Engineering Entrance · Practice Sheet 9

1. 1.

   Physics

   Find the force required to accelerate a 40 kg mass at 9 m/s².

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

   $F = ma$

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2. 2.

   Mathematics

   Evaluate log base 2 of 8.

   Formula:Logarithm Evaluation

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

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3. 3.

   Mathematics

   In an arithmetic progression with first term 10 and common difference 7, find term number 5.

   Formula:AP nth Term

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

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4. 4.

   Physics

   Find the electrical power when 54 V drives a current of 14 A.

   Formula:Electrical Power

   $P = VI$

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5. 5.

   Physics

   A body moving at 10 m/s accelerates at 7 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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6. 6.

   Physics

   If 1,571 J of work is done in 2 s, find the power.

   Formula:Power

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

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7. 7.

   Physics

   A force of 50 N acts on an area of 42 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Physics

   Find the kinetic energy of a 3 kg object moving at 25 m/s.

   Formula:Kinetic Energy

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

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9. 9.

   Chemistry

   How many moles are present in 150 g of calcium carbonate (CaCO₃) (molar mass = 100 g/mol)?

   Formula:Number of Moles

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

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10. 10.

    Mathematics

    For the quadratic 2x² + 7x + 5 = 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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11. 11.

    Mathematics

    Find the sum of the first 6 terms of a GP with first term 5 and common ratio 3.

    Formula:GP Sum of n Terms

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

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12. 12.

    Chemistry

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

    Formula:Number of Moles

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

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13. 13.

    Physics

    An object starts at 9 m/s and accelerates at 5 m/s² for 7 s. Find its final velocity.

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

    $v = u + at$

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14. 14.

    Physics

    A body moving at 1 m/s accelerates at 3 m/s² for 5 s. Find the distance travelled.

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

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

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15. 15.

    Physics

    A projectile is launched at 14 m/s at 60° 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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16. 16.

    Physics

    Find the voltage across a 37 Ω resistor carrying a current of 19 A.

    Formula:Ohm's Law

    $V = IR$

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17. 17.

    Chemistry

    A solution is made by dissolving 6 g of solute in 78 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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18. 18.

    Mathematics

    Find the slope of the line through (-2, -5) and (-3, 7).

    Formula:Slope of a Line

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

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19. 19.

    Mathematics

    Evaluate ∫ from 2 to 5 of 1x^1 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.

    Chemistry

    Find the molarity of a solution containing 2 mol of solute in 4 L of solution.

    Formula:Molarity

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

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