EmSAT Achieve · Practice Sheet 45

1. 1.

   Chemistry

   Find the molarity of a solution containing 1.5 mol of solute in 0.5 L of solution.

   Formula:Molarity

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

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2. 2.

   Mathematics

   Find the sum of the first 22 terms of an AP with first term 8 and common difference 2.

   Formula:AP Sum of n Terms

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

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3. 3.

   Physics

   Find the momentum of a 12 kg body moving at 17 m/s.

   Formula:Linear Momentum

   $p = mv$

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4. 4.

   Chemistry

   How many moles are present in 50 g of calcium carbonate (CaCO₃) (molar mass = 100 g/mol)?

   Formula:Number of Moles

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

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5. 5.

   Physics

   Find the kinetic energy of a 12 kg object moving at 3 m/s.

   Formula:Kinetic Energy

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

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6. 6.

   Biology

   Calculate the BMI of a person weighing 91 kg with height 1.95 m.

   Formula:Body Mass Index

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

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7. 7.

   Mathematics

   Find the slope of the line through (8, -6) and (-3, 7).

   Formula:Slope of a Line

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

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8. 8.

   Physics

   Find the electrical power when 37 V drives a current of 10 A.

   Formula:Electrical Power

   $P = VI$

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9. 9.

   Physics

   An object starts at 3 m/s and accelerates at 10 m/s² for 5 s. Find its final velocity.

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

   $v = u + at$

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10. 10.

    Physics

    Find the density of an object with mass 377 g and volume 37 cm³.

    Formula:Density

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

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11. 11.

    Mathematics

    Evaluate ∫ from 0 to 4 of 3x^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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12. 12.

    Biology

    In a monohybrid cross (Aa × Aa) producing 192 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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13. 13.

    Mathematics

    For the quadratic 3x² − 7x + 2 = 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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14. 14.

    Physics

    Calculate the potential energy of a 1 kg object at a height of 27 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Mathematics

    Find the distance between the points (3, 5) and (5, 6).

    Formula:Distance Between Two Points

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

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16. 16.

    Physics

    A constant force of 124 N moves an object 24 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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17. 17.

    Physics

    A force of 487 N acts on an area of 42 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Physics

    Find the force required to accelerate a 38 kg mass at 13 m/s².

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

    $F = ma$

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19. 19.

    Mathematics

    Evaluate log base 10 of 100.

    Formula:Logarithm Evaluation

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

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20. 20.

    Mathematics

    In an arithmetic progression with first term 20 and common difference 6, find term number 24.

    Formula:AP nth Term

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

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