EmSAT Achieve · Practice Sheet 47

1. 1.

   Mathematics

   For the quadratic 3x² − 8x + 6 = 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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2. 2.

   Physics

   A constant force of 31 N moves an object 34 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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3. 3.

   Chemistry

   Find the pH of a solution with [H⁺] = 5×10⁻2 mol/L.

   Formula:pH of a Solution

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

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4. 4.

   Physics

   Find the voltage across a 28 Ω resistor carrying a current of 16 A.

   Formula:Ohm's Law

   $V = IR$

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5. 5.

   Mathematics

   For the quadratic 5x² − 6x − 7 = 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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6. 6.

   Physics

   Find the electrical power when 52 V drives a current of 19 A.

   Formula:Electrical Power

   $P = VI$

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7. 7.

   Physics

   A constant force of 182 N moves an object 5 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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8. 8.

   Physics

   A projectile is launched at 44 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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9. 9.

   Mathematics

   In an arithmetic progression with first term 16 and common difference 5, find term number 10.

   Formula:AP nth Term

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

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10. 10.

    Mathematics

    Find the sum of the first 6 terms of an AP with first term 13 and common difference 3.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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11. 11.

    Physics

    A force of 691 N acts on an area of 43 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    Mathematics

    For the quadratic 3x² + 2x + 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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13. 13.

    Physics

    Find the kinetic energy of a 9 kg object moving at 6 m/s.

    Formula:Kinetic Energy

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

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14. 14.

    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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15. 15.

    Physics

    Find the electrical power when 134 V drives a current of 20 A.

    Formula:Electrical Power

    $P = VI$

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16. 16.

    Physics

    Find the kinetic energy of a 20 kg object moving at 16 m/s.

    Formula:Kinetic Energy

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

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17. 17.

    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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18. 18.

    Physics

    Find the kinetic energy of a 20 kg object moving at 30 m/s.

    Formula:Kinetic Energy

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

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19. 19.

    Physics

    Find the force required to accelerate a 29 kg mass at 10 m/s².

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

    $F = ma$

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20. 20.

    Chemistry

    How many moles are present in 80 g of oxygen gas (O₂) (molar mass = 32 g/mol)?

    Formula:Number of Moles

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

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