EmSAT Achieve · Practice Sheet 38

1. 1.

   Chemistry

   56 mL of a 5 M solution is diluted to 295 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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2. 2.

   Physics

   A constant force of 163 N moves an object 44 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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3. 3.

   Mathematics

   Evaluate log base 2 of 16.

   Formula:Logarithm Evaluation

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

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4. 4.

   Mathematics

   If f(x) = 5x³ + 3x² + 7x, find f′(1).

   Formula:Derivative of a Polynomial

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

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5. 5.

   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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6. 6.

   Mathematics

   If f(x) = 1x³ + 3x² + 1x, find f′(2).

   Formula:Derivative of a Polynomial

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

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7. 7.

   Mathematics

   For the quadratic 1x² − 6x − 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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8. 8.

   Physics

   A force of 850 N acts on an area of 40 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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9. 9.

   Physics

   Find the kinetic energy of a 6 kg object moving at 20 m/s.

   Formula:Kinetic Energy

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

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10. 10.

    Physics

    Find the voltage across a 15 Ω resistor carrying a current of 15 A.

    Formula:Ohm's Law

    $V = IR$

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11. 11.

    Chemistry

    How many moles are present in 220 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

    Formula:Number of Moles

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

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12. 12.

    Physics

    Calculate the potential energy of a 40 kg object at a height of 4 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Chemistry

    55 mL of a 10 M solution is diluted to 211 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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14. 14.

    Biology

    In a monohybrid cross (Aa × Aa) producing 128 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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15. 15.

    Physics

    If 4,351 J of work is done in 26 s, find the power.

    Formula:Power

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

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16. 16.

    Physics

    A force of 275 N acts on an area of 17 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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17. 17.

    Mathematics

    For the quadratic 2x² + 3x − 9 = 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 distance between the points (-6, -2) and (3, 7).

    Formula:Distance Between Two Points

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

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19. 19.

    Chemistry

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

    Formula:pH of a Solution

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

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20. 20.

    Physics

    Find the force required to accelerate a 28 kg mass at 12 m/s².

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

    $F = ma$

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