Download U1L3 - practice (Highly Advanced)

Integers and Absolute Value – Highly Advanced Problems
The absolute value of an integer is its distance from zero on a number line. You can use that
fact to solve absolute value equations.
Example 1
Solve |n| = 2.
Solution
Both -2 and 2 are at a distance of 2 units
2 units 2 units
from 0 on the number line.
Therefore, n = -2 or n = 2.
-4 -3 -2 -1 0 1 2 3 4
Example 2
Solve |n – 2| = 3
3 units
3 units
Solution
Both -1 and 5 are at a distance of 3 units
from 2 on the number line. Therefore, n
= -1 or n = 5.
-3 -2 -1 0 1 2 3 4 5
Solve by naming the possible values of n. Use the number line.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
0
1 2 3 4 5
6 7 8 9 10
1. |n| = 4
n = ______ or ______
2. |n| = 1
n = ______ or ______
3. |n| = 8
n = ______ or ______
4. |n - 3| = 1
n = ______ or ______
5. |n - 2| = 5
n = ______ or ______
6. |n – (-4)| = 6
n = ______ or ______
7. |5 - n| = 1
n = ______ or ______
8. |2 - n| = 3
n = ______ or ______
9. | - 6 - n| = 2
n = ______ or ______
10. |n| = 0
n = ______
11. |n - 5| = 0
n = ______
12. |-3 – n| = 0
n = ______
13. |-n| = 10
n = ______ or ______
14. |n – (-6)| = 3
n = ______ or ______
15. |n - 7| = 3
n = ______ or ______
16. |-4 - n| = 2
n = ______ or ______
17. |n - 2| = 4
n = ______ or ______
18. |1 - n| = 0
n = ______ or ______
19. How do you know that the equation |n| = -3 has no solution?
20. Temperature Change. It's cold here in Pennsylvania!
At 9:00 p.m. the temperature was -3°C. Between 9:00 p.m. and midnight the
temperature dropped 6°. Between midnight and 10:00 a.m. the temperature rose 8°.
By noon the temperature had dropped another 4 degrees. What was the temperature at
noon? Here is the hard part: Give the noon temperature in degrees Fahrenheit, not
degrees Celsius.
21. Shading Squares. All the outside squares of a 3 x 3 square array are shaded. One square
is not shaded. If all the outside squares of an m x m square array were shaded, express
the number of shaded squares in terms of m.
22. Arranging Operations. Each of the three operation signs (+, -, and x) is used exactly once
in one of the blanks in the expression 5__4__6__3. How many different values result
from such arrangements? What are they?
23. Toothpick Squares. Toothpicks are used to build a rectangular grid that is twenty
toothpicks long, ten toothpicks wide, and filled with squares one toothpick on a side.
What is the total number of toothpicks used? If a represents the number of toothpicks in
the length and b represents the number of toothpicks in the width, write an expression
representing the total number of toothpicks in the figure.
Integers and Absolute Value - Black Solutions
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
20.
-4, 4
2. -1, 1
-8, 8
4. 2, 4
-3, 7
6. -10, 2
4, 6
8. -1, 5
-4, -8
10. 0
5
12. -3
-10, 10
14. -9, -3
4, 10
16. -6, -2
-2, 6
18. 1
Distance cannot be negative.
The temperature at noon was 23 degrees Fahrenheit.
At 9 pm it was -3 degrees Celsius.
It got 6 degrees Celsius colder by midnight.
It is now -9 degrees Celsius.
It got 8 degrees Celsius warmer by 10 am.
It is now -1 degrees Celsius
It got 4 degrees Celsius colder by noon
It is now -5 degrees Celsius
-3
-3 -6 = -9
-9
-9 + 8 = -1
-1
-1 -4 = -5
Using the formula C x (9/5) + 32 = F
C = degrees Celsius
F = degrees Fahrenheit
C x (9/5) + 32 = F
-5 x 1.8 + 32 = F
-9 + 32 = F
23 = F
So at noon it would be 23 degrees Fahrenheit
21. Shading Squares. m²- (m – 2)² or 4m – 4. You can make a table and look for pattern. Or
consider that there are m shaded squares on each of the four edges of the figure. Since
the four corner squares are counted twice, they must be subtracted from the total,
leaving 4m – 4.
22. Arranging Operations. There are six ways to arrange the operation signs. The numbers
resulting are -9, 26, 19, -16, 23, and 17. Make sure you use the correct order of
operations.
23. Toothpicks Squares. 430. There will be 20 x 11 = 220 toothpicks in rows and 10 x 21 =
210 toothpicks in columns, for a total of 220 + 210 = 430 toothpicks. In general, there
will be a(b + 1) toothpicks in rows and b(a + 1) toothpicks columns, for a total of a(b + 1)
+ b(a + 1) = 2ab + a + b toothpicks.