FREE FTCE Grades 6-12 Questions and Answers
The following equation describes a parabola; what is its directrix? (x-4) ² = 8(y-2) (y-2)
The equation of the directrix for the parabola described by the equation (x-4)² = 8(y-2) is y = 0. The directrix is a horizontal line located 2 units below the vertex of the parabola.
A good illustration of this is the New York City subway system.
A functional region is an area organized around a central point or node, where certain activities, interactions, or services are focused. In the case of the New York City subway system, the central point or node would be the subway stations and the train lines that connect them.
What subatomic particle(s) controls an isotope's radioactivity?
Isotopes are atoms of the same element that have the same number of protons (which defines the element) but differ in the number of neutrons in their nuclei. The number of protons determines the element's identity, while the sum of protons and neutrons in the nucleus gives the mass number of the isotope.
How big of a tank would be required to maintain STP and contain the oxygen gas produced when a kilogram of potassium chlorate breaks down?
When 1 kilogram of potassium chlorate (KClO3) undergoes decomposition, it produces approximately 12.24 moles of oxygen gas (O2) at STP (Standard Temperature and Pressure). To contain this amount of oxygen gas at STP, a tank with a volume of approximately 274 liters would be needed.
Which of the following categories of software best describes Microsoft Excel?
Microsoft Excel is an example of spreadsheet software. Spreadsheet software is a type of computer application used to organize, analyze, and manipulate numerical data in a tabular format. In a spreadsheet, data is organized into rows and columns, and each intersection of a row and a column is referred to as a cell.
Which of the following compounds would have the most ionic character given the electronegativity values? H is 2,2, K is 0, Fe is 1,8, Cl is 3,2, and O is 3,4.
Among the given compounds, KCl (potassium chloride) would have the greatest ionic character. This is because it has the largest electronegativity difference between the elements potassium (K) and chlorine (Cl), which indicates a strong ionic bond in the compound. The larger the electronegativity difference, the stronger the ionic character in the bond.
Think about a 10 kilogram item falling at a 0 m/s beginning speed from a cliff. What will the object's speed be after one and two seconds?
A 10 kg object that is free-falling from a cliff with an initial speed of 0 m/s will have the following speeds:
After 1 second: 9.8 m/s
After 2 seconds: 19.6 m/s
The object's speed increases at a rate of approximately 9.8 m/s for each second it falls due to the acceleration of gravity.
Which of the following represents imperialism?
During the era of European imperialism, which took place from the 15th to the 20th century, many European powers sought to expand their empires by acquiring colonies in Africa, Asia, and the Americas. They used military force and superior technology to subjugate indigenous populations, exploit resources, and establish control over the conquered territories.
Betty has $12 in her pocket. She intends to purchase cucumbers and carrots. Cucumbers cost $0.75 and carrots cost $0.90 per piece. What is the maximum number of cucumbers Betty can purchase if she needs to buy at least 10 carrots and a maximum of 8?
Betty can buy at most 6 cucumbers and 8 carrots while spending all her $12. This satisfies the condition of buying at least 10 carrots and at most 8 cucumbers and ensures that she spends the entire amount of $12. The cost of the carrots and cucumbers together would be $11.70.
Which of these falls under the category of application software?
A spreadsheet is categorized as application software. Application software refers to computer programs or software designed to perform specific tasks or applications for end-users. Unlike system software, which manages computer hardware and provides essential services to run the computer, application software is intended to be used by individuals or organizations to perform various tasks.
What comes closest to a mass of 500 mL of water is the following?
Water has a density of about 1 gram per milliliter (g/mL) at standard conditions, which means that 1 milliliter of water weighs approximately 1 gram. Therefore, 500 mL of water would weigh approximately 500 grams.
Which statement regarding ideal gas particle properties is TRUE?
The kinetic theory of gases describes the behavior of gases at the molecular level. According to this theory, gas particles (atoms or molecules) are in constant motion and move in random directions at high speeds. The motion of gas particles is influenced by collisions with other gas particles and the walls of the container they are in.
Which pieces of legislation set requirements that federally constructed buildings and facilities be accessible to individuals with disabilities?
The Architectural Barriers Act requires that certain federally funded buildings and facilities, including those constructed, altered, or leased by federal agencies, be designed and constructed to be accessible to individuals with physical disabilities. The goal of the act is to ensure that people with disabilities have the same opportunities to access and use federal facilities as their non-disabled counterparts.
What is the name of the well-known initiative that successfully mapped human DNA with a 99.999% accuracy rate?
The Human Genome Project was an international research effort that spanned from 1990 to 2003. Its primary goal was to map and sequence the entire human genome, which is the complete set of DNA in a human cell. The project aimed to identify and determine the sequence of all the nucleotide base pairs that make up human DNA.
What kind of software program would be most effective for drafting a report?
A word processing software application would be the best choice for writing a report. Word processing software is designed specifically for creating, editing, and formatting textual documents. It provides a user-friendly interface with various tools and features to help users efficiently write and structure their content.
When plants travel toward the sun, which of the following movements occurs?
Phototropism is a plant's growth response to light. When a plant detects the presence of light, it will tend to grow towards the light source. This growth movement is a result of differential growth rates on opposite sides of the plant stem or shoot.
Think about a mathematical series where the common difference is d=3, and the first term is a=12. What is the sum of the first six terms in a series with 12 terms?
The arithmetic series has a first term (a) of 12, a common difference (d) of 3, and a total of 12 terms. To find the sum of the first 6 terms, we use the formula for the sum of an arithmetic series: Sum = (n/2) * [2a + (n-1) * d]. After substituting the given values, we find that the sum of the first 6 terms is 117.
How do columns in Microsoft Excel get their names?
In Microsoft Excel, columns are identified by letters. The columns are labeled alphabetically from left to right, starting with column A, then B, C, and so on. Once you reach the end of the alphabet (column Z), the next column will be labeled AA, AB, AC, and so forth.
What name does science give the seed leaf?
Scientists use the term "cotyledon" for the seed leaf. Cotyledons are the primary leaves found in the embryos of seed-bearing plants (angiosperms). They are part of the seed structure and play a vital role during germination and early plant development.
What does cloud storage NOT offer?
Cloud Storage can offer cost savings compared to traditional on-premises storage solutions. Cloud providers often offer various pricing models, such as pay-as-you-go or monthly subscriptions, which can be more cost-effective for certain use cases and organizations. Additionally, cloud storage eliminates the need for investing in and maintaining physical hardware, reducing upfront capital expenditures and ongoing operational costs.
What other names are given to optimization?
Alternative algorithms are different methods or approaches used to solve optimization problems. Depending on the complexity of the problem and the nature of the objective function and constraints, various algorithms and techniques may be employed to find the optimal solution efficiently. Some common optimization algorithms include linear programming, nonlinear programming, genetic algorithms, simulated annealing, and gradient-based methods, among others.