EmSAT Achieve · Practice Sheet 23

1. 1.

   Biology

   Calculate the BMI of a person weighing 57 kg with height 1.66 m.

   Formula:Body Mass Index

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

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2. 2.

   Physics

   Find the momentum of a 32 kg body moving at 4 m/s.

   Formula:Linear Momentum

   $p = mv$

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3. 3.

   Physics

   Find the force required to accelerate a 49 kg mass at 5 m/s².

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

   $F = ma$

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4. 4.

   Physics

   A projectile is launched at 23 m/s at 30° 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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5. 5.

   Chemistry

   A solution is made by dissolving 30 g of solute in 164 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 density of an object with mass 126 g and volume 34 cm³.

   Formula:Density

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

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7. 7.

   Mathematics

   For the quadratic 2x² + 8x − 1 = 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.

   Chemistry

   How many moles are present in 96 g of oxygen gas (O₂) (molar mass = 32 g/mol)?

   Formula:Number of Moles

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

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9. 9.

   Chemistry

   Find the pressure of 3 mol of an ideal gas at 333 K in a 18 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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10. 10.

    Biology

    Calculate the BMI of a person weighing 52 kg with height 1.85 m.

    Formula:Body Mass Index

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

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11. 11.

    Physics

    A body moving at 8 m/s accelerates at 2 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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12. 12.

    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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13. 13.

    Physics

    Find the kinetic energy of a 16 kg object moving at 7 m/s.

    Formula:Kinetic Energy

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

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14. 14.

    Physics

    A constant force of 118 N moves an object 46 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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15. 15.

    Physics

    Find the electrical power when 122 V drives a current of 7 A.

    Formula:Electrical Power

    $P = VI$

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16. 16.

    Mathematics

    Find the sum of the first 25 terms of an AP with first term 5 and common difference 10.

    Formula:AP Sum of n Terms

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

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17. 17.

    Mathematics

    If f(x) = 5x³ + 2x² + 6x, find f′(1).

    Formula:Derivative of a Polynomial

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

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18. 18.

    Mathematics

    For the quadratic 1x² − 4x − 1 = 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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19. 19.

    Mathematics

    Find the sum of the first 3 terms of a GP with first term 3 and common ratio 3.

    Formula:GP Sum of n Terms

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

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20. 20.

    Mathematics

    Evaluate ∫ from 2 to 4 of 2x^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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