EmSAT Achieve · Practice Sheet 27

1. 1.

   Mathematics

   In an arithmetic progression with first term 4 and common difference 5, find term number 9.

   Formula:AP nth Term

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

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2. 2.

   Biology

   Calculate the BMI of a person weighing 77 kg with height 1.83 m.

   Formula:Body Mass Index

   $BMI = \dfrac{m}{h^{2}}$

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3. 3.

   Physics

   Find the density of an object with mass 277 g and volume 9 cm³.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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4. 4.

   Mathematics

   In an arithmetic progression with first term 8 and common difference 4, find term number 7.

   Formula:AP nth Term

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

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5. 5.

   Mathematics

   Find term number 7 of a geometric progression with first term 4 and common ratio 3.

   Formula:GP nth Term

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

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6. 6.

   Physics

   A projectile is launched at 34 m/s at 45° 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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7. 7.

   Chemistry

   Find the pH of a solution with [H⁺] = 1×10⁻6 mol/L.

   Formula:pH of a Solution

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

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8. 8.

   Mathematics

   Find term number 5 of a geometric progression with first term 4 and common ratio 2.

   Formula:GP nth Term

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

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9. 9.

   Mathematics

   Find the sum of the first 3 terms of a GP with first term 1 and common ratio 3.

   Formula:GP Sum of n Terms

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

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10. 10.

    Physics

    Find the voltage across a 17 Ω resistor carrying a current of 15 A.

    Formula:Ohm's Law

    $V = IR$

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11. 11.

    Mathematics

    Evaluate log base 2 of 4.

    Formula:Logarithm Evaluation

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

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12. 12.

    Chemistry

    A solution is made by dissolving 40 g of solute in 96 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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13. 13.

    Mathematics

    Evaluate log base 3 of 729.

    Formula:Logarithm Evaluation

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

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14. 14.

    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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15. 15.

    Physics

    A body moving at 15 m/s accelerates at 4 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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16. 16.

    Mathematics

    Find the sum of the first 18 terms of an AP with first term 5 and common difference 9.

    Formula:AP Sum of n Terms

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

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17. 17.

    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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18. 18.

    Physics

    An object starts at 15 m/s and accelerates at 5 m/s² for 8 s. Find its final velocity.

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

    $v = u + at$

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19. 19.

    Mathematics

    Find the sum of the first 6 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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20. 20.

    Mathematics

    Evaluate log base 10 of 1,000.

    Formula:Logarithm Evaluation

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

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