Algebra 1 EOC Review

Agebra I EOC Review

​Topic: Equation of a Line

​To write the equation of any line. You need two pieces of information:

• A point and slope

or

• Two points

Multiple Choice

Which equation represents the data in the table?

• y = 0.25x − 3

• y = x − 3

• y = x − 4

• y = 4x − 4

Multiple Choice

The table compares the gas mileage of a car to the distance the car can travel on one tank of gas. A scatter plot of the data is also shown. For this line of best fit, predict what the gas mileage must be for a car to travel 250 miles.

• 15 mi/gal

• 17 mi/gal

• 19 mi/gal

• 20 mi/gal

Multiple Choice

Write an equation for the line that has a y-intercept of 2 and is perpendicular to the line 3x + y = 6.

• y = −3x + 2

• y = −3x − 2

• $$y=\frac{1}{3}x+2$$

• $$y=-\frac{1}{3}x+2$$

Multiple Choice

Write an equation in slope-intercept form for the line that passes through (3, 7) and (7, 4).

• $$y=-\frac{3}{4}x+\frac{37}{4}$$

• $$y=\frac{3}{4}x+\frac{37}{4}$$

• $$y=-\frac{4}{3}x+\frac{37}{4}$$

• $$y=-\frac{3}{4}x+\frac{4}{37}$$

Multiple Choice

Thomas is a car salesman. The table shows the monthly salary that Thomas earns for the number of cars he sells. Use the data to graph the linear function. Write the equation of the line, identify the slope of the line and explain what the slope means.

Multiple Choice

Which of the following represents the slope of the equation?

• $$-\frac{5}{9}$$

• $$-\frac{9}{5}$$

• $$\frac{5}{9}$$

• $$\frac{9}{5}$$

Multiple Choice

The values in the table show a linear relationship. Find the slope.

• 2

• -2

• $$\frac{1}{2}$$

• $$-\frac{1}{2}$$

Multiple Choice

The temperature of air in a room that began at 55°F is increasing by 8°F per hour. The following equation represents this situation: y = 55 + 8x where x represents the number of hours and y represents the temperature. Which of the following is a graph of this equation?

Multiple Choice

Graph the line described by the equation −2x − 4y = 16.

Topic: Inequalities

Operating with Inequalities is the same as with expressions or equations.

Inequalities have 1 special rule:

When you multiply/divide by a negative; then the inequality symbol flips.

​Example:

Multiple Choice

John is considering accepting one of two sales positions. ABC Company offers a yearly salary of $45,000. XYZ Company offers a yearly salary of $38,000 plus a 2% annual commission on sales. For what amount of sales s is the salary at XYZ Company greater than the salary at ABC Company?

• s > 7000

• s > 35,000

• s > 70,000

• s > 350,000

Multiple Choice

Which of the following is the solution to this inequality?

• n ≥ 2

• n ≥ −2

• n ≤ 2

• n ≤ −2

Multiple Choice

. Which compound inequality is shown by the graph below?

• x ≥ 2 AND x ≤ 8

• x ≥ 2 OR x ≥ 8

• x ≥ 2 OR x ≤ 8

• x ≤ 2 OR x ≤ 8

Multiple Choice

Two snow resorts offer private lessons to their customers. Big Time Ski Mountain charges $5 per hour plus $50 insurance. Powder Hills charges $10 per hour plus $30 insurance. For what number of hours is the cost of lessons the same for each resort?

• 3 hours

• 4 hours

• 5 hours

• 6 hours

Multiple Choice

A printer holds 500 sheets of paper. After printing it held 210 sheets. Of the sheets that were printed, 1/2 of them were color and 1/2 of them were grayscale. Which equation can be used to find s, the number of sheets that were printed in color?

• $$\frac{s}{2}−500=210$$

• $$500-\frac{1}{2}s=210$$

• 210 − 500 = 2s

• 500 − 2s = 210

Multiple Choice

Jasmine and her sister are saving to buy MP3 players. Jasmine has $50 and plans to save $10 per week. Her sister has $80 and plans to save $7 per week. In how many weeks will Jasmine have more money saved than her sister?

• 2 weeks

• 4 weeks

• 10 weeks

• 11 weeks

Multiple Choice

Zahra spent $20.50 on 10 party favors for her party. They party favor for each kid was either a puzzle book or a magic trick. The boys each received a puzzle book that cost $1.75 each. The girls each received a magic trick that cost $2.25 each. How many boys and how many girls attended the party?

• 4 boys and 6 girls

• 5 boys and 5 girls

• 6 boys and 4 girls

• 7 boys and 3 girls

Multiple Choice

Marc sold 461 tickets for the school play. Student tickets cost $3 and adult tickets cost $4. Marc's sales totaled $1624. How many adult tickets and how many student tickets did Marc sell?

• 220 adult, 241 student

• 225 adult, 236 student

• 236 adult, 225 student

• 241 adult, 220 student

Topic: Multiplying Polynomials

Using the Distributive Property, you will distribute each term in the first nomial to the second one.

​Example:

​Notice that you have 4 terms at the beginning and before you combine like terms, there are 4 terms as well. (Good way to check if you have distributed everything.)

​Notice that you have 3 terms in the numerator and 3 separate fractions once you divide each one.

Multiple Choice

$$Add:\ (2x^2−7)+(7x^2+3)$$

• $$2x^2−4$$

• $$9x^2−4$$

• $$9x^2−7$$

• $$9x^4−4$$

Multiple Choice

Find the value of a.

• 2

• 4

• 6

• 8

Multiple Choice

$$Divide\ (4x^5+3x^3−2x^2)\ by\ 2x.$$

• $$2x^4+\frac{3x^2}{2}−x$$

• $$2x^4+3x^2−x$$

• $$4x^4+3x^2−2x$$

• $$2x^4+x^2−x$$

Multiple Choice

Which monomial below writes the product (3x)(3x)(3x)(3x)(3x)(3x) in a more compact form?

• 6(3x)

• $$3x^6$$

• $$\left(3x\right)^6$$

• $$18x^6$$

Multiple Choice

If a ≠ 0 and b ≠ 0, which of the following is a simplified version of the expression above?

• $$a^5b^6−a^5b^4$$

• $$a^{12}b^{10}−a^2b^6$$

• $$a^6b^4$$

• $$a^7b^2$$

Multiple Choice

What are the missing exponents in the equation below? Give the missing exponent on the left side first.

• 7; 14

• 3; 10

• 3; 21

• 7; 21

Topic: Quadratics

Where p(q) = c p+q=b

And -p,-q are solutions (x intercepts)

Topic: Solving Quadratics (2 ways)

Where p(q) = c p+q=b

Factoring Quadratics: (x+p)(x+q)

Multiple Choice

A manufacturing company is building a rectangular room in their warehouse to store their products. The length of the room is 1 more than 3 times its width. The area of the room is 80 square meters. What are the dimensions of the room?

• w = 4 m, l = 20 m

• w = 5 m, l = 16 m

• w = 5 1/3 m, l = 15 m

• w = 8 m, l = 10 m

Multiple Choice

An object is thrown upward with an initial velocity of 35 meters per second. The object’s distance, d, above the ground at any time, t, can be represented by the equation (look at picture) . When will the object be 50 feet above the ground?

• t = 1 sec and t = 0.4 sec

• t = 2 sec and t = 5 sec

• t = 2 sec and t = 10 sec

• t = 5 sec and t = 10 sec

Multiple Choice

Find the height of the highest point of the trajectory and the horizontal distance the potato travels before hitting the ground.

• height: 109 m; distance: 435 m

• height: 121 m; distance: 418 m

• height: 118 m; distance: 421 m

• height: 102 m; distance: 409 m

Multiple Choice

Solve 3(a − 4) + 2(a + 1) = 10 − 5a.

• 0

• 2

• all real numbers

• no solution

Topic: Functions + Domain & Range

Determining if a function is a function:

Vertical line test - Checking if there are any repeated x values.

Parts of a function:

• Domain: All the x values of your function (AKA input)

• Range: All the y values of your function (AKA output)

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Multiple Choice

You’ve already earned $48 washing cars and plan to earn $12 for each additional car you wash. Write an equation to represent d, the amount earned in dollars, as a function of c, the number of additional cars you wash.

• d = 12c

• c = 12d

• d = 48 + 12c

• c = 48 + 12d

Multiple Select

Determine which of the following graphs represent a function. (Could be multiple answers)

• None of these.

Multiple Choice

Give the domain and range of the relation.

• D: {3, 6, –7, 7, 13, –13}; R: {0}

• D: {–7, 0, 3, 6}; R: {–13, 0, 7, 13}

• D: {–7, 3, 6}; R: {–13, 7, 13}

• D: {–13, 0, 7, 13}; R: {–7, 0, 3, 6}

Topic: Basic Arithmetic

Some of the common rules you will need to know when operating with different numbers or symbols:

Multiple Choice

Multiply. Write the product in simplest form.

• $$\sqrt[]{24}+\sqrt[]{36}$$

• $$2\sqrt[]{6}+6$$

• $$12+6\sqrt[]{6}$$

• $$2\sqrt[]{15}$$

Multiple Choice

If Kush simplified the expression correctly, which of the following is his answer?

• $$5\ \sqrt[]{5}+\sqrt[]{5x}$$

• $$7\ \sqrt[]{5}+\sqrt[]{5x}$$

• $$3\ \sqrt[]{5}+\sqrt[]{5x}$$

• $$4\ \sqrt[]{5}+\sqrt[]{5x}$$

Multiple Choice

At a store, 20 feet of fencing cost $36. At that rate, how much will 15 feet of fencing cost?

• $27.00

• $29.75

• $30.25

• $48.00

Multiple Choice

If the exchange rate for 1 U.S. dollar is 1.5 Canadian dollars, how many U.S. dollars will Margie get for 81 Canadian dollars?

• 28

• 52

• 54

• 112

Topic: Number (Set Theory)

Sets:

• A grouping of elements (numbers).

• Written in order always

Set Operations:

• Complement: everything not in the set A.

• Union: all elements together.

• Intersection: only things in common

Multiple Choice

Find the intersection of the pair of sets.

W = the set of whole numbers

P = the set of nonzero integers

• {}

• {0}

• the set of negative integers

• the set of positive integers

Multiple Choice

Look at the Venn diagram below. It shows set A and set B in the universe U. Which description represents the shaded regions?

• the complement of (A∩B) in U

• (A ∪ B) ∪ (the complement of A)

• (the complement of (A∩B) in U ) ∩ (A ∪ B)

• A ∪ B

Multiple Choice

In Mr. Rojo’s music class, 14 students play piano, 18 students play guitar, and 9 play drums. No student plays any other istruments. The following information is also true: 7 students play only guitar; 2 students play all three instruments; 5 students play only piano; 1 student plays piano and drums, but not guitar This information is placed in a Venn diagram as shown:

Which of the following correcly shows the completed Venn diagram?

Multiple Choice

Which of the following is a member of M × N?

M = {20, 30, 55, 60}

N = {30, 55, 65}

• (20, 20)

• (30, 30)

• (55, 60)

• (30, 60)

Multiple Choice

40 candidates apply for a unique job. The job has both a height requirement and a weight requirement. The following information is known about the candidates:

21 candidates meet the height requirement;

17 candidates meet the weight requirement;

8 candidates meet both the weight and height requirements.

How many candidates meet only the height requirement?

• 8

• 9

• 13

• 21

Topic: Equivalent Expressions and Equations

Equivalent: equal value

Any multivariable equation can be rewritten where one variable is isolated:

​Proof that it works:

Assume x = 2, y = 3 and solve for z.

Using new: z = 2x + 4y - 12;

z = 2(2) + 4(3) - 12

z = 4 + 12 - 12

z = 4

Using original: 2x + 4y - z = 12

2(2) + 4(3) - z = 12

4 + 12 - z = 12

16 - z = 12

-z = -4

z = 4

Equivalent Equations

Multiple Choice

$$\frac{E}{x}=C+\frac{3}{x};\ find\ C.$$

• $$C=\frac{E-3}{x}$$

• $$C=\frac{E}{x}-3$$

• $$C=\frac{E}{x-3}$$

• $$C=3-\frac{E}{x}$$

Multiple Choice

$$Solve\ y+w-\frac{3}{4}z=0\ for\ z.$$

• $$z=\frac{4}{3}\left(y+w\right)$$

• $$z=\frac{3}{4}\left(y+w\right)$$

• $$z=\frac{4}{3}w+y$$

• $$z=\frac{4y}{3}+w$$

Multiple Choice

There were T people waiting for buses at the station. When the first bus arrived, n people boarded it. The remaining p people waited for buses to other places.

Use the equation T − n = p, to find n, the number of people who boarded the first bus.

• n = p − T

• n = T/p

• n = T − p

• n = T + p

Multiple Choice

When solving the equation, what property was used to go from Step 2 to Step 3? Step 1: −(2x + 3) = x − 18

Step 2: −2x − 3 = x − 18

Step 3: −3 = 3x − 18

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality