EmSAT Achieve · Practice Sheet 26

1. 1.

   Mathematics

   For the quadratic 5x² − 3x − 5 = 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.

   Mathematics

   In an arithmetic progression with first term 7 and common difference 1, find term number 30.

   Formula:AP nth Term

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

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3. 3.

   Mathematics

   Find the sum of the first 5 terms of a GP with first term 2 and common ratio 3.

   Formula:GP Sum of n Terms

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

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4. 4.

   Mathematics

   Find the slope of the line through (-1, -1) and (0, 5).

   Formula:Slope of a Line

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

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5. 5.

   Physics

   A body moving at 5 m/s accelerates at 5 m/s² for 9 s. Find the distance travelled.

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

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

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6. 6.

   Mathematics

   In an arithmetic progression with first term 1 and common difference 2, find term number 16.

   Formula:AP nth Term

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

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7. 7.

   Biology

   Calculate the BMI of a person weighing 92 kg with height 1.58 m.

   Formula:Body Mass Index

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

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8. 8.

   Physics

   Find the kinetic energy of a 3 kg object moving at 21 m/s.

   Formula:Kinetic Energy

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

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9. 9.

   Chemistry

   Find the pressure of 1 mol of an ideal gas at 368 K in a 2 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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10. 10.

    Mathematics

    Find the slope of the line through (-4, 7) and (8, 7).

    Formula:Slope of a Line

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

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11. 11.

    Chemistry

    How many moles are present in 22 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

    Formula:Number of Moles

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

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12. 12.

    Biology

    Under a microscope, an object of actual size 1.3 mm appears 27.3 mm. Find the magnification.

    Formula:Microscope Magnification

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

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13. 13.

    Physics

    Find the force required to accelerate a 31 kg mass at 3 m/s².

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

    $F = ma$

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14. 14.

    Biology

    In a monohybrid cross (Aa × Aa) producing 136 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 momentum of a 10 kg body moving at 39 m/s.

    Formula:Linear Momentum

    $p = mv$

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16. 16.

    Mathematics

    Find the sum of the first 13 terms of an AP with first term 6 and common difference 2.

    Formula:AP Sum of n Terms

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

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17. 17.

    Mathematics

    If f(x) = 1x³ + 1x² + 5x, find f′(5).

    Formula:Derivative of a Polynomial

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

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18. 18.

    Chemistry

    Find the pH of a solution with [H⁺] = 1×10⁻2 mol/L.

    Formula:pH of a Solution

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

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19. 19.

    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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20. 20.

    Mathematics

    Evaluate ∫ from 0 to 4 of 3x^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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