EmSAT Achieve · Practice Sheet 49

1. 1.

   Mathematics

   Find the sum of the first 6 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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2. 2.

   Biology

   In a population at Hardy–Weinberg equilibrium, the recessive allele frequency q = 0.3. 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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3. 3.

   Mathematics

   Find the distance between the points (-7, 3) and (0, 1).

   Formula:Distance Between Two Points

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

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4. 4.

   Physics

   Find the momentum of a 17 kg body moving at 18 m/s.

   Formula:Linear Momentum

   $p = mv$

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5. 5.

   Mathematics

   Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

   Formula:Binomial Coefficient

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

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6. 6.

   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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7. 7.

   Mathematics

   Evaluate log base 2 of 16.

   Formula:Logarithm Evaluation

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

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8. 8.

   Mathematics

   Find the binomial coefficient C(6, 3) — the coefficient of x^3 in (1 + x)^6.

   Formula:Binomial Coefficient

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

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9. 9.

   Physics

   If 3,006 J of work is done in 37 s, find the power.

   Formula:Power

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

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10. 10.

    Chemistry

    Find the molarity of a solution containing 0.5 mol of solute in 4 L of solution.

    Formula:Molarity

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

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11. 11.

    Mathematics

    In an arithmetic progression with first term 4 and common difference 1, find term number 8.

    Formula:AP nth Term

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

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12. 12.

    Chemistry

    26 mL of a 2 M solution is diluted to 87 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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13. 13.

    Physics

    A constant force of 39 N moves an object 21 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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14. 14.

    Chemistry

    Find the molarity of a solution containing 2.5 mol of solute in 1 L of solution.

    Formula:Molarity

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

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15. 15.

    Mathematics

    Evaluate log base 3 of 27.

    Formula:Logarithm Evaluation

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

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16. 16.

    Biology

    Under a microscope, an object of actual size 3.7 mm appears 222 mm. Find the magnification.

    Formula:Microscope Magnification

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

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17. 17.

    Physics

    A body moving at 6 m/s accelerates at 8 m/s² for 7 s. Find the distance travelled.

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

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

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18. 18.

    Chemistry

    A solution is made by dissolving 50 g of solute in 129 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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19. 19.

    Physics

    Find the momentum of a 35 kg body moving at 40 m/s.

    Formula:Linear Momentum

    $p = mv$

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20. 20.

    Biology

    In a population at Hardy–Weinberg equilibrium, the recessive allele frequency q = 0.1. 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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