Download Week 1 - Student Classroom Worksheet

Week 1
Lesson 1.1 Linear Equations
A linear equation in one variable is an equation that can be written in the form ax + b = 0 where
a and b are real numbers and a ≠ 0.
Determine whether the equation is linear or non-linear.
1. 4x2 + 11x = 1
Solve the equation.
1.
5
𝑥+9
−
4
𝑥−9
=
10𝑥
𝑥 2 −81
Lesson 1.2 Applications of Linear Equations
Write the phrase as a mathematical equation. Let x represent the unknown number.
1. 5 less than the quotient of a number and 6 is equal to 8 less than 3 times the number
Simple Interest Formula: I = PRT where I is interest, P is principal, r is rate (as a decimal) and t is time
Solve the word problem.
1. Larry invested part of his $12,000 advance at 5% annual simple interest and the rest at 6%
annual simple interest. If his total yearly interest from both accounts was $620, find the amount
invested at each rate.
Lesson 1.3 Complex Numbers
The standard form of a complex number is a + bi where a is the real part and b is the imaginary part
with 𝒊 = √−𝟏 and 𝒊𝟐 = −𝟏.
Write the expression as a multiple of i.
1. √−100
To add and subtract complex numbers, combine like terms. Do not forget to distribute the negative
sign when subtracting.
Subtract the complex numbers. Write the answer in the form a + bi.
1. (7 + 3i) – (4 – 2i)
To multiply complex numbers, treat i like a variable and replace i2 with -1.
Multiply the complex numbers. Write the answer in the form a + bi.
1. (6 – 4i) (2 + 4i)
To divide complex numbers, multiply the numerator and the denominator by the conjugate (change
the sign in the middle of the complex number) of the denominator.
Divide the complex numbers. Write the answer in the form a + bi.
1.
5
3−2𝑖
Lesson 1.4 Quadratic Equations
To factor a trinomial of the form x2 + bx + c, find two numbers that multiply to c but add to b.
Factor the expression.
1. x2 + 9x – 22
To factor a trinomial of the form ax2 + bx + c, find two numbers that multiply to ac but add to b and
then use those two numbers to split the middle term in order to factor by grouping.
Zero Product Property: If ab = 0, then a = 0 or b = 0.
Solve the equation.
1. 2x2 + 9x – 5 = 0
Square Root Property: If a2 = b, then a = ±√𝒃.
Solve the equation.
1. (x – 6)2 – 9 = 0
Steps to Solving an Equation by Completing the Square:
1. Isolate the constant on one side of the equation.
2. Make sure that the coefficient in front of the squared term is one. If not, divide every term on
both sides of the equation by the coefficient.
3. Find (b/2)2 and add it to both sides of the equation.
4. Factor the side of the equation with the variables using the complete the square formula.
5. Solve the resulting equation using the square root property.
Completing the Square Formula: x2 + bx + (b/2)2 = (x + b/2)2
Solve the equation by completing the square.
1. x2 – 4x = 5
Quadratic Formula: The solutions of ax2 + bx + c = 0 are 𝒙
=
−𝒃±√𝒃𝟐 −𝟒𝒂𝒄
𝟐𝒂
.
Use the quadratic formula to solve the problem. If the solutions are complex numbers, write the answer
in the form a + bi.
1. x2 – 8x = 21
Discriminant: The discriminant of ax2 + bx + c = 0 is d = b2 – 4ac. If d > 0, then the quadratic equation
has two real solutions. If d < 0, then the quadratic equation has two unreal solutions. If d = 0, then the
quadratic equation has exactly one real solution.
Find the discriminant and then use the discriminant to determine the number and nature of the
solutions to the quadratic equation.
1. 3x2 – 2x – 7 = 0