Engineering Entrance · Practice Sheet 6

1. 1.

   Mathematics

   If f(x) = 1x³ + 3x² + 8x, find f′(3).

   Formula:Derivative of a Polynomial

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

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2. 2.

   Chemistry

   65 mL of a 10 M solution is diluted to 444 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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3. 3.

   Physics

   A force of 185 N acts on an area of 33 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   Mathematics

   Find the sum of the first 7 terms of a GP with first term 5 and common ratio 3.

   Formula:GP Sum of n Terms

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

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5. 5.

   Chemistry

   A solution is made by dissolving 18 g of solute in 113 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

   Find the sum of the first 5 terms of a GP with first term 3 and common ratio 2.

   Formula:GP Sum of n Terms

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

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7. 7.

   Physics

   A force of 441 N acts on an area of 2 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Mathematics

   Find the sum of the first 11 terms of an AP with first term 1 and common difference 6.

   Formula:AP Sum of n Terms

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

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9. 9.

   Chemistry

   Find the pressure of 5 mol of an ideal gas at 252 K in a 18 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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10. 10.

    Chemistry

    25 mL of a 10 M solution is diluted to 336 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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11. 11.

    Physics

    If 1,111 J of work is done in 24 s, find the power.

    Formula:Power

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

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12. 12.

    Mathematics

    Find the slope of the line through (7, -4) and (-6, -5).

    Formula:Slope of a Line

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

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13. 13.

    Mathematics

    Evaluate log base 10 of 10,000.

    Formula:Logarithm Evaluation

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

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14. 14.

    Physics

    A projectile is launched at 29 m/s at 30° 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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15. 15.

    Chemistry

    Find the pH of a solution with [H⁺] = 5×10⁻5 mol/L.

    Formula:pH of a Solution

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

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16. 16.

    Chemistry

    11 mL of a 10 M solution is diluted to 187 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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17. 17.

    Physics

    Find the electrical power when 102 V drives a current of 2 A.

    Formula:Electrical Power

    $P = VI$

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18. 18.

    Mathematics

    Find the sum of the first 4 terms of a GP with first term 3 and common ratio 2.

    Formula:GP Sum of n Terms

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

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19. 19.

    Chemistry

    Find the molarity of a solution containing 2.5 mol of solute in 4 L of solution.

    Formula:Molarity

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

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20. 20.

    Chemistry

    Find the pH of a solution with [H⁺] = 1×10⁻6 mol/L.

    Formula:pH of a Solution

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

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