Abeka 9th Grade Algebra 1 Test 1 Flashcards

Questions and Answers

How many terms are in the expression $3x + \frac{5a}{2y}$?

In the expression $2y - 7z^3$, which of the following is an exponent?

3 (correct)

In the expression $6x^2 + 5$, which of the following correctly identifies the 6?

coefficient (correct)

constant

exponent

variable

Which notation best represents the relationship between the two numbers plotted on the number line below?

-1 < 5 Signup and view all the answers

In the expression $[1 + 7 \cdot (2 - 9)] \div 3 + 12$, which of the following operations is done first?

2 - 9 Signup and view all the answers

What is the opposite of 6?

-6 Signup and view all the answers

What type of number is $\sqrt{23}$?

irrational Signup and view all the answers

Which of the following is true for multiplying two signed numbers with opposite signs?

The product is negative. Signup and view all the answers

What is an unknown value called?

variable Signup and view all the answers

What are natural numbers and zero called?

whole numbers Signup and view all the answers

What is a number's distance from zero called?

absolute value Signup and view all the answers

What are quantities combined by only addition or subtraction called?

terms Signup and view all the answers

Express the sum of x and 3 divided by 2.

x + 3/2 OR (x + 3) ÷ 2 Signup and view all the answers

Half of g multiplied by t squared is equal to d.

1/2gt²=d Signup and view all the answers

The length l of a rectangle is equal to its area A divided by its width w.

l=A/w Signup and view all the answers

Represent the length of the other piece if a piece of yarn 29 inches long is cut into two parts, with one part being m inches long.

29-m Signup and view all the answers

The perimeter of a rectangle is twice the sum of its length l and width w.

P=2(l+w) OR P=2l+2w Signup and view all the answers

The circumference C of a circle is equal to the product of π and the diameter d.

C=πd Signup and view all the answers

Express the gross profit GP of an item if the selling price p minus the cost of 2 dollars is considered.

GP=p-2 Signup and view all the answers

Evaluate the expression $4 + 3^2 ÷ (-1)(4)(-2) - 1$.

75 Signup and view all the answers

What is the value of $-3^2/2^3 + 1$?

-1 Signup and view all the answers

What is the result of $\frac{5}{12} + \frac{1}{12} -\frac{1}{4}$?

1/4 Signup and view all the answers

Simplify $3x + 2y + 5x - y$.

8x + y Signup and view all the answers

Simplify $8mn + 10 - 2(3mn - 1) + 2mn - 5 + 8$.

4mn + 15 Signup and view all the answers

Simplify $a + [a + b - a - (2a - b)]$.

-a + 2b Signup and view all the answers

If $x = -3$ and $y = 5$, find the value of the expression $2x^2 + 4y - 5$.

33 Signup and view all the answers

If $a = -2$, find the value of the expression $|2a + 5|$.

1 Signup and view all the answers

Phil drove for 5 hours at 65 miles per hour. How far did he drive if $d = rt$?

325 mi Signup and view all the answers

Find the value of A in the formula $A = \frac{1}{2}h (a + b)$ when $h = 6$ in., $a = 12$ in., and $b = 8$ in.

60 sq in Signup and view all the answers

What property is represented by $(a + b)c = ac + bc$?

distributive property Signup and view all the answers

What property is represented by $r(s + t) = (s + t)r$?

commutative property Signup and view all the answers

What property is represented by $\frac{3}{5}(\frac{2}{5}) = \frac{3}{5}$?

identity property Signup and view all the answers

What property is represented by $x + (y + z) = (x + y) + z$?

associative property Signup and view all the answers

What property is represented by $3x + 0 = 3x$?

identity property Signup and view all the answers

Study Notes

Algebra Expressions and Terms

The expression 3x + 5a/2y contains two terms.
In 2y − 7z³, the number 3 is identified as the exponent of z.
The coefficient in 6x² + 5 is 6.

Mathematical Relationships and Inequalities

The notation -1 < 5 illustrates the relationship between the two plotted numbers on a number line.

Order of Operations

In the expression [1 + 7 · (2 − 9)] ÷ 3 + 12, the first operation performed is 2 − 9.

Number Properties

The opposite of the number 6 is -6.
The value of √23 is classified as an irrational number.
When multiplying two numbers with opposite signs, the resultant product is negative.

Fundamental Algebra Concepts

Variable represents an unknown value in algebra.
Whole numbers include natural numbers and zero.
Absolute value measures a number's distance from zero in a number line.

Composition of Expressions

Terms are quantities combined solely through addition or subtraction.
The expression for “the sum of x and 3 divided by 2” can be written as (x + 3) ÷ 2.

Formulas and Equations

The relationship for half of g multiplied by t squared equal to d is represented by 1/2gt² = d.
The formula for the length l of a rectangle is l = A/w where A is the area and w is the width.
The perimeter of a rectangle is calculated as P = 2(l + w).

Mathematical Constants and Dimensions

The circumference C of a circle is expressed as C = πd.

Financial Calculations

The gross profit GP from an item is calculated as GP = p - 2, where p is the selling price.

Simplifying Mathematical Expressions

The expression 4 + 3² ÷ (-1)(4)(-2) − 1 simplifies to 75.
The result of -3²/2³ + 1 is -1.
The expression 5/12 + 1/12 − 1/4 simplifies to 1/4.

Combining Like Terms

The expression 3x + 2y + 5x − y can be simplified to 8x + y.
For 8mn + 10 − 2(3mn − 1) + 2mn − 5 + 8, the result is simplified to 4mn + 15.

Value Evaluation Examples

When substituting x = -3 and y = 5 in the expression 2x² + 4y − 5, the resulting value is 33.
If a = -2, the absolute value expression | 2a + 5 | evaluates to 1.

Real-life Applications

Phil drives for 5 hours at a rate of 65 miles per hour, covering a total distance of 325 miles.
In the formula A = 1/2h(a + b) with values h = 6 in, a = 12 in, b = 8 in, the area A is calculated as 60 sq. in..

Algebraic Properties

The distributive property states that (a + b)c = ac + bc.
The commutative property highlights that r(s + t) = (s + t)r.
The identity property is demonstrated with the expression 3/5(2/5) = 3/5.
The associative property allows for grouping changes as shown in x + (y + z) = (x + y) + z.
The expression 3x + 0 = 3x exemplifies the identity property in algebra.

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Test your understanding of 9th grade Algebra 1 concepts with these flashcards. Each card presents a question related to algebraic expressions, coefficients, and exponents. Challenge yourself to recall definitions and solve problems to excel in your studies.