Test 2 - Kims Class
What will come next in the following sequence: ooxooxxooxxxoo ...
D. xxxx In the presented pattern, we see two circles followed by one diamond. Then, there are two circles followed by two diamonds. Next, we see two circles, three diamonds, and then two circles again. We take note that every time circles appear they only appear in pairs. Therefore, we know the next set should not be a circle right away. If we look at the diamonds, we see that at first, we had one diamond, then two, and finally three. They are increasing by 1 each time they appear. Therefore, we should expect to see four diamonds.
Trip 1 lasted 30 minutes, with a speed of 15mph Trip 2 lasted 75 minutes, with a speed of 40mph Trip 3 lasted 180 minutes, with a speed of 65mph
First, convert each time given to hours. Then, calculate the distance traveled for each trip by creating proportions: Trip 1: 30 min = 1/2, or 0.5 hour; , x = 7.5 miles Trip 2: 75 min = 5/4, or 1.25 hour; , y = 50 miles Trip 3: 180 min = 3 hours; , z = 195 miles Now, add all distances traveled for each trip: 7.5 + 50 + 195 = 252.5 miles
Henry works in a bank approving loans. Four bank customers have applied for a loan today, and Henry has just researched their credit scores: Customer Credit Score Mr. Allen 540 Mr. Weaver 710 Mrs. Butler 365 Ms. Kash 775 Henry has his choice of offering an interest rate of 0.75% or 2.50% on loans. Using only their credit scores as guidance, which two customers should receive the 0.75% loan?
Mr. Weaver and Ms. Kash Lower interest rates are generally given to individuals with higher credit scores. Mr. Weaver and Ms. Kash had the two highest scores, so they should receive the lower rate.
Mrs. Paul is a fifth grade math teacher. While reviewing a student's work, she finds this mistake:Using this mistake as a guideline for reteaching, on which skill should Mrs. Paul focus with this particular student?
Placing the decimal appropriately in the product. After multiplying decimals, count the number of decimal places represented in the factors. The product should have the same number of decimals; in this problem, the product should read 52.316.
The following four peoples are waiting in line at the post office: Marcie made a graph showing the relationship between the age and the height of the four people. Which point on the graph represent the teen girl?
Point B This graph shows a function between age and height. As the graph extends upward, the age gets higher; as the graph extends toward the right, the height gets taller. For example, the infant is represented by point A, since he is the shortest and youngest. The teen girl is represented by point B; the teen boy by point C; and the older woman by point D.
Which number property is demonstrated in the equation below? 15(4 + 3) = 15 × 4 + 15 × 3
The distributive property of multiplication over addition This question asks you to identify a basic algebraic property. This distributive property of multiplication over addition states that each time within the parentheses is multiplied by the number outside the parentheses. The products are then added together. A(B +C) = AB + AC.
Algebraic thinking includes several characteristics. Which of the following statements is not a part of algebraic thinking?
Using manipulatives to reason about situations Manipulatives are a tool that can be used to support reasoning (this is Mathematical Practice #5), but it is not one of the three big ideas in algebraic thinking (the other choices name these three areas).
Students are shown this Input-Output table: Rule -- Add 5 Input Output 10 -- 15 30 -- 35 50 -- 55 This function is written as:
X + 5 = Y A function shows a pattern. If x is the input and y is the output, this function follows the rule: add 5 to x in order to get y (x + 5 = y).
An input-output table shown: A-3 B-1 A-6 B-2 A-9 B-3
a. A= B x 3 b. B= A/3 c. A=B x 2 + B D. ALL OF THEM To check, substitute all values in the table for the equations given. For example, 6 = 2 × 3.
What is the correct expansion of (a+b)3 ?
a^3 + 3a^2b +3ab^2 + b^3 Using the F.O.I.L. method, we know that there should be more than two terms in the resulting expansion. Therefore, we may eliminate selections "a3 + b3" and "3a2 + 3b". After expansion, we realize that "a3 + 3a2b + 3ab2 + b3" is correct.
Functions:
describe a relationship between two variables and may be linear or not. Functions describe a relationship between two variables; for example, you might say the cost of grapes is a function of the weight of the grapes. Functions, like the grape example, can be linear, but other functions are not. For example, the volume of a cube is a function of the length of its sides.
Mathematical models are useful in both real life and mathematics because:
models such as equations, graphs, and tables can be used to analyze empirical situations, to understand them better, and to make predictions. All the choices here might be considered advantages of using models, but the reason we need mathematical models is that they allow us to generalize and analyze situations in ways that provide more insights into the situation.
Use this table of coordinate points to answer the question that follows. x -4 ------- y -2 x -2 ------- y -1 x 2 ------- y 1 Which equation represents the values seen in the chart?
y= 1/2x Try each answer choice by substituting in the values for x and y seen in the chart. Conversely, you can see that each y-value is half of its corresponding x-value, which indicates the x-value is multiplied by ½.
A function is shown on the graph below. x-0 y-6 x-1 y-7 x-2 y-8
y=x+6 As shown in the table, in order to find the y-value, simply add 6 to the x-value. Therefore, the equation of the line is y = x + 6.
Use this scenario to answer the follow question: "Emily's softball team is celebrating the end of a winning season at a pizza restaurant. The restaurant charges $8.25 per pizza, and each topping costs $1.75." Emily's team decides to order 7 pizzas and a total of 15 toppings. How much will the team need to pay?
$84 The expression that shows how much money the team will need to pay for their party is 8.25p + 1.75t, where p=the number of pizzas Emily's team orders and t=the number of toppings Emily's team orders. Therefore, (8.25 × 7) + (1.75 × 15) = 84.
What is the value for x in the equation 3x - 5 = 7x + 7?
-3 To solve for x, first combine like terms: subtract 7 from each side of the equation and subtract 3x from each side of the equation. 3x - 5 = 7x + 7 now becomes -12 = 4x. Divide each side of the equation to isolate the x. -3 = x
Use this scenario to answer the following question: "Janice is using a recipe that calls for 3 cups of flour and 1.5 teaspoons of baking soda for every 1 batch of cookies." Janice would like to use 6 cups of flour for her next batch of cookies. What proportion will correctly solve for x, the number of teaspoons of baking soda she needs? (Choose two answers)
1.5/x = 3/6 1.5/3 = x/6 # of teaspoons of baking soda / # of cups of flours = How many teaspoons of baking soda / new # of cups of flour or # of teaspoons of baking soda / How many teaspoons of baking soda = # of cups of flours = / new # of cups of flour
Simplify the following: 2y + 9 + 8y + 7
10y + 16 To simplify this expression, combine like terms: 2y + 8y and 9 + 7.
A garden store buys clay pots from a distributor for $15 each and then sells them for $40 each in the store. What is the profit of each pot as a percentage of the cost price paid to the distributor?
166.7% Profit = selling price - cost price = $25 $25 is what percent of $15? $25 = x%($15). x=166.67%
Stacy went to the store to purchase a loaf of bread. She originally thought she had only $9.55 in nickels in her purse. She then discovered she had 10 extra nickels in her pocket. How many nickels did she originally have in her purse?
191 This problem provides unnecessary information to solve the problem. The fact that Stacy discovers 10 extra nickels in her pocket is inconsequential to the solution of the problem. Since a nickel is $0.05 and she had $9.55 in nickels in her purse, divide $9.55 by $0.05 to obtain the number of nickels she had in her purse.
Students in Mr. Lewis's class took a survey to determine what their favorite school subjects were. The students showed their preferences by writhing their initial in a portion of the Venn diagram below: "According to the diagram, what is the total number of students who like both math and science?"
2 The students who like both math and science are P and T. They are students in both the math circle and the science circle.
If a can weights 14 oz., how many cans would you need to have a ton? (Round your answer to the nearest ones place and pick the best answer.)
2,286 An easy way to solve this problem is to use basic algebra. Knowing that there are 16 oz. in a pound and that there are 2,000 lbs. in a ton helps ease the difficulty of the problem. We want to find out the number of cans x it will take to obtain a ton. Therefore, we have 14/16 X = 2000 . If both sides of the equation are multiplied by 16 and then we divide both sides by 14, we will obtain the approximate number of cans it will take to obtain one ton. X= 16 x 2000/14 = 32000/14 = 2285.9. We see that many of the answers are close to this value. When we round this number, we will obtain 2,286.
Erica is working on her math homework. She has completed 12 problems, which represent 60% of her homework. How many total problems are on Erica's homework?
20 12 problems = 60% of x number of problems, so 12 = 0.6x. x=20.
There are 16 more apples than orange in a basket of 62 apples and oranges. How many oranges are in a basket?
23 This problem is easily solved by using some basic algebraic reasoning. Since we are interested in determining the number of oranges that are in the basket, we will set this as a variable called b. The number of apples, a, and the number of oranges, b, sum to a total of 62. We also know that there are 16 more apples than oranges (a = b + 16). This gives b + (b + 16) = 2b + 16 = 62. Solving for b yields 23 oranges in the basket.
Students are designing a class quilt using squares of fabric. Each day new squares are added to the design. The diagram below shows how the students are arranging the squares of fabric: Picture Monday - 2 squares Tuesday - 4 Squares Wednesday - 8 Squares If the pattern continues, what is the number of fabric squares needed for Friday's quilt?
32 This problem shows a growing pattern. The first day, Monday, two squares were used. On Tuesday, four squares were used, and Wednesday, eight squares were used. The pattern is to double each day's number of squares for the next day. On Thursday, 16 squares would be used, and Friday, 32 squares would be used.
Mrs. Cameron plans to buy carpeting for her living room floor. The room is a rectangle measuring 14 feet by 20 feet. She wants no carpet seams on her floor even if that means that some carpeting will go to waste. The carpeting she wants comes in 16-foot-wide rolls. What is the minimum amount of carpeting that will have to be wasted if Mrs. Cameron insists upon her no-seams requirement?
40ft^2 Since Mrs. Cameron does not want any seams in her carpet, the carpet must be 20 ft long (at least) to cover the entire space. Since the room is only 14 ft wide and the carpet is 16 ft wide, there will be 2 ft of wasted carpet for the entire length of the room (20 ft). Therefore, the amount of carpet that is wasted is 20 × 2 = 40 ft2 of carpet.
Crystal needs to buy bread for her party. She knows that one loaf will feed 8 people, and there are 371 people coming to her party. How many loaves of bread does she need to buy?
47 In this problem, we know there will be 371 people at the party and one loaf of bread will feed 8 people. Dividing 371 by 8 gives 46.375 which is not listed as an option. If she were to purchase 46 loaves of bread she would not have enough bread for everyone. Therefore, she must purchase at least 47 loaves to feed everyone.
Ms. Watson is preparing a recipe that requires 2¾ cups of whole-kernel corn. The nutrition label from the can of corn she will use is shown below.Ms. Watson wants to find the total number of calories contained in the recipe. What is the total number of calories in 2¾ cups of whole-kernel corn?
495 calories This question asks you to use mathematics skills in everyday living. Since there are 4 half cups in 2 cups (4 × 1/2 = 2), multiply 90 times 4 to get 360 calories. To find the number of calories in ¾ cup (¾ = ½ + ¼), add 90 (the calories in ½ cup) to 45 (the calories in ¼ cup) to get 135 calories. Adding 360 to 135 results in 495, the number of calories in 2¾ cups.
In a two-week period (including weekends and holidays), Max spent $71. 47 on lunch. About how much money did Max spend on this daily lunch?
5.00 There are many ways to approach this problem. One way is to realize that there are 14 days in a two-week period. Then, take the amount of money Max spent on lunch ($71.47) and divide this by 14. However, this may result in a messy solution when all we need is an approximation. Instead, try to find a number that, when multiplied by 14, gets you pretty close to the total Max spent. In this case, if $5 is selected, this will approximate an expense of $70 over the two-week period.
Mr. Winter's fifth grade class is conducting a survey at their elementary school about favorite meals served in the cafeteria. When they finish collecting their data, Mr. Winter's class discovers the following facts. 10% of respondents like beef tacos best. 25% of respondents like chicken sandwiches best. 30% of respondents like enchiladas best. 35% of respondents like pizza best. If 18 respondents like enchiladas best, how many people did Mr. Winter's class interview in all?
60
Joe can place a maximum of 5 apples in a sack. If he needs to put 32 apples in sacks, how many sacks will he need?
7 To find out how many sacks are required, we can divide the amount of apples that Joe has by the number that fit in a sack. The result of the division is 6.4. So, it could be assumed that "5" and "8" are not correct from this. However, "6.4" is also incorrect because it is not physically possible to obtain 0.4 of a bag. Therefore, one should round up to 7.
Use this scenario to answer the following question: "Janice is using a recipe that calls for 3 cups of flour and 1.5 teaspoons of baking soda for every 1 batch of cookies." Janice is baking a new batch of cookies and is planning to use 4 teaspoons of baking soda. How many cups of flour will she need to use?
8 Set up a proportional relationship with information found in the scenario: # of teaspoons of baking soda / # of cups of flours = new # of teaspoons of baking soda / How many cups of flour? 1.5/3 =4/X Use cross products to solve: 1.5x = 3(4). x = 8
Use this scenario to answer the follow question: "Emily's softball team is celebrating the end of a winning season at a pizza restaurant. The restaurant charges $8.25 per pizza, and each topping costs $1.75." If p = the number of pizzas Emily's team orders and t = the number of toppings Emily's team orders, write an expression that shows how much money the team will need to pay for their party.
8.25p + 1.75t To find the total amount to pay, multiply both the number of pizzas ordered by the price of one pizza and the number of toppings ordered by the price of one topping. Add these two calculations together to find the total amount.
Mr. Menendez has displayed the following coordinate plane in his sixth grade classroom: Which of the following describe the transformations needed in order to move from Triangle JKL to Triangle J'K'L'?
A translation 1 unit up, followed by a translation 8 units to the left. There is only a series of translations; no reflections.
If a/b = c/d, which of the following statements is true?
A. ad=bc B. a/c = b/d C. (a+b)/b = (c+d)/d D. ALL OF THEM Substitute numbers to solve each answer choice, for example, a = 2, b = 3, c = 4, and d = 6, so, 2/3 = 4/6. Check each answer choice with these values to confirm that each is true.
Which is the following is a linear equation?
ALL OF THEM A. y = x/4-11 B. y=2x C. y= 4.5 D. ALL OF THEM A linear equation is an equation that gives a straight line when it is plotted on a coordinate plane. All of these equations are straight lines; therefore, all are linear equations.
The school bus drives at a constant rate of 35 miles per hour. Based on this rate, which of the following distances are correctly attributed to their time?
All of them C. 1 hour, 15 minutes = 43.75 miles B. 45 minutes = 26.25 miles B & C A. 15 minutes = 7.75 miles B & C Use the 35 miles to 1 hour ratio ( 35 miles/ 1 hours) to create proportions to calculate the distances traveled. In Choice A, 15 minutes is equal to 0.25 of an hour, so the proportion would be: 35 miles/ 1 hour = x miles/ 0.25 hour. Use cross products to solve for x: 35 × 0.25 = 1x; 8.75 = x. Therefore, Choice A is not correct. Use cross products to check choice B and C and confirm they are correct.
Last week, a grocery store sold eggs for $4.25 per dozen. This week, the same store is running a sale on eggs, now charging $5.00 for 2 dozen. David buys 5 dozen eggs this week. What is a reasonable amount David paid for the eggs?
Between $10 and $15 We can break 5 dozen down into 2 dozen + 2 dozen + 1 dozen, and since we know that 2 dozen equals $5.00, we can quickly see that the total price will be just over $5 + $5, or $10.
