EmSAT Achieve · Practice Sheet 6

1. 1.

   Mathematics

   Find the sum of the first 4 terms of a GP with first term 3 and common ratio 3.

   Formula:GP Sum of n Terms

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

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2. 2.

   Chemistry

   A solution is made by dissolving 46 g of solute in 165 g of solvent. Find the mass percentage of the solute.

   Formula:Mass Percentage

   $\%\,\text{mass} = \dfrac{\text{solute}}{\text{solution}}\times 100$

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3. 3.

   Physics

   Find the kinetic energy of a 9 kg object moving at 15 m/s.

   Formula:Kinetic Energy

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

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4. 4.

   Chemistry

   Find the molarity of a solution containing 1.5 mol of solute in 0.5 L of solution.

   Formula:Molarity

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

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5. 5.

   Mathematics

   If f(x) = 3x³ + 6x² + 4x, find f′(1).

   Formula:Derivative of a Polynomial

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

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6. 6.

   Mathematics

   For the quadratic 4x² + 6x + 4 = 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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7. 7.

   Physics

   Find the electrical power when 122 V drives a current of 12 A.

   Formula:Electrical Power

   $P = VI$

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8. 8.

   Biology

   Under a microscope, an object of actual size 4.6 mm appears 138 mm. Find the magnification.

   Formula:Microscope Magnification

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

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9. 9.

   Mathematics

   In an arithmetic progression with first term 4 and common difference 7, find term number 28.

   Formula:AP nth Term

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

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10. 10.

    Physics

    Find the electrical power when 16 V drives a current of 11 A.

    Formula:Electrical Power

    $P = VI$

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11. 11.

    Mathematics

    Find the binomial coefficient C(10, 2) — the coefficient of x^2 in (1 + x)^10.

    Formula:Binomial Coefficient

    $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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12. 12.

    Mathematics

    Find the sum of the first 4 terms of a GP with first term 6 and common ratio 2.

    Formula:GP Sum of n Terms

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

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13. 13.

    Mathematics

    If f(x) = 3x³ + 2x² + 9x, find f′(2).

    Formula:Derivative of a Polynomial

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

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14. 14.

    Chemistry

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

    Formula:pH of a Solution

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

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15. 15.

    Physics

    Find the force required to accelerate a 14 kg mass at 17 m/s².

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

    $F = ma$

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16. 16.

    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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17. 17.

    Physics

    A projectile is launched at 17 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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18. 18.

    Mathematics

    Find the sum of the first 7 terms of a GP with first term 4 and common ratio 2.

    Formula:GP Sum of n Terms

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

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19. 19.

    Mathematics

    Find the sum of the first 17 terms of an AP with first term 7 and common difference 8.

    Formula:AP Sum of n Terms

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

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20. 20.

    Biology

    Calculate the BMI of a person weighing 58 kg with height 1.94 m.

    Formula:Body Mass Index

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

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