EmSAT Achieve · Practice Sheet 20

1. 1.

   Chemistry

   Find the pH of a solution with [H⁺] = 2×10⁻6 mol/L.

   Formula:pH of a Solution

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

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2. 2.

   Mathematics

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

   Formula:Distance Between Two Points

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

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3. 3.

   Physics

   A constant force of 199 N moves an object 46 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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4. 4.

   Physics

   Find the voltage across a 28 Ω resistor carrying a current of 18 A.

   Formula:Ohm's Law

   $V = IR$

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5. 5.

   Physics

   A projectile is launched at 34 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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6. 6.

   Physics

   An object starts at 3 m/s and accelerates at 5 m/s² for 10 s. Find its final velocity.

   Formula:Equation of Motion (v = u + at)

   $v = u + at$

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7. 7.

   Physics

   If 3,784 J of work is done in 21 s, find the power.

   Formula:Power

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

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8. 8.

   Biology

   In a monohybrid cross (Aa × Aa) producing 60 F₂ offspring, how many are expected to show the dominant and the recessive phenotype (3:1 ratio)?

   Formula:Monohybrid Cross (3:1)

   $\text{Dominant}:\text{Recessive} = 3:1$

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9. 9.

   Physics

   A projectile is launched at 33 m/s at 45° 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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10. 10.

    Chemistry

    Find the pressure of 4 mol of an ideal gas at 268 K in a 3 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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11. 11.

    Biology

    In a monohybrid cross (Aa × Aa) producing 196 F₂ offspring, how many are expected to show the dominant and the recessive phenotype (3:1 ratio)?

    Formula:Monohybrid Cross (3:1)

    $\text{Dominant}:\text{Recessive} = 3:1$

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12. 12.

    Physics

    A body moving at 3 m/s accelerates at 2 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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13. 13.

    Physics

    Find the electrical power when 70 V drives a current of 8 A.

    Formula:Electrical Power

    $P = VI$

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14. 14.

    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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15. 15.

    Mathematics

    In an arithmetic progression with first term 12 and common difference 10, find term number 20.

    Formula:AP nth Term

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

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16. 16.

    Physics

    Find the electrical power when 104 V drives a current of 19 A.

    Formula:Electrical Power

    $P = VI$

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17. 17.

    Biology

    Calculate the BMI of a person weighing 69 kg with height 1.75 m.

    Formula:Body Mass Index

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

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18. 18.

    Chemistry

    Find the pH of a solution with [H⁺] = 5×10⁻3 mol/L.

    Formula:pH of a Solution

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

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19. 19.

    Mathematics

    If f(x) = 4x³ + 3x² + 5x, find f′(5).

    Formula:Derivative of a Polynomial

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

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20. 20.

    Biology

    Under a microscope, an object of actual size 4.5 mm appears 387 mm. Find the magnification.

    Formula:Microscope Magnification

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

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