1. Unit 1: Integers and Absolute Value
Test Review

2. He stored 20 oranges in the fridge.
Blake bought 20 oranges from the farmer’s market. Which of the following actions would make his net change in the amount of oranges he owns 0? Select all that apply.
In this question, remember that he begins with 20 oranges. For each answer choice, you need to remember that he has those 20 oranges.
He stored 20 oranges in the fridge.
Start with the 20 Blake has, then he stored (+) 20 more, so = 40. This DOES NOT give us a net of 0.
B. He bought 20 oranges from the store.
Start with the 20 Blake has, then he bought (+) 20 more, so = 40. This DOES NOT give us a net of 0.

3. C. He drank juice made from 20 oranges.
Blake bought 20 oranges from the farmer’s market. Which of the following actions would make his net change in the amount of oranges he owns 0? Select all that apply.
In this question, remember that he begins with 20 oranges. For each answer choice, you need to remember that he has those 20 oranges.
C. He drank juice made from 20 oranges.
Start with the 20 Blake has, then he drank juice of (-) 20 more, so = 0. This DOES give us a net of 0.
D. He gave 20 oranges to his local food pantry.
Start with the 20 Blake has, then he gave away (-) 20 more, so = 0. This DOES give us a net of 0.

4. E. His family ate 10 oranges and then bought 10 more.
Blake bought 20 oranges from the farmer’s market. Which of the following actions would make his net change in the amount of oranges he owns 0? Select all that apply.
In this question, remember that he begins with 20 oranges. For each answer choice, you need to remember that he has those 20 oranges.
E. His family ate 10 oranges and then bought 10 more.
Start with the 20 Blake has, then his family ate (-) 10, then bought (+) 10 more, so 20 – = 20. This DOES NOT give us a net of 0.
F. His daughter gave 40 oranges to her friends at school.
Start with the 20 Blake has, then his daughter gave (-) 40 oranges, so = -20. This DOES NOT give us a net of 0.

5. 2. In Earnest’s yard, the grass grew 2 inches
2. In Earnest’s yard, the grass grew 2 inches. The next week, Earnest cut 2 inches off of the grass. The total change was 0 inches. Which of the following situations also has a total change of 0?
A. It rained 2 inches on Tuesday. Then it rained 2 inches on Wednesday.
2 inches of rain (+2), and 2 more inches of rain (+2) is 2 +2=4. This DOES NOT give us a total change of 0.
B. It snowed 4 inches last week. Then, 8 inches of snow melted during this week.
4 inches of snow (+4), then 8 inches of snow melted (-8) is 4 – 8 = -4. This DOES NOT give us a total change of 0.

6. 2. In Earnest’s yard, the grass grew 2 inches
2. In Earnest’s yard, the grass grew 2 inches. The next week, Earnest cut 2 inches off of the grass. The total change was 0 inches. Which of the following situations also has a total change of 0?
C. I put 5 pounds of birdseed in the feeder. Then, birds ate 5 pounds of birdseed.
5 pounds of birdseed in (+5), then birds ate 5 pounds (-5) is 5 – 5 = 0. This DOES give us a total change of 0.
D. A farmer sold 3 bushels of apples last week. Then she sold 6 bushels of apples this week.
3 bushels of apples sold (-3) and another 6 bushels sold (-6) is -3 – 6 = -9. This DOES NOT give us a total change of 0.

7. 2. In Earnest’s yard, the grass grew 2 inches
2. In Earnest’s yard, the grass grew 2 inches. The next week, Earnest cut 2 inches off of the grass. The total change was 0 inches. Which of the following situations also has a total change of 0?
E. 3 feet of growth was cut from a tree branch last year. Then the tree branch grew 3 feet this year.
3 feet cut (-3), then grew 3 feet (+3) is = 0. This DOES give us a total change of 0.
F. My family painted a 300 square foot barn on Saturday. Then on Sunday, we painted a 300 square foot garage.
300 square foot barn painted (+300) and 300 square foot garage painted (+300) is = This DOES NOT give us a total change of 0.

8. 3. A number line is shown below.
Using the terms additive inverse and absolute value,
explain the relationship between A and B.
A and B are additive inverses because when you add them together, they equal 0. We also refer to additive inverses as “zero pairs” = 0
A and B have the same absolute value of 2 because they are the same distance from zero on the number line. Absolute value is always positive because it tells the distance of a number from 0 on the number line. A B -2 2

9. B. David earned $20 for doing his chores and spent $5 for lunch.
4. Which of the following situations could be represented by the expression ?
A. Sue borrowed $20 from her mom and earned $5 for mowing the neighbor’s lawn.
Sue borrowed $20 (negative value) and earned $5 (positive value), so this CAN be represented by
B. David earned $20 for doing his chores and spent $5 for lunch.
David earned $20 (positive value) and spent $5 (positive value), which is 20 – 5. Therefore, this CAN NOT be represented by

10. 4. Which of the following situations could be represented by the expression -20 + 5?
C. Juan gave 20 M&M’s to his friend Julie and 5 more to his other friend Kyle.
Juan gave 20 M&M’s (negative value) and gave 5 more (negative value), which is -20 – 5. Therefore, this CAN NOT be represented by
D. In the morning, Olivia noticed the temperature had dropped 20° overnight. After an hour, the temperature increased by 5 °.
Temperature dropped 20° (negative value) and then increased 5° (positive value), so this CAN be represented by

11. E. A football team lost 20 yards. Then they gained 5 yards.
4. Which of the following situations could be represented by the expression ?
E. A football team lost 20 yards. Then they gained 5 yards.
Football team lost 20 yards (negative value) and gained 5 yards (positive value), so this CAN be represented by
F. A scuba diver dove 20 feet below sea level. Then swam up 5 feet.
Scuba diver dove 20 feet below sea level (negative value) swam up 5 feet (positive value), so this CAN be represented by

12. 5. When x is a nonzero integer, the sum of 3 + x is sometimes negative and sometimes positive.
A. Identify a value of x for which the sum of 3 + x is negative. Explain.
Think about how many negatives I would need to add in order to make a negative value + + +
= -1
I would need -4 in order to make a negative value, so x can be -4. - - - -
*In order to get the maximum credit for this question, you need to give 2 examples.
Any value that is less than -4 (more negatives) would also work. Examples: -5, -6, -7…

13. 5. When x is a nonzero integer, the sum of 3 + x is sometimes negative and sometimes positive.
B. Identify a value of x for which the sum of 3 + x is positive. Explain.
Can x be a negative value? + + +
= 1
If I add -2, I will still have a positive value, so x can be -2. - -
X can also be any value that is greater than -2 (fewer negatives and all positive numbers) would also work. Examples: -1, 1, 2, 3…
*In order to get the maximum credit for this question, you need to give 2 examples.

14. A. The temperature reached 15°F, then dropped overnight 25°F .
6. The temperature on a cold winter day in Chicago was -10°F. Which of the following situations could explain how the temperature became -10°F ?
A. The temperature reached 15°F, then dropped overnight 25°F .
Started at +15°F, then dropped (negative value) 25°F, so 15°F – 25°F = -10°F. This COULD explain how it became -10°F.
B. The temperature was 12°F, then increased by 22°F.
Started at 12°F, then increased (positive value) by 22°F, so 12°F + 22°F = 32°F. This COULD NOT explain how it became -10°F.

15. C. The temperature was 3°F, then dropped by 13°F.
The temperature on a cold winter day in Chicago was -10°F. Which of the following situations could explain how the temperature became -10°F ?
C. The temperature was 3°F, then dropped by 13°F.
Started at +3°F, then dropped (negative value) 13°F, so 3°F – 13°F = -10°F. This COULD explain how it became -10°F.
D. The low temperature for the day was -15°F, then increased by 5°F.
Started at -15°F, then increased (positive value) by 5°F, so -15°F + 5°F = -10°F. This COULD explain how it became -10°F.

16. F. The temperature was 9°F, then dropped by 19°F.
6. The temperature on a cold winter day in Chicago was -10°F. Which of the following situations could explain how the temperature became -10°F ?
E. The high temperature for the day was 10°F, then it decreased by 10°F.
Started at 10°F, then decreased (negative value) by 10°F, so 10°F - 10°F = 0°F. This COULD NOT explain how it became -10°F.
F. The temperature was 9°F, then dropped by 19°F.
Started at +9°F, then dropped (negative value) 19°F, so 9°F – 19°F = -10°F. This COULD explain how it became -10°F.

17. 7. Which of the following expressions is equal to -32
7. Which of the following expressions is equal to ? Select all that apply.
-20 –(-63) – 11
B –(-11)
Use and N/P chart to organize N P
Opposite of is + 63
-20
+63
So, = 32
Incorrect answer
-11 N P
Opposite of is + 11
-63
+20
So, = -32
Correct answer
+11

18. 7. Which of the following expressions is equal to -32
7. Which of the following expressions is equal to ? Select all that apply.
11 –63 – (-20) B
Use and N/P chart to organize N P
Opposite of is + 20
-63
+11
So, = -32
Correct answer
+20 N P
-20
+11
So, = -72
Incorrect answer
-63

19. 7. Which of the following expressions is equal to -32
7. Which of the following expressions is equal to ? Select all that apply.
63 –20 – 11 B
Use and N/P chart to organize N P
-20
+63
So, = 32
Incorrect answer
-11 N P
-63
+11
So, = -32
Correct answer
+20

20. 8. The temperature at noon on a cold winter day in Alaska was -18°F
8. The temperature at noon on a cold winter day in Alaska was -18°F. By evening, the temperature had dropped by 4°F. Jack thinks that the temperature for the evening could be found by subtracting 4 from 18. Sam thinks that -4 should be added to -18 Their methods are shown in the expressions below.
Jack: -18 – 4
Sam: (- 4 )
Are these two expressions equivalent? Explain.
These two expressions ARE equivalent because in both expressions, both integers are negative. In other words, you start with a negative value, then get more negative. You can see it as subtracting a positive or adding a negative.