EmSAT Achieve · Practice Sheet 34

1. 1.

   Physics

   A body moving at 15 m/s accelerates at 5 m/s² for 6 s. Find the distance travelled.

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

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

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2. 2.

   Mathematics

   Find the sum of the first 7 terms of a GP with first term 5 and common ratio 3.

   Formula:GP Sum of n Terms

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

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3. 3.

   Physics

   A projectile is launched at 29 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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4. 4.

   Biology

   Calculate the BMI of a person weighing 92 kg with height 1.66 m.

   Formula:Body Mass Index

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

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5. 5.

   Physics

   Find the density of an object with mass 151 g and volume 39 cm³.

   Formula:Density

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

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6. 6.

   Chemistry

   Find the pH of a solution with [H⁺] = 1×10⁻6 mol/L.

   Formula:pH of a Solution

   $pH = -\log_{10}[H^{+}]$

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7. 7.

   Physics

   Calculate the potential energy of a 34 kg object at a height of 22 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   Chemistry

   28 mL of a 10 M solution is diluted to 171 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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9. 9.

   Physics

   If 3,033 J of work is done in 36 s, find the power.

   Formula:Power

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

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10. 10.

    Mathematics

    In an arithmetic progression with first term 13 and common difference 3, find term number 15.

    Formula:AP nth Term

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

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11. 11.

    Biology

    Under a microscope, an object of actual size 2.5 mm appears 180 mm. Find the magnification.

    Formula:Microscope Magnification

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

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12. 12.

    Chemistry

    37 mL of a 1 M solution is diluted to 289 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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13. 13.

    Chemistry

    Find the pressure of 2 mol of an ideal gas at 208 K in a 8 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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14. 14.

    Mathematics

    Find term number 7 of a geometric progression with first term 2 and common ratio 3.

    Formula:GP nth Term

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

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15. 15.

    Chemistry

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

    Formula:Molarity

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

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16. 16.

    Mathematics

    If f(x) = 1x³ + 6x² + 4x, find f′(2).

    Formula:Derivative of a Polynomial

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

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17. 17.

    Mathematics

    Find the distance between the points (-4, 7) and (-4, -7).

    Formula:Distance Between Two Points

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

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18. 18.

    Mathematics

    For the quadratic 4x² − 4x + 0 = 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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19. 19.

    Mathematics

    Find the distance between the points (1, 5) and (-4, -6).

    Formula:Distance Between Two Points

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

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20. 20.

    Biology

    Calculate the BMI of a person weighing 75 kg with height 1.83 m.

    Formula:Body Mass Index

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

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