Engineering Entrance · Practice Sheet 22

1. 1.

   Mathematics

   Evaluate log base 5 of 3,125.

   Formula:Logarithm Evaluation

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

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2. 2.

   Mathematics

   Find the slope of the line through (6, 7) and (-8, 4).

   Formula:Slope of a Line

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

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3. 3.

   Physics

   Find the voltage across a 19 Ω resistor carrying a current of 4 A.

   Formula:Ohm's Law

   $V = IR$

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4. 4.

   Mathematics

   Find term number 6 of a geometric progression with first term 6 and common ratio 2.

   Formula:GP nth Term

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

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5. 5.

   Physics

   A constant force of 44 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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6. 6.

   Mathematics

   Evaluate log base 2 of 64.

   Formula:Logarithm Evaluation

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

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7. 7.

   Chemistry

   90 mL of a 1 M solution is diluted to 408 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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8. 8.

   Physics

   Find the kinetic energy of a 3 kg object moving at 9 m/s.

   Formula:Kinetic Energy

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

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9. 9.

   Physics

   Find the momentum of a 9 kg body moving at 14 m/s.

   Formula:Linear Momentum

   $p = mv$

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10. 10.

    Physics

    Find the kinetic energy of a 19 kg object moving at 21 m/s.

    Formula:Kinetic Energy

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

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11. 11.

    Mathematics

    Evaluate log base 10 of 100,000.

    Formula:Logarithm Evaluation

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

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12. 12.

    Mathematics

    For the quadratic 3x² + 3x − 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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13. 13.

    Mathematics

    Find the distance between the points (-3, 1) and (-4, 0).

    Formula:Distance Between Two Points

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

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14. 14.

    Chemistry

    A solution is made by dissolving 44 g of solute in 193 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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15. 15.

    Mathematics

    Evaluate ∫ from 2 to 5 of 2x^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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16. 16.

    Mathematics

    Find the sum of the first 8 terms of an AP with first term 9 and common difference 8.

    Formula:AP Sum of n Terms

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

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17. 17.

    Physics

    A constant force of 55 N moves an object 2 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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18. 18.

    Mathematics

    In an arithmetic progression with first term 3 and common difference 7, find term number 5.

    Formula:AP nth Term

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

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19. 19.

    Physics

    Find the density of an object with mass 333 g and volume 2 cm³.

    Formula:Density

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

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20. 20.

    Chemistry

    Find the pH of a solution with [H⁺] = 5×10⁻2 mol/L.

    Formula:pH of a Solution

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

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