EmSAT Achieve · Practice Sheet 9

1. 1.

   Biology

   Under a microscope, an object of actual size 3.7 mm appears 292.3 mm. Find the magnification.

   Formula:Microscope Magnification

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

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2. 2.

   Biology

   In a population at Hardy–Weinberg equilibrium, the recessive allele frequency q = 0.2. 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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3. 3.

   Physics

   Find the electrical power when 22 V drives a current of 14 A.

   Formula:Electrical Power

   $P = VI$

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4. 4.

   Chemistry

   A solution is made by dissolving 21 g of solute in 95 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.

   Physics

   Find the force required to accelerate a 11 kg mass at 5 m/s².

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

   $F = ma$

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6. 6.

   Physics

   A force of 458 N acts on an area of 41 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Physics

   Find the density of an object with mass 183 g and volume 20 cm³.

   Formula:Density

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

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8. 8.

   Biology

   Calculate the BMI of a person weighing 78 kg with height 1.79 m.

   Formula:Body Mass Index

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

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9. 9.

   Mathematics

   Evaluate log base 5 of 3,125.

   Formula:Logarithm Evaluation

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

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10. 10.

    Mathematics

    Evaluate ∫ from 1 to 5 of 5x^3 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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11. 11.

    Chemistry

    Find the pH of a solution with [H⁺] = 5×10⁻2 mol/L.

    Formula:pH of a Solution

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

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12. 12.

    Physics

    Find the momentum of a 3 kg body moving at 15 m/s.

    Formula:Linear Momentum

    $p = mv$

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13. 13.

    Mathematics

    Find term number 4 of a geometric progression with first term 4 and common ratio 2.

    Formula:GP nth Term

    $a_n = a\,r^{\,n-1}$

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14. 14.

    Mathematics

    For the quadratic 2x² + 7x − 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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15. 15.

    Physics

    A projectile is launched at 38 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.

    Physics

    Find the momentum of a 27 kg body moving at 12 m/s.

    Formula:Linear Momentum

    $p = mv$

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17. 17.

    Mathematics

    In an arithmetic progression with first term 17 and common difference 10, find term number 29.

    Formula:AP nth Term

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

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18. 18.

    Physics

    Find the force required to accelerate a 24 kg mass at 19 m/s².

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

    $F = ma$

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19. 19.

    Chemistry

    Find the molarity of a solution containing 0.5 mol of solute in 2 L of solution.

    Formula:Molarity

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

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20. 20.

    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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