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Comprehensive Finals Review Checklist for Algebra Concepts

This comprehensive review checklist covers essential algebra concepts necessary for finals preparation. It includes objectives related to solving one and two-variable equations, simplifying expressions using exponent properties, evaluating expressions with order of operations, and graphing functions with proper window settings. Additionally, the checklist addresses simplifying expressions with multiple variables, understanding function notation, identifying functions, and determining domain and range. It emphasizes solving inequalities, proportions, absolute value problems, and systems of linear equations. Practice problems are provided to enhance understanding.

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Comprehensive Finals Review Checklist for Algebra Concepts

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  1. Finals Review Checklist

  2. Chapter 0 – Objectives • Solve for a variable in one-variable equations • ex: Solve -3(x+5) = 10 • Solve for a variable in two-variable equations • ex: Solve for y: 3x – 4y = 15 • Simplify expressions using properties of exponents • ex: Simplify (3x2y3)4 • Evaluate using order of operations • ex: Evaluate -6(7.1) – 4(-8.1)2 + 33 • Adjust your window setting to best fit a function • ex: Zoom Out, Zoom Decimal, Window

  3. Chapter 1 – Objectives • Simplify expressions with two or more variables • ex: Simplify -3(x+y) – 2y2 + 6x + y • Evaluate using function notation • ex: Given f(x) = 3x – 10, find f(-1) • Determine whether a relation is a function • ex: Function? {(0,1)(2,1)(-1,3)(4,3)} • Determine the domain and range • ex: {(0,1)(2,1)(-1,3)(4,3)} • Write equations for real-world situations • ex: #8 on study guide

  4. Warm-up – Chapter 2 Solve the following a) 10x–5 > 3x+16 c) ∣x + 5∣ = 13 b) 4x+10 = 6x+8–2x+2 d) 2) What is -2x + 3y = 12 in slope-int. form? 3) Which is the equation for: a) y = -2x - 3 c) y = -3x – 1 b) y = -x – 5 d) y = ½x - 6

  5. Chapter 2 – Objectives • Solve linear inequalities • ex: Solve -3x – 4 < 8 • Solve proportion problems • ex: Solve • Determine when special solutions arise • ex: No solutions, infinitely many solutions • Solve absolute value problems • ex: Solve ∣x + 3∣ = 12 • Write linear equations in slope-intercept form • ex: -2x + 5y = 15

  6. Warm-up – Chapter 3 Solve the following a) b) 2) Find the max value for the function C = 5x + 7y for the region shown. 3) Graph the following:

  7. Chapter 3 – Objectives • Solve a system of linear equations • ex: Solve • Solve a system of linear inequalities • ex: Solve • Determine when special solutions arise • ex: No solutions, infinitely many solutions • Solve max and min problems • ex: Maximize C = 3x + 4y given constraints • Write the constraints of a word problem • ex: #32 in study guide

  8. Warm-up – Chapter 12 • Evaluate: • 2) Find the 7th term of the sequence • t1= -2 and tn = 2tn-1 – 5 • 3) Find S12 for each of the following • series: • a) -3–5–7–9… b) 2–4+8–16… • 4) Find four terms between the following arithmetic sequence: 16 and 44

  9. Chapter 12 – Objectives • Evaluate series written in sigma notation • ex: Evaluate • Find the sum of a geometric or arithmetic series • ex: Find S15 for -1+4+9+14+… • Identify the common difference or ratio • ex: -2,-4,-8,-16,… or -5, 2, 9, 16,… • Find the nth term of a sequence • ex: Find t20 for tn = -2n + 17 • Generate terms from explicit or recursive forms • ex: Find the first five terms of:

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