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# Abeka 9th Grade Algebra 1 Test 1 Flashcards

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@BrainiestDouglasFir

2

• 7
• 3 (correct)
• y
• 2
• ### 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?

<p>-1 &lt; 5</p> 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?

<p>2 - 9</p> Signup and view all the answers

### What is the opposite of 6?

<p>-6</p> Signup and view all the answers

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

<p>irrational</p> Signup and view all the answers

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

<p>The product is negative.</p> Signup and view all the answers

### What is an unknown value called?

<p>variable</p> Signup and view all the answers

### What are natural numbers and zero called?

<p>whole numbers</p> Signup and view all the answers

### What is a number's distance from zero called?

<p>absolute value</p> Signup and view all the answers

### What are quantities combined by only addition or subtraction called?

<p>terms</p> Signup and view all the answers

### Express the sum of x and 3 divided by 2.

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

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

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

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

<p>l=A/w</p> 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.

<p>29-m</p> Signup and view all the answers

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

<p>P=2(l+w) OR P=2l+2w</p> Signup and view all the answers

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

<p>C=πd</p> 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.

<p>GP=p-2</p> Signup and view all the answers

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

<p>75</p> Signup and view all the answers

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

<p>-1</p> Signup and view all the answers

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

<p>1/4</p> Signup and view all the answers

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

<p>8x + y</p> Signup and view all the answers

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

<p>4mn + 15</p> Signup and view all the answers

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

<p>-a + 2b</p> Signup and view all the answers

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

<p>33</p> Signup and view all the answers

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

<p>1</p> Signup and view all the answers

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

<p>325 mi</p> 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.

<p>60 sq in</p> Signup and view all the answers

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

<p>distributive property</p> Signup and view all the answers

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

<p>commutative property</p> Signup and view all the answers

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

<p>identity property</p> Signup and view all the answers

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

<p>associative property</p> Signup and view all the answers

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

<p>identity property</p> 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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## Description

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.

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