EmSAT Achieve · Practice Sheet 42

1. 1.

   Physics

   A projectile is launched at 49 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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2. 2.

   Mathematics

   If f(x) = 2x³ + 1x² + 4x, find f′(1).

   Formula:Derivative of a Polynomial

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

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3. 3.

   Biology

   Calculate the BMI of a person weighing 75 kg with height 1.63 m.

   Formula:Body Mass Index

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

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4. 4.

   Mathematics

   Find the slope of the line through (-1, 4) and (7, -4).

   Formula:Slope of a Line

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

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5. 5.

   Chemistry

   A solution is made by dissolving 25 g of solute in 172 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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6. 6.

   Physics

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

   Formula:Kinetic Energy

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

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7. 7.

   Physics

   Find the voltage across a 49 Ω resistor carrying a current of 1 A.

   Formula:Ohm's Law

   $V = IR$

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8. 8.

   Physics

   If 740 J of work is done in 26 s, find the power.

   Formula:Power

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

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9. 9.

   Physics

   Find the momentum of a 24 kg body moving at 13 m/s.

   Formula:Linear Momentum

   $p = mv$

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10. 10.

    Physics

    Find the electrical power when 141 V drives a current of 10 A.

    Formula:Electrical Power

    $P = VI$

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11. 11.

    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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12. 12.

    Mathematics

    Find term number 5 of a geometric progression with first term 6 and common ratio 2.

    Formula:GP nth Term

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

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13. 13.

    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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14. 14.

    Chemistry

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

    Formula:Molarity

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

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15. 15.

    Chemistry

    85 mL of a 2 M solution is diluted to 381 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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16. 16.

    Physics

    Find the momentum of a 44 kg body moving at 37 m/s.

    Formula:Linear Momentum

    $p = mv$

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17. 17.

    Physics

    A constant force of 154 N moves an object 25 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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18. 18.

    Biology

    In a monohybrid cross (Aa × Aa) producing 112 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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19. 19.

    Mathematics

    Find term number 7 of a geometric progression with first term 5 and common ratio 2.

    Formula:GP nth Term

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

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20. 20.

    Physics

    A force of 314 N acts on an area of 5 m². Find the pressure.

    Formula:Pressure

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

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