-6, 1).

    Formula:Slope of a Line

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

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20. 20.

    Physics

    Find the momentum of a 42 kg body moving at 8 m/s.

    Formula:Linear Momentum

    $p = mv$

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