EmSAT Achieve · Practice Sheet 18

1. 1.

   Chemistry

   How many moles are present in 132 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

   Formula:Number of Moles

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

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2. 2.

   Chemistry

   Find the molarity of a solution containing 1.5 mol of solute in 2.5 L of solution.

   Formula:Molarity

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

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3. 3.

   Mathematics

   For the quadratic 4x² + 8x + 9 = 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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4. 4.

   Mathematics

   Find the sum of the first 25 terms of an AP with first term 12 and common difference 2.

   Formula:AP Sum of n Terms

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

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5. 5.

   Mathematics

   Evaluate ∫ from 0 to 4 of 1x^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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6. 6.

   Physics

   Calculate the potential energy of a 30 kg object at a height of 2 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Physics

   Find the momentum of a 27 kg body moving at 35 m/s.

   Formula:Linear Momentum

   $p = mv$

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8. 8.

   Physics

   Calculate the potential energy of a 18 kg object at a height of 6 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   Mathematics

   Find term number 3 of a geometric progression with first term 2 and common ratio 3.

   Formula:GP nth Term

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

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10. 10.

    Chemistry

    20 mL of a 5 M solution is diluted to 265 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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11. 11.

    Mathematics

    Find term number 7 of a geometric progression with first term 3 and common ratio 3.

    Formula:GP nth Term

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

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12. 12.

    Chemistry

    Find the pH of a solution with [H⁺] = 5×10⁻6 mol/L.

    Formula:pH of a Solution

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

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13. 13.

    Physics

    Find the voltage across a 24 Ω resistor carrying a current of 2 A.

    Formula:Ohm's Law

    $V = IR$

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14. 14.

    Physics

    A body moving at 2 m/s accelerates at 4 m/s² for 5 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.

    Mathematics

    Evaluate log base 5 of 15,625.

    Formula:Logarithm Evaluation

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

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16. 16.

    Mathematics

    Find the binomial coefficient C(5, 4) — the coefficient of x^4 in (1 + x)^5.

    Formula:Binomial Coefficient

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

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17. 17.

    Physics

    A force of 675 N acts on an area of 50 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Chemistry

    Find the pressure of 4 mol of an ideal gas at 240 K in a 16 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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19. 19.

    Chemistry

    How many moles are present in 29.25 g of sodium chloride (NaCl) (molar mass = 58.5 g/mol)?

    Formula:Number of Moles

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

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20. 20.

    Physics

    If 2,660 J of work is done in 41 s, find the power.

    Formula:Power

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

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