EmSAT Achieve · Practice Sheet 11

1. 1.

   Physics

   Find the density of an object with mass 479 g and volume 48 cm³.

   Formula:Density

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

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2. 2.

   Physics

   Find the voltage across a 31 Ω resistor carrying a current of 18 A.

   Formula:Ohm's Law

   $V = IR$

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3. 3.

   Mathematics

   Find the slope of the line through (4, -8) and (8, -2).

   Formula:Slope of a Line

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

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4. 4.

   Physics

   Find the density of an object with mass 368 g and volume 36 cm³.

   Formula:Density

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

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5. 5.

   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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6. 6.

   Chemistry

   Find the pressure of 1 mol of an ideal gas at 271 K in a 6 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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7. 7.

   Physics

   A projectile is launched at 12 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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8. 8.

   Chemistry

   How many moles are present in 48 g of oxygen gas (O₂) (molar mass = 32 g/mol)?

   Formula:Number of Moles

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

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9. 9.

   Physics

   An object starts at 19 m/s and accelerates at 2 m/s² for 3 s. Find its final velocity.

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

   $v = u + at$

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10. 10.

    Physics

    Calculate the potential energy of a 3 kg object at a height of 20 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Physics

    Find the force required to accelerate a 48 kg mass at 19 m/s².

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

    $F = ma$

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12. 12.

    Mathematics

    In an arithmetic progression with first term 16 and common difference 10, find term number 25.

    Formula:AP nth Term

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

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13. 13.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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14. 14.

    Physics

    A body moving at 15 m/s accelerates at 7 m/s² for 3 s. Find the distance travelled.

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

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

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15. 15.

    Physics

    A constant force of 104 N moves an object 44 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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16. 16.

    Physics

    Find the electrical power when 174 V drives a current of 12 A.

    Formula:Electrical Power

    $P = VI$

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17. 17.

    Physics

    If 3,678 J of work is done in 11 s, find the power.

    Formula:Power

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

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18. 18.

    Mathematics

    Find term number 5 of a geometric progression with first term 4 and common ratio 2.

    Formula:GP nth Term

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

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19. 19.

    Chemistry

    Find the pressure of 2 mol of an ideal gas at 370 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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20. 20.

    Physics

    A constant force of 103 N moves an object 20 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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