EmSAT Achieve · Practice Sheet 8

1. 1.

   Physics

   If 1,547 J of work is done in 20 s, find the power.

   Formula:Power

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

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2. 2.

   Physics

   Find the kinetic energy of a 4 kg object moving at 24 m/s.

   Formula:Kinetic Energy

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

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3. 3.

   Physics

   Calculate the potential energy of a 8 kg object at a height of 47 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Mathematics

   Find the distance between the points (0, -2) and (2, -3).

   Formula:Distance Between Two Points

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

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5. 5.

   Chemistry

   Find the molarity of a solution containing 2 mol of solute in 4 L of solution.

   Formula:Molarity

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

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6. 6.

   Mathematics

   Evaluate ∫ from 2 to 3 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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7. 7.

   Biology

   Under a microscope, an object of actual size 1.4 mm appears 124.6 mm. Find the magnification.

   Formula:Microscope Magnification

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

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8. 8.

   Mathematics

   Find the slope of the line through (-5, 2) and (5, -3).

   Formula:Slope of a Line

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

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9. 9.

   Physics

   Find the momentum of a 36 kg body moving at 24 m/s.

   Formula:Linear Momentum

   $p = mv$

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10. 10.

    Physics

    A projectile is launched at 49 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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11. 11.

    Mathematics

    Find the binomial coefficient C(9, 3) — the coefficient of x^3 in (1 + x)^9.

    Formula:Binomial Coefficient

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

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12. 12.

    Mathematics

    Find term number 3 of a geometric progression with first term 1 and common ratio 2.

    Formula:GP nth Term

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

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13. 13.

    Mathematics

    Find the slope of the line through (2, 1) and (-3, -7).

    Formula:Slope of a Line

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

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14. 14.

    Biology

    In a population at Hardy–Weinberg equilibrium, the recessive allele frequency q = 0.2. 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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15. 15.

    Mathematics

    Find the slope of the line through (2, -7) and (-3, 4).

    Formula:Slope of a Line

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

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16. 16.

    Physics

    A constant force of 40 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.

    Mathematics

    Evaluate log base 2 of 16.

    Formula:Logarithm Evaluation

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

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18. 18.

    Chemistry

    Find the molarity of a solution containing 2 mol of solute in 2.5 L of solution.

    Formula:Molarity

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

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19. 19.

    Mathematics

    Find term number 4 of a geometric progression with first term 5 and common ratio 3.

    Formula:GP nth Term

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

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20. 20.

    Mathematics

    Find the distance between the points (-8, 7) and (-8, -3).

    Formula:Distance Between Two Points

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

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