Download Unit 3 Items to Support Formative Assessment

Algebra II Items to Support Formative Assessment
Unit 3: Expanding Understanding of Quadratic Functions
Perform arithmetic operations with complex numbers
N.CN.A.1 Know there is a complex number i such that i2=-1, and every complex number has the
form a + bi with a and b real.
N.CN.A.1 Item 1
Part A
Which one of the following is in the simplest form of
-48 ?
a. -4i 3
b. 4 -3
c. -4 3
d. 4i 3
Part B
Categorize the following numbers. Some numbers may belong to more than one category.
-3i
2+4i
5
-9
-20
7i+3
i²
7i4
-11+5i
-1- i
Answers:
Part A: d
Part B:
Real: 5, -20, i² , 7i4
Complex: -3i, 2+4i, 5,
Imaginary: -3i,
-9 , -11+5i, -20, 7i+3, i², 7i4, -1-i
-9 , i², 7i4
N.CN.A.1 Item 2
Which of the following expressions are equivalent to i19?
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under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
-i, - i 3 , i 7 , i27 , - i19 , - i 21
Answers:
-i,
i 7 , i27 ,
- i21
N.CN.A.1 Item 3
For the expression i n-3 , for what values of n will the expression to be equivalent to:
a. -1
b.
-1
c. - -1
d. 1
Answers: Solutions include:
a. 5, 9, 13, 17, etc
b. 4, 8, 12, 16, etc
c. 6, 10, 14, 18, etc
d. 7, 11, 15, 19, etc
N.CN.A.1 Item 4
Consider the following expressions
i8 - i2
i 7 - i5
i6 - i
4i 4 - 2i 3
6i 4 - 2i2
a. Which of these expressions can be expressed as in the form a + 0i?
b. Which of these expressions can be expressed as an imaginary number 0 + bi?
Answers:
a. i8 - i2 = 2 , 6i 4 - 2i2 = 8
b. i 7 - i5 = -2i
Perform arithmetic operations with complex numbers
N.CN.A.2 Use the relation i2=-1 and the commutative, associative, and distributive properties to
add, subtract, and multiply complex numbers.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
N.CN.A.2 Item 1
For which of the following operations will the complex numbers (4 – 3i) and (1 + 2i) produce a
real solution? Find the solution.
Addition
Subtraction
Multiplication
Answer:
None of these operations will produce a real solution.
Addition
5–i
Subtraction 3 – 5i and -3 + i
Multiplication 10 + 5i
N.CN.A.2 Item 2
Complete the chart with the product of the complex numbers. Then label whether the product is
real or complex.
9i + 3
3i
-5
9i + 3
3i
-5
6i
-54 + 18i; complex
-18; real
-30i; complex
9i - 3
-90; real
-27 - 9i; complex
15 - 45i; complex
7
21 + 63i; complex
21i; complex
-35; real
6i
9i - 3
7
Answer:
N.CN.A.2 Item 3
Let x = 4-3i, y = 4+3i and z = -3. Evaluate the following.
a. x+y
b. y²
c. (x+y)(x-y)
d. xyz
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
Answers:
a. 8
b. 7+24i
c. -48i
d. -75
N.CN.A.2 Item 4
Which of the following expressions are equivalent to (4 - 2i)(4 + 2i)?
16 – 4i
16 + 4i2
4(4 + 2i) – 4i(2 + i)
20
20 + 8i
4(2 + i)(2 – i)
16(2 – i)(2 + i)
Answers:
4(4 + 2i) – 4i(2 + i)
20
4(2 + i)(2 – i)
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.