Engineering Entrance · Practice Sheet 5

1. 1.

   Physics

   Find the force required to accelerate a 16 kg mass at 2 m/s².

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

   $F = ma$

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2. 2.

   Physics

   Find the density of an object with mass 32 g and volume 41 cm³.

   Formula:Density

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

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3. 3.

   Chemistry

   How many moles are present in 117 g of sodium chloride (NaCl) (molar mass = 58.5 g/mol)?

   Formula:Number of Moles

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

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4. 4.

   Physics

   Find the electrical power when 93 V drives a current of 10 A.

   Formula:Electrical Power

   $P = VI$

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5. 5.

   Mathematics

   For the quadratic 2x² − 6x + 6 = 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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6. 6.

   Chemistry

   A solution is made by dissolving 29 g of solute in 181 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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7. 7.

   Physics

   If 2,126 J of work is done in 4 s, find the power.

   Formula:Power

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

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8. 8.

   Mathematics

   Find the slope of the line through (7, 0) and (8, -2).

   Formula:Slope of a Line

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

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9. 9.

   Mathematics

   For the quadratic 2x² + 9x − 1 = 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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10. 10.

    Chemistry

    24 mL of a 1 M solution is diluted to 248 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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11. 11.

    Chemistry

    A solution is made by dissolving 32 g of solute in 200 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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12. 12.

    Chemistry

    How many moles are present in 720 g of glucose (C₆H₁₂O₆) (molar mass = 180 g/mol)?

    Formula:Number of Moles

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

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13. 13.

    Chemistry

    Find the molarity of a solution containing 1.5 mol of solute in 4 L of solution.

    Formula:Molarity

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

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14. 14.

    Physics

    A force of 336 N acts on an area of 36 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    Mathematics

    Evaluate ∫ from 2 to 3 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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16. 16.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 2 and common ratio 2.

    Formula:GP Sum of n Terms

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

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17. 17.

    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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18. 18.

    Physics

    A constant force of 72 N moves an object 41 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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19. 19.

    Physics

    A body moving at 11 m/s accelerates at 5 m/s² for 8 s. Find the distance travelled.

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

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

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20. 20.

    Physics

    A force of 62 N acts on an area of 41 m². Find the pressure.

    Formula:Pressure

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

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