EmSAT Achieve · Practice Sheet 43

1. 1.

   Biology

   Calculate the BMI of a person weighing 70 kg with height 1.77 m.

   Formula:Body Mass Index

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

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2. 2.

   Physics

   A constant force of 107 N moves an object 42 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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3. 3.

   Physics

   Find the electrical power when 68 V drives a current of 10 A.

   Formula:Electrical Power

   $P = VI$

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4. 4.

   Physics

   Find the force required to accelerate a 8 kg mass at 5 m/s².

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

   $F = ma$

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5. 5.

   Chemistry

   A solution is made by dissolving 5 g of solute in 124 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.

   Mathematics

   Find the sum of the first 21 terms of an AP with first term 1 and common difference 10.

   Formula:AP Sum of n Terms

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

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7. 7.

   Mathematics

   Find the distance between the points (-2, 1) and (-7, -2).

   Formula:Distance Between Two Points

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

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8. 8.

   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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9. 9.

   Mathematics

   If f(x) = 5x³ + 4x² + 1x, find f′(4).

   Formula:Derivative of a Polynomial

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

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10. 10.

    Chemistry

    How many moles are present in 900 g of glucose (C₆H₁₂O₆) (molar mass = 180 g/mol)?

    Formula:Number of Moles

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

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11. 11.

    Physics

    An object starts at 3 m/s and accelerates at 6 m/s² for 9 s. Find its final velocity.

    Formula:Equation of Motion (v = u + at)

    $v = u + at$

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12. 12.

    Mathematics

    Find the binomial coefficient C(7, 3) — the coefficient of x^3 in (1 + x)^7.

    Formula:Binomial Coefficient

    $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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13. 13.

    Chemistry

    Find the pH of a solution with [H⁺] = 1×10⁻2 mol/L.

    Formula:pH of a Solution

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

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14. 14.

    Physics

    Find the electrical power when 110 V drives a current of 2 A.

    Formula:Electrical Power

    $P = VI$

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15. 15.

    Biology

    Under a microscope, an object of actual size 3.8 mm appears 326.8 mm. Find the magnification.

    Formula:Microscope Magnification

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

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16. 16.

    Mathematics

    Find the sum of the first 3 terms of a GP with first term 2 and common ratio 2.

    Formula:GP Sum of n Terms

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

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17. 17.

    Chemistry

    A solution is made by dissolving 28 g of solute in 171 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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18. 18.

    Physics

    If 4,359 J of work is done in 19 s, find the power.

    Formula:Power

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

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19. 19.

    Physics

    Find the electrical power when 61 V drives a current of 11 A.

    Formula:Electrical Power

    $P = VI$

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20. 20.

    Biology

    Calculate the BMI of a person weighing 85 kg with height 1.5 m.

    Formula:Body Mass Index

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

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