University:
Montgomery College
Course:
MATH 165: Precalculus
Academic year:

2020
Views:

283

Pages:

4
Author:

Kaiden Murphy

Math 165 – Reviewing concepts needed in 1.1 - 1.4 Name ______________________________ In prior math classes you have studied all of the concepts included in this paper. Please, Goggle them if you don’t remember. You can also use the power point presentations for sections 1.1, 1.2, 1.3, 1.4 and 1.5 This paper is due on the first class of the semester – as you walk into the classroom, put this paper on my desk – not accepted late. NEATNESS required – Messy papers will not be graded. Section 1.1 – Pythagorean Theorem 1) Write the Pythagorean Theorem; Sketch a right triangle. Label vertices with A, B, C (C at the right angle). Label opposite sides with a, b, c. Write the Pythagorean Theorem. Section 1.2 – Intercepts 2) How do you find the x-intercept of an equation? 3) How do you find the y-intercept of an equation? 4) Find the x- and the y-intercepts of the equation 2x – 5y = 23. Show ALL work. Show a rough sketch of the line on this paper; label intercepts. 1 Section 1.3 – Solving Quadratic Equations Using Algebra Google if necessary 5) Solve a quadratic equation using the factoring technique: First set equation = 0, then, factor and solve using the zero factor property Solve: 3 x 2 − 8 =−2 x 6) Solve a quadratic equation using the quadratic formula Solve: 2 x2 − 4 x + 1 = 0 Answer exact in radical form: __________________________ Answer with two decimal places: _______________________________ 7) Solve a quadratic equation using the square root method. (1) Example 1: If 𝒙𝒙𝟐𝟐 = 𝒌𝒌 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 𝒙𝒙 = √𝒌𝒌 𝒂𝒂𝒂𝒂𝒂𝒂 𝒙𝒙 = −√𝒌𝒌 Solve: 𝑥𝑥 2 = 5 Give exact answer with radicals ______________ Give decimal approximations __________ (2) Example 2: If (𝒙𝒙 + 𝟑𝟑)𝟐𝟐 = 𝟕𝟕 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 𝒙𝒙 + 𝟑𝟑 = ±√𝟕𝟕 ; 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕, 𝒙𝒙 = −𝟑𝟑 ± √𝟕𝟕 = −𝟑𝟑 ± 𝟐𝟐. 𝟔𝟔; 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕, 𝒙𝒙 = −𝟓𝟓. 𝟔𝟔 𝒂𝒂𝒂𝒂𝒂𝒂 𝒙𝒙 = −𝟎𝟎. 𝟒𝟒 2 Solve (𝑥𝑥 − 2) = 6 Give exact answer with radicals ______________ Give decimal approximations __________ 2 8) Multiplying Binomials. Use the distributive property (FOIL method) to perform the following operations Careful! (𝑥𝑥 + 𝑦𝑦)2 𝐼𝐼𝐼𝐼 𝑁𝑁𝑁𝑁𝑁𝑁 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑇𝑇𝑇𝑇 𝑥𝑥 2 + 𝑦𝑦 2 a. (2𝑥𝑥 − 1)(3𝑥𝑥 + 5) b. (𝑥𝑥 − 5)2 c. (𝑦𝑦 + 2)2 9) Section 1.4 - Find the equation of a line going through two points – Sketch the line Here is an EXAMPLE: Find y = mx + b Find equation of the line through A(-2, 5) and B(7, -3) a) Find the slope: 𝑚𝑚 = −3 − 5 −8 8 = =− 7 − (−2) 9 9 b) Find the y-intercept. Use the given point A(-2, 5) 𝑦𝑦 = 𝑚𝑚𝑚𝑚 + 𝑏𝑏 8 𝑦𝑦 = − 𝑥𝑥 + 𝑏𝑏 9 8 5 = − (−2) + 𝑏𝑏 9 16 5= + 𝑏𝑏 9 16 5− = 𝑏𝑏 9 45 − 16 = 𝑏𝑏 9 29 = 𝑏𝑏 9 The equation of the line is: 8 29 𝑦𝑦 = − 𝑥𝑥 + 9 9 You complete the problem on the next page NOTE: If you know another method to find the equation of the line, use it. Just show me all the steps 3 You do this problem Plot the points C and D Sketch the line through CD Show algebraic procedure to find the equation of the line going through the points C(-2, -8) and D(4, 7) First, plot the two points and sketch the line through them Second, find the slope: Third, find the equation of the line 4