EmSAT Achieve · Practice Sheet 16

1. 1.

   Physics

   A projectile is launched at 20 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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2. 2.

   Physics

   Find the voltage across a 21 Ω resistor carrying a current of 14 A.

   Formula:Ohm's Law

   $V = IR$

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3. 3.

   Chemistry

   How many moles are present in 180 g of glucose (C₆H₁₂O₆) (molar mass = 180 g/mol)?

   Formula:Number of Moles

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

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4. 4.

   Mathematics

   Find the slope of the line through (-6, -2) and (-3, 4).

   Formula:Slope of a Line

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

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5. 5.

   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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6. 6.

   Physics

   Find the density of an object with mass 10 g and volume 16 cm³.

   Formula:Density

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

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7. 7.

   Mathematics

   Find the distance between the points (5, 8) and (-6, 1).

   Formula:Distance Between Two Points

   $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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8. 8.

   Chemistry

   34 mL of a 10 M solution is diluted to 359 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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9. 9.

   Mathematics

   Find the sum of the first 13 terms of an AP with first term 6 and common difference 3.

   Formula:AP Sum of n Terms

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

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10. 10.

    Mathematics

    Find the distance between the points (-8, 4) and (1, 4).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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11. 11.

    Biology

    In a population at Hardy–Weinberg equilibrium, the recessive allele frequency q = 0.5. 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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12. 12.

    Mathematics

    For the quadratic 1x² − 5x − 8 = 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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13. 13.

    Physics

    A projectile is launched at 21 m/s at 30° 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.

    Mathematics

    In an arithmetic progression with first term 5 and common difference 1, find term number 6.

    Formula:AP nth Term

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

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15. 15.

    Physics

    Find the electrical power when 105 V drives a current of 18 A.

    Formula:Electrical Power

    $P = VI$

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16. 16.

    Physics

    Find the momentum of a 22 kg body moving at 12 m/s.

    Formula:Linear Momentum

    $p = mv$

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17. 17.

    Mathematics

    Evaluate log base 10 of 10,000.

    Formula:Logarithm Evaluation

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

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18. 18.

    Physics

    A constant force of 71 N moves an object 4 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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19. 19.

    Mathematics

    Evaluate log base 2 of 32.

    Formula:Logarithm Evaluation

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

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20. 20.

    Physics

    Calculate the potential energy of a 30 kg object at a height of 41 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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