EmSAT Achieve · Practice Sheet 7

1. 1.

   Physics

   Find the kinetic energy of a 5 kg object moving at 15 m/s.

   Formula:Kinetic Energy

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

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2. 2.

   Mathematics

   Evaluate ∫ from 2 to 3 of 1x^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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3. 3.

   Chemistry

   A solution is made by dissolving 38 g of solute in 55 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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4. 4.

   Mathematics

   For the quadratic 1x² − 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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5. 5.

   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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6. 6.

   Physics

   Find the momentum of a 6 kg body moving at 21 m/s.

   Formula:Linear Momentum

   $p = mv$

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7. 7.

   Physics

   A force of 378 N acts on an area of 35 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Physics

   Find the electrical power when 17 V drives a current of 14 A.

   Formula:Electrical Power

   $P = VI$

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9. 9.

   Physics

   Find the kinetic energy of a 14 kg object moving at 29 m/s.

   Formula:Kinetic Energy

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

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10. 10.

    Physics

    Find the voltage across a 44 Ω resistor carrying a current of 4 A.

    Formula:Ohm's Law

    $V = IR$

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11. 11.

    Physics

    Calculate the potential energy of a 42 kg object at a height of 44 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Biology

    In a monohybrid cross (Aa × Aa) producing 104 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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13. 13.

    Mathematics

    For the quadratic 5x² + 8x + 6 = 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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14. 14.

    Mathematics

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

    Formula:GP Sum of n Terms

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

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15. 15.

    Mathematics

    If f(x) = 4x³ + 3x² + 5x, find f′(3).

    Formula:Derivative of a Polynomial

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

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16. 16.

    Physics

    A constant force of 199 N moves an object 27 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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17. 17.

    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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18. 18.

    Mathematics

    Find the binomial coefficient C(5, 3) — the coefficient of x^3 in (1 + x)^5.

    Formula:Binomial Coefficient

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

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19. 19.

    Chemistry

    Find the pressure of 3 mol of an ideal gas at 300 K in a 11 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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20. 20.

    Physics

    An object starts at 16 m/s and accelerates at 9 m/s² for 3 s. Find its final velocity.

    Formula:Equation of Motion (v = u + at)

    $v = u + at$

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