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Coordinate Algebra with Support Midterm Review Unit 1

Unit 1: Relationships Among Quantities Key Ideas  Unit Conversions  Vocabulary  Linear Models  Exponential Models  Consecutive Integers  Averages  Rectangle Problems  2 Variable Equations  Solve for a Varialbe  Solve Exponentials  Solve for y and Graph

Example 1: Convert 5 miles to feet.

Tip There are situations when the units in an answer tell us if the answer is wrong. For example, if the question called for weight and the answer is given in cubic feet, we know the answer cannot be correct.

Vocabulary # of terms Coefficients Factors Constant

Example 2: 4 x 2 +7 xy – 3 # of terms - Coefficients - Factors - Constant - 3 4, 7 4&x 2, 7&x&y -3

Writing Linear & Exponential Equations If the numbers are going up or down by a constant amount, the equation is a linear equation and should be written in the form y = mx + b. If the numbers are going up or down by a common multiplier (doubling, tripling, etc.), the equation is an exponential equation and should be written in the form y = a(b) x.

Example 3: April is moving apartments. Her family needs to rent an U-Haul truck and found out they charge $19.99 for the truck and $0.20 per mile. Write an equation to represent the cost. How much will it cost if the family drives 40 miles?

Example 4: The number of mosquitos triples every day, with 10 mosquitos to start. Write an equation to represent the situation. How many mosquitos will there be after 15 days?

Example 5: Find 2 consecutive integers whose sum is 225.

Example 6: Peyton wants to get an A in her Biology class this semester. Her first 4 tests were a 94, 83, 88, and 91. What does she need to make on her 5 th test to get a 90% average?

Example 7: Bill is building a sand box for his son to play in. The length is 2 feet more than the width. He has 20 feet of boards. What are the dimensions of his sand box?

Example 8: 2-Variable Equations Kyle is celebrating his birthday and his mom gave him $50 to take his friends out to celebrate. He decided he was going to buy appetizers and desserts for everyone. It cost 5 dollars per dessert and 10 dollars per appetizer. Kyle is wondering what kind of combinations he can buy for his friends. a) Write an equation using 2 variables to represent Kyle’s purchasing decision. (Let a = number of appetizers and d = number of desserts.) b) Use your equation to figure out how many desserts Kyle can get if he buys 4 appetizers. c) How many appetizers can Kyle buy if he buys 6 desserts?

Example 9: Solve for h.

Solving Exponential Equations If the bases are the same, you can just set the exponents equal to each other and solve the resulting linear equation. If the bases are not the same, you must make them the same by changing one or both of the bases. – Distribute the exponent to the given exponent. – Then, set the exponents equal to each other and solve.

Example 10: Solve the exponential equation a) b)

Example 11: Solve for y and graph

CW/HW Unit 1 Review Sheet