EmSAT Achieve · Practice Sheet 4

1. 1.

   Chemistry

   A solution is made by dissolving 19 g of solute in 126 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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2. 2.

   Mathematics

   Find the binomial coefficient C(6, 3) — the coefficient of x^3 in (1 + x)^6.

   Formula:Binomial Coefficient

   $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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3. 3.

   Physics

   Find the force required to accelerate a 39 kg mass at 12 m/s².

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

   $F = ma$

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4. 4.

   Mathematics

   Find the slope of the line through (5, -5) and (6, 4).

   Formula:Slope of a Line

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

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5. 5.

   Physics

   A body moving at 13 m/s accelerates at 8 m/s² for 2 s. Find the distance travelled.

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

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

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6. 6.

   Physics

   Find the density of an object with mass 376 g and volume 35 cm³.

   Formula:Density

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

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7. 7.

   Physics

   A body moving at 1 m/s accelerates at 8 m/s² for 2 s. Find the distance travelled.

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

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

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8. 8.

   Chemistry

   How many moles are present in 44 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

   Formula:Number of Moles

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

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9. 9.

   Physics

   Find the voltage across a 25 Ω resistor carrying a current of 13 A.

   Formula:Ohm's Law

   $V = IR$

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10. 10.

    Mathematics

    Evaluate log base 3 of 9.

    Formula:Logarithm Evaluation

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

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11. 11.

    Chemistry

    How many moles are present in 450 g of glucose (C₆H₁₂O₆) (molar mass = 180 g/mol)?

    Formula:Number of Moles

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

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12. 12.

    Chemistry

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

    Formula:pH of a Solution

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

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13. 13.

    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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14. 14.

    Chemistry

    Find the pressure of 4 mol of an ideal gas at 365 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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15. 15.

    Physics

    Find the momentum of a 25 kg body moving at 23 m/s.

    Formula:Linear Momentum

    $p = mv$

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16. 16.

    Mathematics

    Find the sum of the first 8 terms of an AP with first term 16 and common difference 9.

    Formula:AP Sum of n Terms

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

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17. 17.

    Chemistry

    A solution is made by dissolving 28 g of solute in 197 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.

    Biology

    Under a microscope, an object of actual size 1.3 mm appears 84.5 mm. Find the magnification.

    Formula:Microscope Magnification

    $M = \dfrac{\text{image size}}{\text{actual size}}$

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19. 19.

    Biology

    Calculate the BMI of a person weighing 51 kg with height 1.45 m.

    Formula:Body Mass Index

    $BMI = \dfrac{m}{h^{2}}$

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20. 20.

    Physics

    Find the kinetic energy of a 15 kg object moving at 5 m/s.

    Formula:Kinetic Energy

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

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