EmSAT Achieve · Practice Sheet 22

1. 1.

   Chemistry

   Find the molarity of a solution containing 3 mol of solute in 4 L of solution.

   Formula:Molarity

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

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2. 2.

   Physics

   Find the momentum of a 15 kg body moving at 7 m/s.

   Formula:Linear Momentum

   $p = mv$

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3. 3.

   Mathematics

   Find the distance between the points (-4, -7) and (2, 3).

   Formula:Distance Between Two Points

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

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4. 4.

   Biology

   Under a microscope, an object of actual size 3.7 mm appears 151.7 mm. Find the magnification.

   Formula:Microscope Magnification

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

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5. 5.

   Physics

   A force of 385 N acts on an area of 6 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   Chemistry

   How many moles are present in 900 g of glucose (C₆H₁₂O₆) (molar mass = 180 g/mol)?

   Formula:Number of Moles

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

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7. 7.

   Physics

   If 2,437 J of work is done in 12 s, find the power.

   Formula:Power

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

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8. 8.

   Mathematics

   Find the sum of the first 3 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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9. 9.

   Physics

   Find the momentum of a 24 kg body moving at 12 m/s.

   Formula:Linear Momentum

   $p = mv$

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10. 10.

    Mathematics

    Evaluate ∫ from 0 to 5 of 5x^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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11. 11.

    Mathematics

    Find the sum of the first 7 terms of a GP with first term 5 and common ratio 3.

    Formula:GP Sum of n Terms

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

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12. 12.

    Physics

    Find the momentum of a 25 kg body moving at 13 m/s.

    Formula:Linear Momentum

    $p = mv$

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13. 13.

    Physics

    Find the electrical power when 79 V drives a current of 13 A.

    Formula:Electrical Power

    $P = VI$

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14. 14.

    Physics

    A body moving at 11 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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15. 15.

    Biology

    In a population at Hardy–Weinberg equilibrium, the recessive allele frequency q = 0.2. 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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16. 16.

    Chemistry

    Find the pH of a solution with [H⁺] = 1×10⁻5 mol/L.

    Formula:pH of a Solution

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

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17. 17.

    Mathematics

    In an arithmetic progression with first term 4 and common difference 7, find term number 18.

    Formula:AP nth Term

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

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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 3.

    Formula:GP Sum of n Terms

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

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19. 19.

    Physics

    A projectile is launched at 25 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

    How many moles are present in 16 g of oxygen gas (O₂) (molar mass = 32 g/mol)?

    Formula:Number of Moles

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

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