Engineering Entrance · Practice Sheet 44

1. 1.

   Mathematics

   Find the distance between the points (-5, -6) and (-6, 2).

   Formula:Distance Between Two Points

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

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2. 2.

   Chemistry

   How many moles are present in 80 g of oxygen gas (O₂) (molar mass = 32 g/mol)?

   Formula:Number of Moles

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

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3. 3.

   Chemistry

   Find the molarity of a solution containing 1 mol of solute in 2 L of solution.

   Formula:Molarity

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

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4. 4.

   Mathematics

   Evaluate ∫ from 2 to 4 of 5x^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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5. 5.

   Mathematics

   In an arithmetic progression with first term 10 and common difference 10, find term number 16.

   Formula:AP nth Term

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

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6. 6.

   Physics

   A force of 712 N acts on an area of 27 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Mathematics

   Find the slope of the line through (2, -8) and (-6, -2).

   Formula:Slope of a Line

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

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8. 8.

   Mathematics

   Find the sum of the first 4 terms of a GP with first term 6 and common ratio 2.

   Formula:GP Sum of n Terms

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

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9. 9.

   Mathematics

   Find the distance between the points (1, 0) and (-6, -4).

   Formula:Distance Between Two Points

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

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10. 10.

    Chemistry

    Find the pH of a solution with [H⁺] = 5×10⁻4 mol/L.

    Formula:pH of a Solution

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

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11. 11.

    Mathematics

    If f(x) = 1x³ + 5x² + 1x, find f′(4).

    Formula:Derivative of a Polynomial

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

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12. 12.

    Mathematics

    Evaluate ∫ from 2 to 4 of 1x^2 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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13. 13.

    Mathematics

    Evaluate log base 3 of 27.

    Formula:Logarithm Evaluation

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

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14. 14.

    Physics

    Find the voltage across a 49 Ω resistor carrying a current of 19 A.

    Formula:Ohm's Law

    $V = IR$

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15. 15.

    Physics

    A force of 78 N acts on an area of 28 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Mathematics

    For the quadratic 5x² − 5x + 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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17. 17.

    Physics

    Find the voltage across a 41 Ω resistor carrying a current of 3 A.

    Formula:Ohm's Law

    $V = IR$

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18. 18.

    Chemistry

    How many moles are present in 48 g of oxygen gas (O₂) (molar mass = 32 g/mol)?

    Formula:Number of Moles

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

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19. 19.

    Physics

    Find the kinetic energy of a 5 kg object moving at 11 m/s.

    Formula:Kinetic Energy

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

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20. 20.

    Physics

    A projectile is launched at 31 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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