EmSAT Achieve · Practice Sheet 14

1. 1.

   Mathematics

   Find the distance between the points (-2, 1) and (-3, -4).

   Formula:Distance Between Two Points

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

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2. 2.

   Mathematics

   In an arithmetic progression with first term 20 and common difference 2, find term number 26.

   Formula:AP nth Term

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

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3. 3.

   Mathematics

   Find the sum of the first 21 terms of an AP with first term 1 and common difference 3.

   Formula:AP Sum of n Terms

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

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4. 4.

   Biology

   In a monohybrid cross (Aa × Aa) producing 120 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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5. 5.

   Chemistry

   Find the pressure of 1 mol of an ideal gas at 217 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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6. 6.

   Physics

   Find the force required to accelerate a 43 kg mass at 4 m/s².

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

   $F = ma$

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7. 7.

   Mathematics

   Evaluate log base 3 of 81.

   Formula:Logarithm Evaluation

   $\log_{b}(b^{k}) = k$

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8. 8.

   Physics

   A force of 370 N acts on an area of 24 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   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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10. 10.

    Biology

    Under a microscope, an object of actual size 1.4 mm appears 117.6 mm. Find the magnification.

    Formula:Microscope Magnification

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

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11. 11.

    Mathematics

    Evaluate ∫ from 2 to 5 of 5x^3 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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12. 12.

    Physics

    A body moving at 10 m/s accelerates at 1 m/s² for 10 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.

    Biology

    In a monohybrid cross (Aa × Aa) producing 32 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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14. 14.

    Mathematics

    For the quadratic 4x² + 7x − 8 = 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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15. 15.

    Physics

    Find the electrical power when 115 V drives a current of 7 A.

    Formula:Electrical Power

    $P = VI$

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16. 16.

    Physics

    A body moving at 4 m/s accelerates at 7 m/s² for 2 s. Find the distance travelled.

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

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

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17. 17.

    Mathematics

    Find the slope of the line through (7, 3) and (-8, -1).

    Formula:Slope of a Line

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

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18. 18.

    Physics

    A body moving at 1 m/s accelerates at 1 m/s² for 8 s. Find the distance travelled.

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

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

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19. 19.

    Physics

    A projectile is launched at 10 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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20. 20.

    Chemistry

    Find the molarity of a solution containing 0.5 mol of solute in 0.5 L of solution.

    Formula:Molarity

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

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