Engineering Entrance · Practice Sheet 45

1. 1.

   Mathematics

   Evaluate ∫ from 0 to 5 of 1x^3 dx.

   Formula:Definite Integral of a Power

   $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

   View formula →
2. 2.

   Physics

   A body moving at 15 m/s accelerates at 1 m/s² for 6 s. Find the distance travelled.

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

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

   View formula →
3. 3.

   Physics

   Calculate the potential energy of a 10 kg object at a height of 32 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
4. 4.

   Chemistry

   47 mL of a 2 M solution is diluted to 258 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

   View formula →
5. 5.

   Physics

   Find the electrical power when 187 V drives a current of 13 A.

   Formula:Electrical Power

   $P = VI$

   View formula →
6. 6.

   Mathematics

   Find the distance between the points (-5, 3) and (-6, 1).

   Formula:Distance Between Two Points

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

   View formula →
7. 7.

   Chemistry

   How many moles are present in 270 g of glucose (C₆H₁₂O₆) (molar mass = 180 g/mol)?

   Formula:Number of Moles

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

   View formula →
8. 8.

   Physics

   Find the density of an object with mass 439 g and volume 23 cm³.

   Formula:Density

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

   View formula →
9. 9.

   Physics

   Find the voltage across a 17 Ω resistor carrying a current of 13 A.

   Formula:Ohm's Law

   $V = IR$

   View formula →
10. 10.

    Chemistry

    A solution is made by dissolving 35 g of solute in 61 g of solvent. Find the mass percentage of the solute.

    Formula:Mass Percentage

    $\%\,\text{mass} = \dfrac{\text{solute}}{\text{solution}}\times 100$

    View formula →
11. 11.

    Physics

    Find the voltage across a 20 Ω resistor carrying a current of 18 A.

    Formula:Ohm's Law

    $V = IR$

    View formula →
12. 12.

    Physics

    An object starts at 1 m/s and accelerates at 8 m/s² for 8 s. Find its final velocity.

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

    $v = u + at$

    View formula →
13. 13.

    Mathematics

    Find the distance between the points (1, -3) and (-1, 5).

    Formula:Distance Between Two Points

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

    View formula →
14. 14.

    Physics

    A body moving at 4 m/s accelerates at 2 m/s² for 10 s. Find the distance travelled.

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

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

    View formula →
15. 15.

    Physics

    If 381 J of work is done in 6 s, find the power.

    Formula:Power

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

    View formula →
16. 16.

    Physics

    Find the density of an object with mass 390 g and volume 42 cm³.

    Formula:Density

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

    View formula →
17. 17.

    Chemistry

    How many moles are present in 400 g of calcium carbonate (CaCO₃) (molar mass = 100 g/mol)?

    Formula:Number of Moles

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

    View formula →
18. 18.

    Chemistry

    Find the molarity of a solution containing 1 mol of solute in 2 L of solution.

    Formula:Molarity

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

    View formula →
19. 19.

    Physics

    An object starts at 11 m/s and accelerates at 3 m/s² for 3 s. Find its final velocity.

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

    $v = u + at$

    View formula →
20. 20.

    Chemistry

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

    Formula:Number of Moles

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

    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.