EmSAT Achieve · Practice Sheet 5

1. 1.

   Physics

   Find the electrical power when 149 V drives a current of 18 A.

   Formula:Electrical Power

   $P = VI$

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2. 2.

   Physics

   Find the kinetic energy of a 9 kg object moving at 16 m/s.

   Formula:Kinetic Energy

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

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3. 3.

   Mathematics

   For the quadratic 4x² + 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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4. 4.

   Chemistry

   A solution is made by dissolving 16 g of solute in 180 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 voltage across a 7 Ω resistor carrying a current of 9 A.

   Formula:Ohm's Law

   $V = IR$

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6. 6.

   Chemistry

   Find the pressure of 2 mol of an ideal gas at 214 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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7. 7.

   Physics

   Find the electrical power when 43 V drives a current of 18 A.

   Formula:Electrical Power

   $P = VI$

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8. 8.

   Physics

   A projectile is launched at 48 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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9. 9.

   Biology

   Calculate the BMI of a person weighing 87 kg with height 1.9 m.

   Formula:Body Mass Index

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

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10. 10.

    Physics

    Find the momentum of a 18 kg body moving at 7 m/s.

    Formula:Linear Momentum

    $p = mv$

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11. 11.

    Mathematics

    Find the binomial coefficient C(5, 3) — the coefficient of x^3 in (1 + x)^5.

    Formula:Binomial Coefficient

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

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12. 12.

    Mathematics

    Find the sum of the first 7 terms of an AP with first term 18 and common difference 9.

    Formula:AP Sum of n Terms

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

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13. 13.

    Physics

    Find the kinetic energy of a 8 kg object moving at 27 m/s.

    Formula:Kinetic Energy

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

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14. 14.

    Physics

    A force of 452 N acts on an area of 41 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    Mathematics

    Find the distance between the points (5, -3) and (8, 0).

    Formula:Distance Between Two Points

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

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16. 16.

    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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17. 17.

    Mathematics

    For the quadratic 5x² − 1x + 3 = 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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18. 18.

    Chemistry

    Find the molarity of a solution containing 1 mol of solute in 2.5 L of solution.

    Formula:Molarity

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

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19. 19.

    Physics

    A projectile is launched at 26 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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20. 20.

    Biology

    Calculate the BMI of a person weighing 75 kg with height 1.56 m.

    Formula:Body Mass Index

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

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