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# 1.2: Practice Questions

Difficulty Level: At Grade Created by: CK-12

Directions: For this section, solve each problem and decide which is the best of the choices given. You may use any available space for scratchwork.

1. (Numbers and Operations) — A racecar driver has completed laps of a race. What fractional part of the race remains?

ANSWER EXPLANATIONS — The driver has or laps to go out of the . Therefore, is the fractional part of the race remaining. This is equivalent to , which is answer C.

1. This is the fraction of the race that the driver has completed.
2. This comes from mistakenly dividing by , the latter number coming from adding both lap amounts. The race is only .
3. Correct
4. This comes from taking the fraction in response B and subtracting it from 1.
5. This comes from , but that’s how many laps are left - the driver is only in one race, not !
2. (Numbers and Operations) — If is the set of positive multiples of less than and is the set of positive multiples of less than , how many members are there in ?

ANSWER EXPLANATIONS — The only elements in both sets are multiples of or . The multiples of less than are and . These are the elements that are in the intersection of both sets. Thus, B is the correct response.

1. There are elements that are in both sets.
2. Correct
3. There are elements in both sets, not .
4. This is the number that the elements are multiples of.
5. This is the number of multiples of less than
6. .
3. (Algebra and Functions) — If , then

ANSWER EXPLANATIONS — Both fractions each , so adding twice gives an answer of . This is choice E.

1. Both fractions are not equal to , so we do not have like terms.
2. The other parts of the fractions are not eliminated, so this is not possible.
3. Each fraction equals , so this result is not possible.
4. Each fraction equals , so adding twice gives .
5. Correct
4. (Algebra and Functions) — If , what is the value of ? ANSWER EXPLANATION The value is , so .
5. (Algebra and Functions) — If Dave drove one-third of the distance of his trip on the first day, and on the second day, he figured out that he still had of the trip to drive. What was the total length, in miles, of his trip?

ANSWER EXPLANATIONS — We can model this situation by the equation . Solving for , we get , which is answer A.

1. Correct
2. This is the number of miles he drove before he figured out how much of his trip was left.
3. This amount is how much he drove the first day.
4. This is how much he drove the second day.
5. This amount is half of the distance he covered by the end of the second day.
6. (Geometry) — What is for the graph of below?

ANSWER EXPLANATIONS — Asking for the value of is just a way of saying “what does equal when ?” So you look for when . On the graph, we have the point . Note that exact numbers are not provided in the graph, but standard practice indicates that each tick mark is one unit. So we moved tick marks to the right, and then the line crosses through a point on the axis between and . Therefore, is equal to . Choice B is the only possible choice.

7. (Geometry) — Find the perimeter of lsosceles triangle if and . Round to the nearest hundredth.

ANSWER EXPLANATIONS — Correct answer: D — The first step is to find one of the other sides of the triangle. The easiest is . Since we have the side adjacent (next to) the angle we know, we can use cosine. Cosine of an angle (adjacent) (hypotenuse) The setup is Multiplying to the left gives Dividing by gives Using a calculator gives us Since , we know that . Also, since , we know that Therefore, the sum of all three sides is .

8. (Geometry) — Which segment is congruent to ?

ANSWER EXPLANATION Correct answer: D Congruent segments (or shapes of any kind) are exactly equal in length. The only segment in the diagram that we know is the same as BE is CE. Incorrect answers: A, E: Incorrectly assuming diagonals of a parallelogram are all equal B, C: Incorrectly assuming that the sides of the parallelogram are the same as BE just because they look like they are - never assume two segments are congruent just because they look like it. D: Correct answer

9. (Probability and Statistics) According to the graph, the greatest change in the profit of the Sports Shack occurred between which two consecutive months?
1. January and February
2. February and March
3. March and April
4. April and May
5. May and June

ANSWER EXPLANATION — The profit in January was . The profit in February was . This represents a change in profit of , which is the greatest that the graph shows.

10. (Probability and Statistics) — An automobile company made automobiles in the proportions shown in the table below. How many of the automobiles produced were either SUVs or vans?

ANSWER EXPLANATION — SUVs and vans, together, made up of the total production.

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