EmSAT Achieve · Practice Sheet 19

1. 1.

   Physics

   A force of 410 N acts on an area of 21 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   Physics

   A projectile is launched at 50 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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3. 3.

   Mathematics

   Find the distance between the points (1, -1) and (4, 0).

   Formula:Distance Between Two Points

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

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4. 4.

   Biology

   Under a microscope, an object of actual size 2.9 mm appears 252.3 mm. Find the magnification.

   Formula:Microscope Magnification

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

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5. 5.

   Mathematics

   Evaluate log base 3 of 27.

   Formula:Logarithm Evaluation

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

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6. 6.

   Physics

   A body moving at 10 m/s accelerates at 4 m/s² for 5 s. Find the distance travelled.

   Formula:Equation of Motion (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^{2}$

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7. 7.

   Physics

   A force of 353 N acts on an area of 36 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Mathematics

   Find term number 6 of a geometric progression with first term 5 and common ratio 2.

   Formula:GP nth Term

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

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9. 9.

   Chemistry

   A solution is made by dissolving 48 g of solute in 199 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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10. 10.

    Physics

    Find the density of an object with mass 50 g and volume 48 cm³.

    Formula:Density

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

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11. 11.

    Physics

    A constant force of 31 N moves an object 25 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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12. 12.

    Mathematics

    Find the distance between the points (-2, 1) and (-8, 1).

    Formula:Distance Between Two Points

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

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13. 13.

    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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14. 14.

    Chemistry

    Find the pressure of 4 mol of an ideal gas at 208 K in a 7 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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15. 15.

    Chemistry

    Find the molarity of a solution containing 2.5 mol of solute in 0.5 L of solution.

    Formula:Molarity

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

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16. 16.

    Physics

    Find the voltage across a 12 Ω resistor carrying a current of 9 A.

    Formula:Ohm's Law

    $V = IR$

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17. 17.

    Mathematics

    Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

    Formula:Binomial Coefficient

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

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18. 18.

    Chemistry

    Find the pressure of 4 mol of an ideal gas at 267 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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19. 19.

    Mathematics

    Evaluate ∫ from 0 to 3 of 2x^1 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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20. 20.

    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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