Unit 3 Lesson 19 Practice Problems IM® Algebra 2TM authored by Illustrative Mathematics®

This product is based on the IM K-12 MathTM authored by Illustrative Mathematics® and offered under a CC BY 4.0 License.

Unit Title: Complex Numbers and Rational Exponents
Title: Real and Non-Real Solutions

Common Core Standards in This Lesson:
CCSS.HSA-REI.B.4.b
CCSS.HSA-REI.B.4.b: Solve quadratic equations by inspection (e.g., for 𝘹² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as 𝘢 ± 𝘣𝘪 for real numbers 𝘢 and 𝘣.
CCSS.HSN-CN.C.7
CCSS.HSN-CN.C.7: Solve quadratic equations with real coefficients that have complex solutions.
CCSS.MP7
CCSS.MP7: Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression 𝑥² + 9𝑥 + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(𝑥 – 𝑦)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers 𝑥 and 𝑦.

[SeanMarshallSM]

I just want to say that I am so grateful for you taking the time to make all of these videos for the IM math curriculum. I tutor Algebra 1, Geometry, and Algebra 2 at my school, and the IM math curriculum was recently implemented, so it is new to me a bit 😅. Some of the problems were a bit of a challenge since the previous curriculum didnt focus a lot on contextual applications. You made them so much simpler, and I really appreciate it! Thank you!