EmSAT Achieve · Practice Sheet 46

1. 1.

   Biology

   In a population at Hardy–Weinberg equilibrium, the recessive allele frequency q = 0.4. 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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2. 2.

   Physics

   If 3,054 J of work is done in 35 s, find the power.

   Formula:Power

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

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3. 3.

   Chemistry

   How many moles are present in 16 g of oxygen gas (O₂) (molar mass = 32 g/mol)?

   Formula:Number of Moles

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

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4. 4.

   Physics

   Find the density of an object with mass 459 g and volume 10 cm³.

   Formula:Density

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

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5. 5.

   Physics

   A constant force of 29 N moves an object 39 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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6. 6.

   Biology

   In a population at Hardy–Weinberg equilibrium, the recessive allele frequency q = 0.1. 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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7. 7.

   Physics

   Find the momentum of a 40 kg body moving at 9 m/s.

   Formula:Linear Momentum

   $p = mv$

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8. 8.

   Chemistry

   Find the pH of a solution with [H⁺] = 2×10⁻6 mol/L.

   Formula:pH of a Solution

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

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9. 9.

   Physics

   If 400 J of work is done in 35 s, find the power.

   Formula:Power

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

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10. 10.

    Physics

    Find the kinetic energy of a 13 kg object moving at 28 m/s.

    Formula:Kinetic Energy

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

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11. 11.

    Physics

    Find the force required to accelerate a 42 kg mass at 7 m/s².

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

    $F = ma$

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12. 12.

    Chemistry

    73 mL of a 2 M solution is diluted to 228 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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13. 13.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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14. 14.

    Chemistry

    Find the molarity of a solution containing 2.5 mol of solute in 0.5 L of solution.

    Formula:Molarity

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

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15. 15.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 2 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

    For the quadratic 1x² + 1x + 6 = 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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17. 17.

    Physics

    A body moving at 5 m/s accelerates at 2 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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18. 18.

    Physics

    Calculate the potential energy of a 16 kg object at a height of 50 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    Physics

    Find the electrical power when 221 V drives a current of 20 A.

    Formula:Electrical Power

    $P = VI$

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20. 20.

    Chemistry

    A solution is made by dissolving 9 g of solute in 176 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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