EmSAT Achieve · Practice Sheet 33

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

   Find the kinetic energy of a 13 kg object moving at 2 m/s.

   Formula:Kinetic Energy

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

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3. 3.

   Biology

   Calculate the BMI of a person weighing 93 kg with height 1.83 m.

   Formula:Body Mass Index

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

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4. 4.

   Chemistry

   How many moles are present in 87.75 g of sodium chloride (NaCl) (molar mass = 58.5 g/mol)?

   Formula:Number of Moles

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

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5. 5.

   Mathematics

   Find the binomial coefficient C(8, 3) — the coefficient of x^3 in (1 + x)^8.

   Formula:Binomial Coefficient

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

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6. 6.

   Chemistry

   Find the molarity of a solution containing 3 mol of solute in 1 L of solution.

   Formula:Molarity

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

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7. 7.

   Biology

   Under a microscope, an object of actual size 1.5 mm appears 78 mm. Find the magnification.

   Formula:Microscope Magnification

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

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8. 8.

   Chemistry

   Find the pH of a solution with [H⁺] = 5×10⁻4 mol/L.

   Formula:pH of a Solution

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

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9. 9.

   Mathematics

   Find the slope of the line through (-1, -8) and (4, -1).

   Formula:Slope of a Line

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

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10. 10.

    Mathematics

    Find the distance between the points (5, 6) and (4, 5).

    Formula:Distance Between Two Points

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

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11. 11.

    Physics

    Find the force required to accelerate a 50 kg mass at 7 m/s².

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

    $F = ma$

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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.

    Mathematics

    In an arithmetic progression with first term 17 and common difference 4, find term number 8.

    Formula:AP nth Term

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

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14. 14.

    Physics

    An object starts at 5 m/s and accelerates at 7 m/s² for 2 s. Find its final velocity.

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

    $v = u + at$

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15. 15.

    Biology

    In a population at Hardy–Weinberg equilibrium, the recessive allele frequency q = 0.5. 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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16. 16.

    Physics

    An object starts at 12 m/s and accelerates at 6 m/s² for 11 s. Find its final velocity.

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

    $v = u + at$

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17. 17.

    Mathematics

    If f(x) = 4x³ + 4x² + 7x, find f′(2).

    Formula:Derivative of a Polynomial

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

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18. 18.

    Physics

    An object starts at 7 m/s and accelerates at 10 m/s² for 4 s. Find its final velocity.

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

    $v = u + at$

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19. 19.

    Chemistry

    Find the pH of a solution with [H⁺] = 5×10⁻4 mol/L.

    Formula:pH of a Solution

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

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20. 20.

    Mathematics

    In an arithmetic progression with first term 1 and common difference 1, find term number 27.

    Formula:AP nth Term

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

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