Engineering Entrance · Practice Sheet 21

1. 1.

   Physics

   Find the density of an object with mass 391 g and volume 13 cm³.

   Formula:Density

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

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2. 2.

   Mathematics

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

   Formula:Slope of a Line

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

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3. 3.

   Mathematics

   For the quadratic 5x² + 6x − 7 = 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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4. 4.

   Physics

   An object starts at 16 m/s and accelerates at 9 m/s² for 6 s. Find its final velocity.

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

   $v = u + at$

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5. 5.

   Chemistry

   23 mL of a 10 M solution is diluted to 394 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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6. 6.

   Physics

   A body moving at 12 m/s accelerates at 2 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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7. 7.

   Physics

   If 2,973 J of work is done in 34 s, find the power.

   Formula:Power

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

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8. 8.

   Physics

   Find the voltage across a 46 Ω resistor carrying a current of 15 A.

   Formula:Ohm's Law

   $V = IR$

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9. 9.

   Physics

   Find the momentum of a 35 kg body moving at 7 m/s.

   Formula:Linear Momentum

   $p = mv$

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10. 10.

    Mathematics

    In an arithmetic progression with first term 10 and common difference 4, find term number 28.

    Formula:AP nth Term

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

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11. 11.

    Mathematics

    Evaluate log base 2 of 8.

    Formula:Logarithm Evaluation

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

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12. 12.

    Mathematics

    In an arithmetic progression with first term 12 and common difference 8, find term number 18.

    Formula:AP nth Term

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

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13. 13.

    Mathematics

    If f(x) = 2x³ + 4x² + 2x, find f′(4).

    Formula:Derivative of a Polynomial

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

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14. 14.

    Physics

    Calculate the potential energy of a 43 kg object at a height of 16 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Physics

    Find the force required to accelerate a 46 kg mass at 16 m/s².

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

    $F = ma$

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16. 16.

    Physics

    Find the voltage across a 39 Ω resistor carrying a current of 20 A.

    Formula:Ohm's Law

    $V = IR$

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17. 17.

    Mathematics

    Evaluate ∫ from 2 to 5 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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18. 18.

    Physics

    If 1,889 J of work is done in 12 s, find the power.

    Formula:Power

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

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19. 19.

    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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20. 20.

    Physics

    A projectile is launched at 36 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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