EmSAT Achieve · Practice Sheet 35

1. 1.

   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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2. 2.

   Physics

   Find the electrical power when 215 V drives a current of 5 A.

   Formula:Electrical Power

   $P = VI$

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3. 3.

   Chemistry

   Find the molarity of a solution containing 0.5 mol of solute in 1 L of solution.

   Formula:Molarity

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

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4. 4.

   Mathematics

   Find the sum of the first 8 terms of an AP with first term 10 and common difference 4.

   Formula:AP Sum of n Terms

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

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5. 5.

   Physics

   Find the electrical power when 215 V drives a current of 5 A.

   Formula:Electrical Power

   $P = VI$

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6. 6.

   Mathematics

   Evaluate log base 3 of 243.

   Formula:Logarithm Evaluation

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

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7. 7.

   Physics

   Find the voltage across a 38 Ω resistor carrying a current of 3 A.

   Formula:Ohm's Law

   $V = IR$

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8. 8.

   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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9. 9.

   Physics

   Find the force required to accelerate a 47 kg mass at 14 m/s².

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

   $F = ma$

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10. 10.

    Biology

    In a monohybrid cross (Aa × Aa) producing 20 F₂ offspring, how many are expected to show the dominant and the recessive phenotype (3:1 ratio)?

    Formula:Monohybrid Cross (3:1)

    $\text{Dominant}:\text{Recessive} = 3:1$

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11. 11.

    Chemistry

    A solution is made by dissolving 33 g of solute in 180 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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12. 12.

    Chemistry

    Find the pH of a solution with [H⁺] = 1×10⁻3 mol/L.

    Formula:pH of a Solution

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

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13. 13.

    Mathematics

    Evaluate ∫ from 0 to 5 of 3x^1 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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14. 14.

    Physics

    A constant force of 53 N moves an object 35 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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15. 15.

    Physics

    A projectile is launched at 24 m/s at 60° 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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16. 16.

    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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17. 17.

    Mathematics

    For the quadratic 2x² − 3x + 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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18. 18.

    Mathematics

    Find the sum of the first 25 terms of an AP with first term 5 and common difference 2.

    Formula:AP Sum of n Terms

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

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19. 19.

    Biology

    In a monohybrid cross (Aa × Aa) producing 96 F₂ offspring, how many are expected to show the dominant and the recessive phenotype (3:1 ratio)?

    Formula:Monohybrid Cross (3:1)

    $\text{Dominant}:\text{Recessive} = 3:1$

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20. 20.

    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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