EmSAT Achieve · Practice Sheet 48

1. 1.

   Chemistry

   Find the pressure of 3 mol of an ideal gas at 270 K in a 11 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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2. 2.

   Mathematics

   Evaluate ∫ from 2 to 5 of 4x^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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3. 3.

   Physics

   Calculate the potential energy of a 24 kg object at a height of 41 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Mathematics

   For the quadratic 2x² + 2x + 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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5. 5.

   Physics

   If 1,372 J of work is done in 39 s, find the power.

   Formula:Power

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

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6. 6.

   Physics

   Find the force required to accelerate a 44 kg mass at 14 m/s².

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

   $F = ma$

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7. 7.

   Mathematics

   Evaluate ∫ from 1 to 3 of 1x^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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8. 8.

   Biology

   Under a microscope, an object of actual size 4.6 mm appears 110.4 mm. Find the magnification.

   Formula:Microscope Magnification

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

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9. 9.

   Mathematics

   For the quadratic 4x² + 9x − 8 = 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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10. 10.

    Biology

    Calculate the BMI of a person weighing 84 kg with height 1.67 m.

    Formula:Body Mass Index

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

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11. 11.

    Physics

    A force of 719 N acts on an area of 36 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    Physics

    If 4,215 J of work is done in 26 s, find the power.

    Formula:Power

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

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13. 13.

    Chemistry

    Find the pressure of 5 mol of an ideal gas at 318 K in a 12 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

    View formula →
14. 14.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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15. 15.

    Physics

    Find the force required to accelerate a 49 kg mass at 6 m/s².

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

    $F = ma$

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16. 16.

    Mathematics

    Evaluate log base 2 of 64.

    Formula:Logarithm Evaluation

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

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17. 17.

    Chemistry

    Find the pressure of 1 mol of an ideal gas at 314 K in a 15 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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18. 18.

    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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19. 19.

    Mathematics

    Find the sum of the first 4 terms of a GP with first term 6 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.

    Biology

    Under a microscope, an object of actual size 3.3 mm appears 290.4 mm. Find the magnification.

    Formula:Microscope Magnification

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

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