Engineering Entrance · Practice Sheet 35

1. 1.

   Chemistry

   Find the pH of a solution with [H⁺] = 1×10⁻2 mol/L.

   Formula:pH of a Solution

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

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2. 2.

   Mathematics

   Find the slope of the line through (7, -2) and (-4, 8).

   Formula:Slope of a Line

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

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3. 3.

   Chemistry

   Find the molarity of a solution containing 1 mol of solute in 1 L of solution.

   Formula:Molarity

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

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4. 4.

   Chemistry

   Find the pressure of 2 mol of an ideal gas at 337 K in a 14 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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5. 5.

   Chemistry

   Find the pH of a solution with [H⁺] = 1×10⁻2 mol/L.

   Formula:pH of a Solution

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

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6. 6.

   Physics

   Find the force required to accelerate a 13 kg mass at 5 m/s².

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

   $F = ma$

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7. 7.

   Mathematics

   Evaluate log base 3 of 27.

   Formula:Logarithm Evaluation

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

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8. 8.

   Physics

   Find the voltage across a 38 Ω resistor carrying a current of 18 A.

   Formula:Ohm's Law

   $V = IR$

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9. 9.

   Physics

   Find the electrical power when 181 V drives a current of 4 A.

   Formula:Electrical Power

   $P = VI$

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10. 10.

    Mathematics

    Find the binomial coefficient C(5, 3) — the coefficient of x^3 in (1 + x)^5.

    Formula:Binomial Coefficient

    $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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11. 11.

    Physics

    An object starts at 12 m/s and accelerates at 6 m/s² for 3 s. Find its final velocity.

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

    $v = u + at$

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12. 12.

    Chemistry

    41 mL of a 10 M solution is diluted to 350 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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13. 13.

    Physics

    A body moving at 8 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.

    Physics

    Find the voltage across a 41 Ω resistor carrying a current of 14 A.

    Formula:Ohm's Law

    $V = IR$

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15. 15.

    Physics

    Find the kinetic energy of a 4 kg object moving at 26 m/s.

    Formula:Kinetic Energy

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

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16. 16.

    Mathematics

    Evaluate ∫ from 1 to 4 of 4x^1 dx.

    Formula:Definite Integral of a Power

    $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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17. 17.

    Physics

    An object starts at 17 m/s and accelerates at 7 m/s² for 12 s. Find its final velocity.

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

    $v = u + at$

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18. 18.

    Physics

    A body moving at 9 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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19. 19.

    Chemistry

    44 mL of a 1 M solution is diluted to 255 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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20. 20.

    Physics

    Find the force required to accelerate a 23 kg mass at 11 m/s².

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

    $F = ma$

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