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EmSAT Achieve · Practice Sheet 30

Sheet code: EMSAT-S30 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find the sum of the first 7 terms of a GP with first term 3 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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2.
Biology
In a population at Hardy–Weinberg equilibrium, the recessive allele frequency q = 0.4. 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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3.
Chemistry
Find the pressure of 3 mol of an ideal gas at 313 K in a 2 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).
Formula:Ideal Gas Law
$PV = nRT$
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4.
Biology
In a monohybrid cross (Aa × Aa) producing 20 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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5.
Mathematics
Find the sum of the first 5 terms of a GP with first term 4 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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6.
Mathematics
Find the distance between the points (-6, -8) and (1, -4).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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7.
Biology
In a monohybrid cross (Aa × Aa) producing 92 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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8.
Chemistry
Find the pressure of 2 mol of an ideal gas at 305 K in a 18 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).
Formula:Ideal Gas Law
$PV = nRT$
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9.
Physics
A projectile is launched at 45 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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10.
Mathematics
Evaluate ∫ from 0 to 3 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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11.
Physics
A force of 744 N acts on an area of 11 m². Find the pressure.
Formula:Pressure
$P = \dfrac{F}{A}$
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12.
Physics
Find the voltage across a 45 Ω resistor carrying a current of 15 A.
Formula:Ohm's Law
$V = IR$
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13.
Chemistry
A solution is made by dissolving 13 g of solute in 116 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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14.
Physics
Find the electrical power when 36 V drives a current of 13 A.
Formula:Electrical Power
$P = VI$
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15.
Physics
A force of 922 N acts on an area of 6 m². Find the pressure.
Formula:Pressure
$P = \dfrac{F}{A}$
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16.
Physics
A body moving at 14 m/s accelerates at 7 m/s² for 7 s. Find the distance travelled.
Formula:Equation of Motion (s = ut + ½at²)
$s = ut + \tfrac{1}{2}at^{2}$
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17.
Chemistry
How many moles are present in 360 g of glucose (C₆H₁₂O₆) (molar mass = 180 g/mol)?
Formula:Number of Moles
$n = \dfrac{m}{M}$
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18.
Physics
An object starts at 8 m/s and accelerates at 4 m/s² for 3 s. Find its final velocity.
Formula:Equation of Motion (v = u + at)
$v = u + at$
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19.
Physics
A force of 620 N acts on an area of 26 m². Find the pressure.
Formula:Pressure
$P = \dfrac{F}{A}$
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20.
Mathematics
For the quadratic 2x² + 8x − 4 = 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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