Advanced Math MCQ Quiz - Objective Question with Answer for Advanced Math - Download Free PDF

Given:

Initial population (P₀) = 50

Growth rate (r) = 0.1 per hour

Time (t) = 10 hours

Formula used:

P(t) = P₀ × e^rt

Where e ≈ 2.718, r = Growth rate, t = time.

Calculations:

\(\Rightarrow P(10) = 50 × e^{0.1 × 10} = 50 × e^1 = 50 × 2.718\)

\(\Rightarrow P(10) ≈ 135.9\)

∴ The approximate population after 10 hours is 136 cells

Given: The sum of a number and twice its square is 105.

Let the number be denoted as x.

Concept Used:

The problem involves solving a quadratic equation using trial and error or logical substitution.

The equation can be represented as: x + 2x² = 105

Calculation: Start solving the equation step by step:   x + 2x² = 105

⇒ Substitute x = 7: 7 + 2 × 7² = 105

This satisfies the equation.

Final Answer:

∴ The correct number is x = 7.

The function \( p(n) = 300,000(1.12)^n \) provides the profit \( n \) years after the product launch. \( p(7) \approx 545,616 \) implies that after 7 years, the profit is approximately \( 545,616 \) dollars.

Option 1 is correct, as it directly reflects the profit at \( n = 7 \). 

Substitute \( t = 5 \) into \( h(t) = -4.9t^2 + 50t + 5 \). Compute \( -4.9(5)^2 + 50(5) + 5 \). \( 5^2 = 25 \), so \( -4.9 \times 25 = -122.5 \). Then, \( 50 \times 5 = 250 \). \( -122.5 + 250 + 5 = 132.5 \). Therefore, \( h(5) = 132.5 \). The correct answer is 132.5.

Let \(w\) be the width of the rectangle. The length is \(2w\). The area is given by \(w \times 2w = 50\). This simplifies to \(2w^2 = 50\). Dividing by \(2\), we have \(w^2 = 25\). Taking the square root of both sides gives \(w = 5\) or \(w = -5\). Since width cannot be negative, \(w = 5\).

Choice C is correct. The first expression (1.5x - 2.4)² can be rewritten as (1.5x - 2.4)(1.5x - 2.4). Applying the distributive property to this product yields (2.25x² - 3.6x - 3.6x + 5.76)-(5.2x² - 6.4). This difference can be rewritten as (2.25x² - 3.6x - 3.6x + 5.76) + (-1)(5.2x² - 6.4). Distributing the factor of -1 through the second expression yields 2.25x² - 3.6x - 3.6x + 5.76 - 5.2x² + 6.4. Regrouping like terms, the expression becomes (2.25x² - 5.2x²) + (-3.6x - 3.6x) + (5.76 + 6.4). Combining like terms yields -2.95x² - 7.2x + 12.16.

Choices A, B, and D are incorrect and likely result from errors made when applying the distributive property or combining the resulting like terms.

Given: The sum of a number and twice its square is 105.

Let the number be denoted as x.

Concept Used:

The problem involves solving a quadratic equation using trial and error or logical substitution.

The equation can be represented as: x + 2x² = 105

Calculation: Start solving the equation step by step:   x + 2x² = 105

⇒ Substitute x = 7: 7 + 2 × 7² = 105

This satisfies the equation.

Final Answer:

∴ The correct number is x = 7.

The correct answer is \(\frac{14}{3}\). It's given that 3 teaspoons is equivalent to 1 tablespoon. Therefore, 14 teaspoons is equivalent to \(\left(14 \text { teaspoons) }\left(\frac{1 \text { tablespoon }}{3 \text { teaspoons }}\right) \text {, or } \frac{14}{3}\right.\)teaspoons. Note that 14/3, 4.666, and 4.667 are examples of ways to enter a correct answer.

The correct answer is 73,920. It's given that 1 furlong = 220 yards and 1 yard = 3 feet. It follows that a distance of 112 furlongs is equivalent to \((112 \text { furlongs })\left(\frac{220 \text { yards }}{1 \text { furlong }}\right)\left(\frac{3 \text { foet }}{1 \text { yard }}\right)\), or 73,920 feet.

The correct answer is 40,260. It's given that 1 furlong = 220 yards and 1 yard = 3 feet. It follows that a distance of 61 furlongs is equivalent to \((61 \text { furlongs })\left(\frac{220 \text { yards }}{1 \text { furlong }}\right)\left(\frac{3 \text { foet }}{1 \text { yard }}\right)\). or 40,260 feet.

Choice A is correct. Since 1 kilometer is equal to 1,000 meters, it follows that 90 kilometers is equal to 90(1,000)=90,000  meters. Since 1 hour is equal to 60 minutes and 1 minute is equal to 60 seconds, it follows that 1 hour is equal to 60(60) = 3,600 seconds. Now is equal to \(\frac{90 \text { kilometers }}{1 \text { hour }} \text { is equal to } \frac{90,000 \text { meters }}{3,600 \text { seconds }}\), which reduces to \(\frac{25 \text { meters }}{1 \text { second }}\) or 25 meters per second. 
Choices B, C, and D are incorrect and may result from conceptual or calculation errors. 

Choice C is correct. It's given that 3 teaspoons is equivalent to 1 tablespoon. Therefore, 44 tablespoons is equivalent to \(\left(44 \text { tablespoons) }\left(\frac{3 \text { teaspoons }}{1 \text { tableapoon }}\right)\right.\), or 132 teaspoons.
Choice A is incorrect. This is equivalent to approximately 15.66 tablespoons, not 44 tablespoons.
Choice B is incorrect. This is equivalent to approximately 29.33 tablespoons, not 44 tablespoons.
Choice D is incorrect. This is equivalent to approximately 58.66 tablespoons, not 44 tablespoons.

Choice A is correct. It's given that t = 4u. Multiplying both sides of this equation by 2 yields 2t = 2(4u), or 2t = 8u.
Choice B is incorrect and may result from dividing, instead of multiplying, the right-hand side of the equation by 2. Choices C and D are incorrect and may result from calculation errors.

The correct answer is 102. It's given that 1 yard is equivalent to 3 feet. Therefore, 34 yards is equivalent to \((34 \text { yards })\left(\frac{3 \text { feet }}{1 \text { yard }}\right)\). or 102 feet.

Choice B is correct. It's given that 1 yard = 36 inches. Therefore, 612 inches is equivalent to \(612 \text { inches }\left(\frac{1 \text { yard }}{38 \text { inches }}\right),\) which can be rewritten as \(\frac{612 \text { yards }}{36} \text {, }\)or 17 yards. 36
Choice A is incorrect. This is the number of yards that are equivalent to 2.124 inches.
Choice C is incorrect. This is the number of yards that are equivalent to 20,736 inches.
Choice D is incorrect. This is the number of yards that are equivalent to 793,152 inches.