EmSAT Achieve · Practice Sheet 29

1. 1.

   Mathematics

   In an arithmetic progression with first term 15 and common difference 2, find term number 8.

   Formula:AP nth Term

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

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2. 2.

   Chemistry

   Find the molarity of a solution containing 1 mol of solute in 2.5 L of solution.

   Formula:Molarity

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

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3. 3.

   Chemistry

   Find the pressure of 4 mol of an ideal gas at 284 K in a 14 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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4. 4.

   Physics

   An object starts at 19 m/s and accelerates at 10 m/s² for 9 s. Find its final velocity.

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

   $v = u + at$

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5. 5.

   Physics

   Find the kinetic energy of a 19 kg object moving at 29 m/s.

   Formula:Kinetic Energy

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

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6. 6.

   Mathematics

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

   Formula:Distance Between Two Points

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

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7. 7.

   Biology

   Calculate the BMI of a person weighing 54 kg with height 1.43 m.

   Formula:Body Mass Index

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

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8. 8.

   Mathematics

   Evaluate log base 2 of 16.

   Formula:Logarithm Evaluation

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

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9. 9.

   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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10. 10.

    Chemistry

    How many moles are present in 9 g of water (H₂O) (molar mass = 18 g/mol)?

    Formula:Number of Moles

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

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11. 11.

    Chemistry

    63 mL of a 1 M solution is diluted to 134 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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12. 12.

    Chemistry

    A solution is made by dissolving 46 g of solute in 119 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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13. 13.

    Biology

    Calculate the BMI of a person weighing 59 kg with height 1.95 m.

    Formula:Body Mass Index

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

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14. 14.

    Mathematics

    Evaluate ∫ from 2 to 4 of 3x^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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15. 15.

    Chemistry

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

    Formula:Molarity

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

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16. 16.

    Mathematics

    Find the sum of the first 10 terms of an AP with first term 1 and common difference 7.

    Formula:AP Sum of n Terms

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

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17. 17.

    Physics

    If 1,735 J of work is done in 6 s, find the power.

    Formula:Power

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

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18. 18.

    Physics

    Find the density of an object with mass 169 g and volume 30 cm³.

    Formula:Density

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

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19. 19.

    Chemistry

    Find the molarity of a solution containing 1.5 mol of solute in 4 L of solution.

    Formula:Molarity

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

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20. 20.

    Biology

    Under a microscope, an object of actual size 2.5 mm appears 40 mm. Find the magnification.

    Formula:Microscope Magnification

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

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