Engineering Entrance · Practice Sheet 48

1. 1.

   Physics

   A constant force of 186 N moves an object 40 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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2. 2.

   Physics

   An object starts at 12 m/s and accelerates at 4 m/s² for 3 s. Find its final velocity.

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

   $v = u + at$

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3. 3.

   Chemistry

   Find the pH of a solution with [H⁺] = 5×10⁻6 mol/L.

   Formula:pH of a Solution

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

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4. 4.

   Physics

   Find the density of an object with mass 455 g and volume 4 cm³.

   Formula:Density

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

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5. 5.

   Mathematics

   Evaluate log base 3 of 9.

   Formula:Logarithm Evaluation

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

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6. 6.

   Chemistry

   21 mL of a 5 M solution is diluted to 323 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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7. 7.

   Chemistry

   A solution is made by dissolving 41 g of solute in 107 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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8. 8.

   Physics

   Find the electrical power when 58 V drives a current of 5 A.

   Formula:Electrical Power

   $P = VI$

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9. 9.

   Mathematics

   Find the binomial coefficient C(8, 4) — the coefficient of x^4 in (1 + x)^8.

   Formula:Binomial Coefficient

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

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10. 10.

    Mathematics

    Evaluate ∫ from 0 to 5 of 3x^3 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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11. 11.

    Chemistry

    How many moles are present in 540 g of glucose (C₆H₁₂O₆) (molar mass = 180 g/mol)?

    Formula:Number of Moles

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

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12. 12.

    Physics

    A constant force of 162 N moves an object 15 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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13. 13.

    Physics

    A force of 180 N acts on an area of 6 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    Physics

    Find the kinetic energy of a 6 kg object moving at 19 m/s.

    Formula:Kinetic Energy

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

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15. 15.

    Physics

    A force of 813 N acts on an area of 43 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Mathematics

    Find the slope of the line through (-6, -6) and (2, 2).

    Formula:Slope of a Line

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

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17. 17.

    Mathematics

    Find the distance between the points (5, 1) and (-7, -6).

    Formula:Distance Between Two Points

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

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18. 18.

    Mathematics

    For the quadratic 2x² − 1x − 7 = 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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19. 19.

    Mathematics

    Evaluate ∫ from 2 to 5 of 4x^3 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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20. 20.

    Physics

    A force of 375 N acts on an area of 15 m². Find the pressure.

    Formula:Pressure

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

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