Engineering Entrance · Practice Sheet 41

1. 1.

   Mathematics

   Find the distance between the points (8, 3) and (8, -5).

   Formula:Distance Between Two Points

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

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2. 2.

   Physics

   A projectile is launched at 18 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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3. 3.

   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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4. 4.

   Mathematics

   For the quadratic 2x² − 2x − 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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5. 5.

   Mathematics

   Evaluate ∫ from 2 to 5 of 5x^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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6. 6.

   Physics

   Find the force required to accelerate a 27 kg mass at 2 m/s².

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

   $F = ma$

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7. 7.

   Mathematics

   Find the sum of the first 25 terms of an AP with first term 18 and common difference 1.

   Formula:AP Sum of n Terms

   $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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8. 8.

   Chemistry

   15 mL of a 5 M solution is diluted to 147 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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9. 9.

   Physics

   Find the electrical power when 229 V drives a current of 2 A.

   Formula:Electrical Power

   $P = VI$

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10. 10.

    Chemistry

    Find the pressure of 2 mol of an ideal gas at 364 K in a 19 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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11. 11.

    Chemistry

    Find the pH of a solution with [H⁺] = 2×10⁻6 mol/L.

    Formula:pH of a Solution

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

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12. 12.

    Mathematics

    In an arithmetic progression with first term 1 and common difference 8, find term number 11.

    Formula:AP nth Term

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

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13. 13.

    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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14. 14.

    Physics

    A body moving at 1 m/s accelerates at 8 m/s² for 9 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.

    Mathematics

    Evaluate log base 3 of 729.

    Formula:Logarithm Evaluation

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

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16. 16.

    Mathematics

    Find the slope of the line through (-1, -4) and (0, -4).

    Formula:Slope of a Line

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

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17. 17.

    Chemistry

    Find the pH of a solution with [H⁺] = 5×10⁻2 mol/L.

    Formula:pH of a Solution

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

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18. 18.

    Physics

    An object starts at 2 m/s and accelerates at 7 m/s² for 6 s. Find its final velocity.

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

    $v = u + at$

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19. 19.

    Mathematics

    Find the sum of the first 5 terms of an AP with first term 10 and common difference 3.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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20. 20.

    Physics

    An object starts at 3 m/s and accelerates at 1 m/s² for 6 s. Find its final velocity.

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

    $v = u + at$

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