EmSAT Achieve · Practice Sheet 15

1. 1.

   Physics

   A body moving at 11 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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2. 2.

   Mathematics

   Find the binomial coefficient C(7, 2) — the coefficient of x^2 in (1 + x)^7.

   Formula:Binomial Coefficient

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

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3. 3.

   Physics

   Find the force required to accelerate a 29 kg mass at 5 m/s².

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

   $F = ma$

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4. 4.

   Mathematics

   Evaluate ∫ from 0 to 4 of 3x^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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5. 5.

   Chemistry

   22 mL of a 1 M solution is diluted to 116 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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6. 6.

   Mathematics

   Find term number 5 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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7. 7.

   Mathematics

   In an arithmetic progression with first term 16 and common difference 5, find term number 8.

   Formula:AP nth Term

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

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8. 8.

   Chemistry

   A solution is made by dissolving 13 g of solute in 58 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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9. 9.

   Physics

   If 631 J of work is done in 26 s, find the power.

   Formula:Power

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

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10. 10.

    Chemistry

    Find the pH of a solution with [H⁺] = 1×10⁻2 mol/L.

    Formula:pH of a Solution

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

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11. 11.

    Physics

    A body moving at 10 m/s accelerates at 8 m/s² for 8 s. Find the distance travelled.

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

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

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12. 12.

    Physics

    A force of 521 N acts on an area of 30 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    Physics

    A projectile is launched at 34 m/s at 60° 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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14. 14.

    Chemistry

    Find the pressure of 4 mol of an ideal gas at 272 K in a 12 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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15. 15.

    Physics

    A force of 371 N acts on an area of 19 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Chemistry

    59 mL of a 10 M solution is diluted to 254 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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17. 17.

    Biology

    In a monohybrid cross (Aa × Aa) producing 124 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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18. 18.

    Physics

    Find the force required to accelerate a 36 kg mass at 8 m/s².

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

    $F = ma$

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19. 19.

    Mathematics

    For the quadratic 4x² − 1x + 7 = 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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20. 20.

    Mathematics

    In an arithmetic progression with first term 6 and common difference 10, find term number 30.

    Formula:AP nth Term

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

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