Engineering Entrance · Practice Sheet 28

1. 1.

   Physics

   A force of 247 N acts on an area of 40 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   Physics

   If 2,537 J of work is done in 2 s, find the power.

   Formula:Power

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

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3. 3.

   Mathematics

   Find the sum of the first 7 terms of a GP with first term 6 and common ratio 2.

   Formula:GP Sum of n Terms

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

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4. 4.

   Physics

   Find the force required to accelerate a 27 kg mass at 13 m/s².

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

   $F = ma$

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5. 5.

   Physics

   Find the kinetic energy of a 19 kg object moving at 18 m/s.

   Formula:Kinetic Energy

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

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6. 6.

   Chemistry

   13 mL of a 10 M solution is diluted to 120 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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7. 7.

   Mathematics

   Evaluate ∫ from 2 to 4 of 3x^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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8. 8.

   Physics

   Find the kinetic energy of a 15 kg object moving at 15 m/s.

   Formula:Kinetic Energy

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

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9. 9.

   Physics

   A projectile is launched at 22 m/s at 45° 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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10. 10.

    Physics

    A force of 526 N acts on an area of 33 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    Mathematics

    For the quadratic 3x² + 8x + 8 = 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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12. 12.

    Mathematics

    Find the sum of the first 25 terms of an AP with first term 1 and common difference 6.

    Formula:AP Sum of n Terms

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

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13. 13.

    Mathematics

    Find the slope of the line through (2, -1) and (-3, -7).

    Formula:Slope of a Line

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

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14. 14.

    Physics

    A body moving at 1 m/s accelerates at 5 m/s² for 10 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

    Find the sum of the first 5 terms of a GP with first term 1 and common ratio 3.

    Formula:GP Sum of n Terms

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

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16. 16.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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17. 17.

    Chemistry

    Find the molarity of a solution containing 1 mol of solute in 0.5 L of solution.

    Formula:Molarity

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

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18. 18.

    Mathematics

    Evaluate log base 2 of 16.

    Formula:Logarithm Evaluation

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

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19. 19.

    Physics

    A projectile is launched at 21 m/s at 45° 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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20. 20.

    Physics

    An object starts at 11 m/s and accelerates at 10 m/s² for 7 s. Find its final velocity.

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

    $v = u + at$

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