EmSAT Achieve · Practice Sheet 2

1. 1.

   Physics

   A body moving at 14 m/s accelerates at 7 m/s² for 3 s. Find the distance travelled.

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

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

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2. 2.

   Chemistry

   Find the pressure of 1 mol of an ideal gas at 380 K in a 11 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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3. 3.

   Physics

   Calculate the potential energy of a 5 kg object at a height of 30 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Mathematics

   Find term number 6 of a geometric progression with first term 5 and common ratio 3.

   Formula:GP nth Term

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

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5. 5.

   Mathematics

   Find the distance between the points (-8, 6) and (7, -3).

   Formula:Distance Between Two Points

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

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6. 6.

   Biology

   Under a microscope, an object of actual size 2.7 mm appears 91.8 mm. Find the magnification.

   Formula:Microscope Magnification

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

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7. 7.

   Mathematics

   Find the slope of the line through (-2, -8) and (5, -4).

   Formula:Slope of a Line

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

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8. 8.

   Chemistry

   92 mL of a 10 M solution is diluted to 468 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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9. 9.

   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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10. 10.

    Physics

    Calculate the potential energy of a 49 kg object at a height of 46 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Physics

    A projectile is launched at 26 m/s at 30° 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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12. 12.

    Physics

    If 3,483 J of work is done in 49 s, find the power.

    Formula:Power

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

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13. 13.

    Chemistry

    Find the pressure of 1 mol of an ideal gas at 338 K in a 5 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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14. 14.

    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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15. 15.

    Physics

    An object starts at 6 m/s and accelerates at 1 m/s² for 6 s. Find its final velocity.

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

    $v = u + at$

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16. 16.

    Chemistry

    Find the pH of a solution with [H⁺] = 2×10⁻3 mol/L.

    Formula:pH of a Solution

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

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17. 17.

    Physics

    A constant force of 47 N moves an object 3 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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18. 18.

    Chemistry

    Find the molarity of a solution containing 2 mol of solute in 4 L of solution.

    Formula:Molarity

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

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19. 19.

    Biology

    In a population at Hardy–Weinberg equilibrium, the recessive allele frequency q = 0.3. Find the dominant allele frequency p and the percentage of heterozygous carriers.

    Formula:Hardy–Weinberg Equilibrium

    $p + q = 1,\;\; 2pq = \text{carriers}$

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20. 20.

    Mathematics

    Find the binomial coefficient C(5, 2) — the coefficient of x^2 in (1 + x)^5.

    Formula:Binomial Coefficient

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

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