ALGEBRA I END-OF-COURSE, Lecture notes of Algebra

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ALGEBRA I END‐OF‐COURSE

Curriculum and Instruction

Division of Mathematics, Science, and Advanced Academic Programs

THE SCHOOL BOARD OF MIAMI-DADE COUNTY, FLORIDA

Perla Tabares Hantman, Chair

Dr. Lawrence S. Feldman, Vice Chair

Dr. Dorothy Bendross-Mindingall

Carlos L. Curbelo

Renier Diaz de la Portilla

Dr. Wilbert “Tee” Holloway

Dr. Martin Karp

Dr. Marta Pérez

Raquel A. Regalado

Hope Wilcox

Student Advisor

Alberto M. Carvalho

Superintendent of Schools

Milagros R. Fornell

Associate Superintendent

Curriculum and Instruction

Dr. Maria P. de Armas

Assistant Superintendent

Curriculum and Instruction, K-12 Core

Beatriz Zarraluqui

Administrative Director

Division of Mathematics, Science, and Advanced Academic Program

PRACTICE

3. Shaniqua is constructing an isosceles triangle to use as a model in her Algebra class. The perimeter of her triangle is 24 inches. Shaniqua uses the equation to find b , the length of the triangle’s third side, in terms of s , the length of each of its two congruent sides. What is her equation written in terms of s?

A. s  2 ( b  24 )

B. s ^242  b

C. s  2 ( b  24 )

D. s ^242  b

4. Each month Jessie’s phone bill includes a $25 basic fee plus a charge of $.07 per minute for the number of minutes of long-distance calls she makes. Which equation best describes the total amount of Jessie’s monthly phone bill, t , in terms of m , the number of minutes of long-distance calls she makes? A. t = 0.07 + 25m B. t = 25 + 0.07m C. t = 25(0.07m) D. t = 25(7m)
5. The pressure exerted on the floor by a person’s shoe heel depends on the weight of the person and the width of the heel. The formula is

2

H

P .^ W ,

where P is pressure in pounds per square inch, W is weight in pounds, and H is heel width in inches. Which of the following shows the pressure formula solved for H?

A. H  1. 2 WP

B.

P

H  ^1.^2 W

C. H  ^1.^2 PW

D. H ^12.^2 PW

PRACTICE

6. Pauola was given the equation y = – x + 3. Which of the following is an equivalent representation of this equation? A. f ( x ) = – x + 3 B. f ( y ) = x C. y = – f ( x ) +  3 D. f ( y ) = – x +  3
7. Dr. Chait is considering joining the Garden Club. If he pays a $25 membership fee, he can buy rosebushes from the club at a reduced price of $10 each. If he does not join the club, he can buy rosebushes from a local nursery for $15 each. The graph below compares the cost of buying rosebushes from the Garden Club and from the local nursery.

How many rosebushes will Dr. Chait have to buy from the Garden Club before he would begin to save money? A. 5 B. 7 C. 25 D. 75

PRACTICE

11. Alyssa is enrolled in a public-speaking class. Each week she is required to give a speech of greater length than the speech she gave the week before. The table below shows the lengths of several of her speeches. Alyssa’s Speeches Week Number 3 4 5 6 Length of Speech (seconds) 150 180 210 240 If this trend continues, in which week will she give a 12-minute speech? A. 22 B. 12 C. 15 D. 24
12. Brock is six feet tall. He climbs a ladder to paint some trim on his house. For each rung that he climbs, Brock is 1.2 feet higher above the ground. Which equation could you use to calculate the distance, d, from the top of Brock’s head to the ground if r represents the number of ladder rungs he has climbed? A. d = 1.2r + 6 B. d = 1.2r C. d = r + D. d = 6r + 1.
13. Which sequence uses the algebraic expression 4 n + 5 to describe the relationship between a term in the sequence and its position, n , in the sequence? A. 4, 9, 14, 19, 24 … B. 4, 8, 12, 16, 20 … C. 9, 13, 17, 21, 25 … D. 9, 10, 11, 12, 13 …
14. Which expression is equivalent to the following expression?

21 x (^4 x −^6 )+^3 ( x^2 −^1 )

A. 5 x^2 – 3 x + 3 B. x^2 + 3 x – 6 C. 5 x^2 – 3 x – 3 D. – x^2 + 3 x + 3

PRACTICE

15. What is the slope of the equation 2x – 5y = 10?

A. − 2

B. 52

C. 5

D.

−^2

16. Ryan is writing a composition for homework. He decides to keep track of the number of sentences he writes compared to the time in minutes he works. The graph below shows the data he collected.

At what rate does Ryan write his composition? A. 0.5 sentence per minute B. 1 sentence per minute C. 1.5 sentences per minute D. 2 sentences per minute

PRACTICE

19. A South Dade farmer knows that the number of potatoes harvested varies directly with the number of potato plants grown. Last year the farmer harvested 189 potatoes from 9 potato plants. If the farmer plants 14 potato plants this year, how many potatoes can he expect to harvest? A. 21 B. 23 C. 294 D. 2646
20. To which of the following situations can the function y = 5 x + 10 best be applied?

A. The number of miles a person walks if he walks for 5 hours at the rate of 10 miles per hour B. The total weight on a scale if 5 pounds is placed there initially and a series of 10-pound weights are added to it C. The total wages earned by a waiter who is paid $5 per hour and earns $10 in tips D. The combined length of 5 boards, each 10 feet longer than the width of a doorway

21. Gemma and her cousin went to a restaurant for dinner. Gemma’s dinner cost $5 more than her cousin’s. If their combined bill was under $25, which inequality best describes the cost of their dinners? A. x + 5 < 25 x B. x + ( x + 5) < 25 C. x + ( x + 25) < 5 D. x - ( x + 5) < 25
22. The population of Williston is currently 15,400 people. If the population increases at an average rate of 325 people per year, which equation could be used to find the approximate number of years it will take for the population to reach 18,000 people? A. 15,400 + 325 n = 18, B. 325 n = 18, C. 15,400 n + 325 = 18, D. 15,400 n = 18,

PRACTICE

23. Dosset’s Mobile Service Station uses the graph below to determine how much a mechanic should charge for labor for automobile repairs.

If the labor charge on an automobile repair bill was $67.50, for approximately how many hours, h , did the mechanic work? A. 2.25 < h < 2. B. 2.75 < h < 3. C. 2.00 < h < 2. D. 2.50 < h < 2.

24. The gas tank in Mina’s car holds 15 gallons. Her car gets between 25 and 30 miles to the gallon. If Mina fills up the gas tank and then drives until she runs out of gas, what is the least number of miles she can drive? A. 300 mi B. 375 mi C. 405 mi D. 450 mi

PRACTICE

28. The area of a parallelogram is 35 p^6 q^6 square units. If the base of the parallelogram measures 5 pq^2 units, what is the height of the parallelogram? ( p> 0 and q >0) A. 7 p^5 q^4 units B. 7 p^6 q^3 units C. 30 p^5 q^4 units D. 30 p^6 q^3 units
29. The side length of a square is 4 x^3 yz^4 units. What is the area of the square?

A. 8 x^6 y^2 z^8 square units B. 8 x^9 yz^16 square units C. 16 x^6 y^2 z^8 square units D. 16 x^9 yz^16 square units

30. Julia estimated that it would take her 4 hours to write a 4-page report. It actually took her only 38 minutes to write the first page of the report. If she keeps writing at this same rate, by how many hours and minutes did she overestimate the time it would take her to complete the report? A. 1 hour 28 minutes B. 2 hours 8 minutes C. 2 hours 28 minutes D. 2 hours 32 minutes

PRACTICE

31. A student incorrectly solved the equation 3(2 x + 6) - 4 = 14 as shown below.

Step 1: 6 x + 6 – 4 = 14 Step 2: 6 x + 2 = 14 Step 3: 6 x = 12 Step 4: x = 2

In what step did the student first make a mistake? A. In Step 1, the student should have multiplied both terms in parentheses by 3, not just the first term. B. In Step 2, the student should have subtracted 4 from the right side of the equation, not the left side. C. In Step 3, the student should have added 2 to both sides of the equation instead of subtracting 2. D. In Step 4, the student should have multiplied both sides of the equation by 6 instead of dividing by 6.

32. Kroner asked 100 adults whether they had studied French, Spanish or Japanese in school.

According to the Venn diagram how many adults had studied French and Spanish but not Japanese?

PRACTICE

36. The Venn diagram below shows the number of web pages that were found by using the keywords “math” and “education” on Google in spring 2005. How many millions of web sites were found that contain the work “math”?
37. Twenty-eight girls went camping. The girls were able to choose to participate in volleyball and swimming. Fourteen girls went swimming, 5 participated in both activities, and 4 girls did neither. How many girls only played volleyball?
38. Let C = {1, 4, 5, 7, 9 10}, A = {1, 9, 17}, and T = {9, 10, 13}. What is the greatest value in

the set ( A ∪ T )∩ C?

PRACTICE

39. Which expression represents (^6)

2 6

x

( x )( x ) in simplest form?

A. x^2

B. x^9

C. 4 x^2

D. 4 x^9

40. Which property is illustrated by the equation ax + ay = a ( x + y )?

A. Associative B. Commutative C. Distributive D. Identity

41. The equations 5 x + 2 y = 48 and 3 x + 2 y = 32 represent the money collected from school concert ticket sales during two class periods. If x represents the cost for each adult ticket and y represents the cost for each student ticket, what is the cost for each adult ticket? A. $ B. $ C. $ D. $
42. Given: Set A = {(–2,–1), (–1,0), (1,8)} and Set B = {(–3,–4), (–2,–1), (–1,2), (1,8)}. What is ? A. {(1, 8)} B. {(–2,–1)} C. {(–2,–1), (1, 8)} D. {(–3,–4), (–2,–1), (–1, 2), (–1, 0), (1, 8)}

PRACTICE

45. Which expression is equivalent to x^6 x^2?

A. x^4 x^3

B. x^5 x^3

C. x^7 x^3

D. x^9 x^3

46. The Langiappe restaurant has used the following equation to calculate the number of sandwich trays needed for a very large party. Which equation is equivalent to 4(2 – 5x) = 6 – 3(1 – 3x). A. 8x = 5 B. 8x = 17 C. 29x = 5 D. 29x = 17
47. The total cost f(d) in dollars of renting a sailboat for d days is given by the function

f(d) =120 +60d. If the total cost was $360, for how many days, d, was the sailboat rented?

A. 2 B. 4 C. 6 D. 8

48. The cost to rent a construction crane is $750 per day plus $250 per hour of use. What is the maximum number of hours the crane can be used each day if the rental cost is not to exceed $2500 per day?

PRACTICE

49. Mike’s solution to an equation is shown below.

Which statement about Mike’s solution is true? A. Mike’s solution is correct. B. Mike made a mistake in Step 1. C. Mike made a mistake in Step 3. D. Mike made a mistake in Step 5.

50. What is the y- intercept of the graph of 4x + 2y = 12?