Mathematics 2

Question 1

What are two methods for solving equations with two unknowns?

Answer 1

1. Using one letter and obtaining one equation

2. Using two letters and obtaining two equations

Question 2

In number problems having two unknowns, _____ concerning the unknowns are needed.

Answer 2

two relationships

Question 3

What are the two relationships established when solving an equation for two unknowns using one letter and obtaining one equation?

Answer 3

One of the relationships is used to represent the two unknowns in terms of one letter. The other relationship is then used to obtain a single equation.

Question 4

What are the two relationships used for when using two letters and obtaining two equations to solve an equation with two unknowns?

Answer 4

Each of the unknowns is represented by a different letter. Each of the two relationships is then used to obtain a separate equation.

Question 5

When you find a value for an unknown, is it sufficient to check your answer using the equation you developed?

Answer 5

No, you must check your answer against the original problem.

Question 6

What is an integer?

Answer 6

A signed whole number.

Question 7

Can an integer be negative?

Answer 7

An integer may be a positive whole number, a negative whole number, or zero.

Question 8

What is a consecutive integer problem?

Answer 8

Each consecutive-integer problems involves a set of consecutive integers, a set of consecutive even integers, or a set of consecutive odd integers. Each such set involves integers arranged in increasing order from left to right.

Question 9

What is the first general principle of ratios?

Answer 9

To find the ratios between quantities, the quantities must have the same unit.

Question 10

What is the second general principle of ratios?

Answer 10

A ratio is an abstract number, that is, a number without a unit of measure.

Question 11

What is the third general principle of ratios?

Answer 11

A ratio should be simplified by reducing to lowest terms and eliminating fractions contained in the ratio.

Question 12

What is the fourth general principle of ratios?

Answer 12

The ratios of three or more quantities may be expressed as a continued ratio. This is simply an enlarged ratio statement.

Question 13

What is the ratio of $2 to $3 to $5?

Answer 13

This is a continued ratio: 2:3:5 made up of separate ratios: 2:3, 3:5, 2:5.

Question 14

How do you factor the difference of two squares?

Answer 14

1. Obtain principal square root of each square.

2. One factor is the sum of the principal square roots. The other factor is their difference.

Question 15

Will a trinomial in the form of x^2 + bx + c always be factorable into binomial factors?

Answer 15

Not always

Question 16

What are the three steps to factoring trinomials in the form of x^2 + bx + c into binomials?

Answer 16

1. Obtain the factors x and x of x2. Use each as the first term of each binomial.
2. Select from the factors of the last term “c” those factors whose sum = b, the coefficient of x. Use each as the second term of each binomial.
3. Form binomial factors from factors obtained in steps 1 and 2.