Engineering Entrance · Practice Sheet 24

1. 1.

   Physics

   A body moving at 5 m/s accelerates at 4 m/s² for 7 s. Find the distance travelled.

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

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

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2. 2.

   Mathematics

   Find term number 5 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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3. 3.

   Mathematics

   If f(x) = 4x³ + 1x² + 3x, find f′(5).

   Formula:Derivative of a Polynomial

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

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4. 4.

   Physics

   Find the force required to accelerate a 6 kg mass at 1 m/s².

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

   $F = ma$

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5. 5.

   Mathematics

   In an arithmetic progression with first term 6 and common difference 6, find term number 28.

   Formula:AP nth Term

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

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6. 6.

   Physics

   Find the momentum of a 41 kg body moving at 13 m/s.

   Formula:Linear Momentum

   $p = mv$

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7. 7.

   Mathematics

   Evaluate ∫ from 0 to 4 of 2x^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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8. 8.

   Physics

   A force of 326 N acts on an area of 40 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   Chemistry

   How many moles are present in 27 g of water (H₂O) (molar mass = 18 g/mol)?

   Formula:Number of Moles

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

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10. 10.

    Mathematics

    Find the distance between the points (6, 7) and (-7, 1).

    Formula:Distance Between Two Points

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

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11. 11.

    Mathematics

    Evaluate log base 10 of 10,000.

    Formula:Logarithm Evaluation

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

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12. 12.

    Physics

    Find the momentum of a 37 kg body moving at 11 m/s.

    Formula:Linear Momentum

    $p = mv$

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13. 13.

    Physics

    Find the force required to accelerate a 34 kg mass at 20 m/s².

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

    $F = ma$

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14. 14.

    Mathematics

    In an arithmetic progression with first term 15 and common difference 7, find term number 19.

    Formula:AP nth Term

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

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15. 15.

    Physics

    Find the kinetic energy of a 8 kg object moving at 11 m/s.

    Formula:Kinetic Energy

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

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16. 16.

    Mathematics

    Evaluate ∫ from 1 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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17. 17.

    Chemistry

    A solution is made by dissolving 13 g of solute in 169 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.

    Physics

    If 4,665 J of work is done in 5 s, find the power.

    Formula:Power

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

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19. 19.

    Chemistry

    A solution is made by dissolving 37 g of solute in 82 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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20. 20.

    Chemistry

    Find the pressure of 4 mol of an ideal gas at 249 K in a 2 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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