EmSAT Achieve · Practice Sheet 31

1. 1.

   Mathematics

   In an arithmetic progression with first term 8 and common difference 1, find term number 9.

   Formula:AP nth Term

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

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2. 2.

   Chemistry

   A solution is made by dissolving 42 g of solute in 91 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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3. 3.

   Physics

   A projectile is launched at 31 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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4. 4.

   Physics

   Calculate the potential energy of a 15 kg object at a height of 30 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Physics

   If 1,704 J of work is done in 44 s, find the power.

   Formula:Power

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

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6. 6.

   Biology

   In a population at Hardy–Weinberg equilibrium, the recessive allele frequency q = 0.3. 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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7. 7.

   Biology

   Under a microscope, an object of actual size 4 mm appears 176 mm. Find the magnification.

   Formula:Microscope Magnification

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

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8. 8.

   Physics

   A force of 391 N acts on an area of 3 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   Physics

   A constant force of 134 N moves an object 37 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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10. 10.

    Mathematics

    Find the slope of the line through (-7, -3) and (-2, -8).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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11. 11.

    Biology

    Calculate the BMI of a person weighing 77 kg with height 1.58 m.

    Formula:Body Mass Index

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

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12. 12.

    Mathematics

    Find the sum of the first 7 terms of a GP with first term 6 and common ratio 3.

    Formula:GP Sum of n Terms

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

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13. 13.

    Mathematics

    For the quadratic 2x² − 6x − 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

    In an arithmetic progression with first term 13 and common difference 10, find term number 9.

    Formula:AP nth Term

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

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15. 15.

    Mathematics

    Find term number 5 of a geometric progression with first term 6 and common ratio 2.

    Formula:GP nth Term

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

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16. 16.

    Physics

    Find the density of an object with mass 82 g and volume 32 cm³.

    Formula:Density

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

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17. 17.

    Mathematics

    For the quadratic 5x² + 5x − 2 = 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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18. 18.

    Physics

    Find the density of an object with mass 422 g and volume 21 cm³.

    Formula:Density

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

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19. 19.

    Mathematics

    Evaluate ∫ from 0 to 4 of 1x^2 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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20. 20.

    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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