Engineering Entrance · Practice Sheet 15

1. 1.

   Chemistry

   Find the molarity of a solution containing 0.5 mol of solute in 1 L of solution.

   Formula:Molarity

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

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2. 2.

   Chemistry

   33 mL of a 2 M solution is diluted to 175 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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3. 3.

   Chemistry

   Find the pressure of 2 mol of an ideal gas at 373 K in a 8 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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4. 4.

   Mathematics

   Find the distance between the points (5, 8) and (-6, 2).

   Formula:Distance Between Two Points

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

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5. 5.

   Physics

   A constant force of 160 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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6. 6.

   Physics

   Find the density of an object with mass 127 g and volume 44 cm³.

   Formula:Density

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

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7. 7.

   Mathematics

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

   Formula:GP Sum of n Terms

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

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8. 8.

   Physics

   Find the voltage across a 26 Ω resistor carrying a current of 4 A.

   Formula:Ohm's Law

   $V = IR$

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9. 9.

   Chemistry

   Find the pressure of 1 mol of an ideal gas at 313 K in a 8 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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10. 10.

    Chemistry

    Find the molarity of a solution containing 1.5 mol of solute in 1 L of solution.

    Formula:Molarity

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

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11. 11.

    Physics

    Find the electrical power when 223 V drives a current of 2 A.

    Formula:Electrical Power

    $P = VI$

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12. 12.

    Physics

    A body moving at 5 m/s accelerates at 5 m/s² for 2 s. Find the distance travelled.

    Formula:Equation of Motion (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^{2}$

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13. 13.

    Mathematics

    Find the slope of the line through (6, -2) and (-1, 0).

    Formula:Slope of a Line

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

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14. 14.

    Physics

    Find the voltage across a 18 Ω resistor carrying a current of 13 A.

    Formula:Ohm's Law

    $V = IR$

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15. 15.

    Mathematics

    Evaluate ∫ from 2 to 3 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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16. 16.

    Mathematics

    Find term number 7 of a geometric progression with first term 5 and common ratio 2.

    Formula:GP nth Term

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

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17. 17.

    Physics

    If 4,727 J of work is done in 30 s, find the power.

    Formula:Power

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

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18. 18.

    Mathematics

    Find the sum of the first 3 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.

    Mathematics

    If f(x) = 5x³ + 1x² + 8x, find f′(2).

    Formula:Derivative of a Polynomial

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

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20. 20.

    Chemistry

    How many moles are present in 300 g of calcium carbonate (CaCO₃) (molar mass = 100 g/mol)?

    Formula:Number of Moles

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

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