Final Algebra 1

Question 1

What is the first step in this equation? x/9 + 5 = 7

Answer 1

Subtract 5 from each side.

Question 2

What is the solution to this equation? 4x + xy = 6

Answer 2

y ≠ -4
You are trying to get y alone, and since the denominator of a fraction cannot be 0, you know that y cannot be equal to 4.

Question 3

What is an inverse of a relation?

Answer 3

An inverse of a relation is where the domain and range switch. (x,y) -> (y,x)

Question 4

What do these symbols mean in function notation? f(x) = x - 2

Answer 4

f is the name or rule of the function. x is the input value. f(x) is the output when rule f is applied to x.

Question 5

Fill in the missing words: A sequence is a set of _ in a specific order, with each number being a term. An _ sequence is a sequence that increases (adding) or decreases (subtracting) by a _ value. The constant value in an arithmetic sequence is the common _. _ formulas are used to determine the next term of a sequence from one or more of the preceding terms. _ formulas are used to determine ANY term in a sequence.

Answer 5

1. numbers
2. arithmetic
3. constant
4. difference (ratio is for geo)
5. Recursive
6. Explicit

Question 6

To find a rate of change, set up a ratio of the _ variable to the _ variable.

Answer 6

1. dependent.
2. independent.

Question 7

Write the equation of a line in slope-intercept form with a slope of 4 that passes through the point (6, -3).

Answer 7

y=4x−27

Question 8

What is standard form?

Answer 8

Ax + Bx = C

Question 9

In basketball, a free throw is worth 1 point and a field goal is worth 2 or 3 points. In the 2001‑2002 NBA basketball season, Shaquille O’Neal won an NBA championship with the L.A. Lakers. He scored a total of 1822 points that season, all through free throws or 2‑point field goals; he did not make any 3‑pointers that year. The number of field goals he made was 84 less than twice the number of free throws. Write a system of equations to find out the number of free throws and field goals that Shaq made that year. Let x represent the number of free throws, and let y represent the number of 2-point field goals. Solve the system of linear equations.

Answer 9

These are the two equations you should have used.
1822 = x + 2y
y = 2x - 84
The answer is 398, 712

Question 10

What is the Negative Exponent Property?

Answer 10

For all numbers a and n where a ≠ 0, a^-n = 1/a^n.

Question 11

What is the Product of Powers Property?

Answer 11

For all numbers a, m, and n where a ≠ 0, a^m * a^n = a^ m+n

Question 12

What is the Power of a Quotient Property?

Answer 12

For all numbers a, b, and m where a ≠ 0 and b ≠ 0, (a/b)^m = a^m/b^m

Question 13

What is the Exponent Property of Equality?

Answer 13

For all numbers b, x, and y where b ≠ 0, If b^x = b^y, then x = y

Question 14

What is the Zero Exponent Property?

Answer 14

For any nonzero number a, a^0 = 1

Question 15

What is the Power of a Product Property?

Answer 15

For all numbers a, b, and m where a ≠ 0 and b ≠ 0, (ab)^m = a^m * b^m

Question 16

What is the Quotient of Powers Property?

Answer 16

For all numbers a, m, and n where a ≠ 0, a^m/a^n = a^m-n

Question 17

What is the Power of a Power Property?

Answer 17

For all numbers a, m, and n where a ≠ 0, (a^m)^n = a^mn

Question 18

Simplify √5(2+√3)

Answer 18

2√5+√15

Question 19

Fill in the blanks: A square root is in its simplest form when: the radicand has no _ factors other than 1, the radicand is not a _, and a radical is not in the _ of a fraction.

Answer 19

1. perfect square
2. fraction
3. denominator