EmSAT Achieve · Practice Sheet 13

1. 1.

   Mathematics

   Evaluate log base 5 of 125.

   Formula:Logarithm Evaluation

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

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2. 2.

   Physics

   Find the density of an object with mass 314 g and volume 33 cm³.

   Formula:Density

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

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3. 3.

   Physics

   A body moving at 2 m/s accelerates at 6 m/s² for 5 s. Find the distance travelled.

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

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

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4. 4.

   Chemistry

   A solution is made by dissolving 5 g of solute in 168 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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5. 5.

   Mathematics

   For the quadratic 2x² − 5x + 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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6. 6.

   Physics

   Find the voltage across a 28 Ω resistor carrying a current of 8 A.

   Formula:Ohm's Law

   $V = IR$

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7. 7.

   Mathematics

   Find the sum of the first 16 terms of an AP with first term 3 and common difference 4.

   Formula:AP Sum of n Terms

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

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8. 8.

   Biology

   In a monohybrid cross (Aa × Aa) producing 136 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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9. 9.

   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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10. 10.

    Biology

    Under a microscope, an object of actual size 0.6 mm appears 13.2 mm. Find the magnification.

    Formula:Microscope Magnification

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

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11. 11.

    Physics

    Find the electrical power when 89 V drives a current of 9 A.

    Formula:Electrical Power

    $P = VI$

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12. 12.

    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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13. 13.

    Physics

    A constant force of 12 N moves an object 9 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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14. 14.

    Mathematics

    In an arithmetic progression with first term 18 and common difference 4, find term number 27.

    Formula:AP nth Term

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

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15. 15.

    Mathematics

    Evaluate log base 5 of 15,625.

    Formula:Logarithm Evaluation

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

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16. 16.

    Physics

    Find the voltage across a 35 Ω resistor carrying a current of 6 A.

    Formula:Ohm's Law

    $V = IR$

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17. 17.

    Biology

    Calculate the BMI of a person weighing 48 kg with height 1.88 m.

    Formula:Body Mass Index

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

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18. 18.

    Physics

    Find the kinetic energy of a 19 kg object moving at 8 m/s.

    Formula:Kinetic Energy

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

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19. 19.

    Mathematics

    Evaluate ∫ from 0 to 4 of 4x^2 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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20. 20.

    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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