IM3 Fall Final 2024 Review (PDF)

# IM3 fall final 2024 ## Solve each equation by factoring. | Equation | Answer | |---|---| | 3n² = 12 | D) {-2, 2} | | r² = - 3r | C) {-3, 0} | | x² + 3 = -4x | D) {-2, 3} | | 2m² = 4m + 6 | B) {1, -2} | | m² + 2m = 0 | A) {-2, 0} | | 3r² - 1 = 2r | B) {-2, 1/3} | ## Solve each equation by taking...

# IM3 fall final 2024 ## Solve each equation by factoring. | Equation | Answer | |---|---| | 3n² = 12 | D) {-2, 2} | | r² = - 3r | C) {-3, 0} | | x² + 3 = -4x | D) {-2, 3} | | 2m² = 4m + 6 | B) {1, -2} | | m² + 2m = 0 | A) {-2, 0} | | 3r² - 1 = 2r | B) {-2, 1/3} | ## Solve each equation by taking square roots. | Equation | Answer | |---|---| | 2x² - 2 = 16 | B) {√7, -√7} | ## Solve each equation with the quadratic formula. | Equation | Answer | |---|---| | n² - 2n = 4 | D) {-1 + i√3, -1 - i√3} | | 2x² = -3 + x | D) {-1 + √7/2, -1 - √7/2} | ## Solve each equation. Remember to check for extraneous solutions. | Equation | Answer | |---|---| | 4 = √x | A) {16} | | √v + 1 + √v + 2 = √v | C) {-1, 2} | | (3m² + 7m + 2)/2m = 1 | A) 8/3, 0 | ## Solve each equation. Round your answers to the nearest ten-thousandth. | Equation | Answer | |---|---| | 2.9^10x = 57 | B) 0.1525 | | e^3n + 3 = 97 | A) 0.6577 | ## Solve each equation. | Equation | Answer | |---|---| | log(-4b-3) = log(9-3b) | D) -15 | | -log(x+6) = 1 | D) -10 | ## Sketch the graph of each function. | Function | Answer | |---|---| | y = 2 * 2^(x+1) - 2 | D) | ## Solve each continous exponential growth/decay problem. | Equation | Answer | |---|---| | 103e^(-0.02 * 5) | D) 103e(-0.01 * 5) ≈ 98.0 °C | ## Factor each completely. | Equation | Answer | |---|---| | x² - 16 | D) (x+4)(x-4) | ## Find the inverse of each function. | Function | Answer | |---|---| | g(x) = (5-2x) / 5 | A) g^-1(x) = 4x + 4 | | f(n) = (n-2)^3 + 3 | A) f^-1(n) = ^3√n - 3 | ## Sketch the graph of each line. | Equation | Answer | |---|---| | y = (-9/5)x + 4 | A) | ## Identify the vertex, focus, and directrix of each. Then sketch the graph. | Equation | Answer | |---|---| | y = x² - 8x +19 | A) Vertex: (-4, -3) <br>Focus: (-4, 11/4) <br>Directrix: y = -13/4 | | y = -(x+4)² - 5 | A) Vertex: (-4, -5) <br>Focus: (-4, 19/4) <br>Directrix: y = -21/4 | ## Sketch the graph of each function. | Function | Answer | |---|---| | f(x) = -x³ - 11x² - 40x - 47 | D) | | f(x) = x^4 - 2x² - 2x - 3 | C) | ## Identify the domain and range of each. | Function | Answer | |---|---| | y = -3 + √x -3 | A) Domain: x ≥ 3 <br>Range: y ≥ -3 | | f(x) = -2 / x | B) Domain: All reals except -2 <br> Range: All reals except 2 | ## Evaluate each function | Function | Answer | |---|---| | w(x) = 2.5^(x-2); Find w(1) | B) 2/25 | | f(n) = -2n²-3; Find f(6) | B) -75 | ## State if the given functions are inverses. | Function | Answer | |---|---| | f(x) = (x-1)^5 <br> g(x) = √x +1 | B) No | | f(x) = 4/(-x+2) <br> h(x) = (-x+2)/2 | A) No | ## Solve each system by graphing. | Function | Answer | |---|---| | 5x + 3y = -21 <br> x + 3y = -9 | C) (-2, 3) | | 3x + 4y = 16 <br> 3x + 4y = 12 | C) No Solution | ## Write the slope-intercept form of the equation of each line. | Line | Answer | |---|---| | The line shown in the graph | D) y = (-4/3)x - 1| ## Factor each completely. | Equation | Answer | |---|---| | 2x² - 19x + 35 | D) (2x-5)(x-7) | | 30x² -216x - 486 | B) 6(5x - 9)(x+9) | ## Graph each equation. | Equation | Answer | |---|---| | y = |x+4| | A) | ## Find each measurement indicated. Round your answers to the nearest tenth. | Measurement | Answer | |---|---| | Find BC | B) 21 | ## Find m∠A | Measurement | Answer | |---|---| | m∠A | B) 29° | ## Use a calculator to approximate each to the nearest thousandth. | Value | Answer | |---|---| | log₄ 27 | B) 2.018 | | ln 22 | B) 3.091 | ## Evaluate each expression | Value | Answer | |---|---| | log₄ 64 | A) 6 | | log₃ 27 | B) 3 | | log₂ 16 | D) 8 | ## Find the inverse of each function | Function | Answer | |---|---| | y = -8log₃(-3x) | B) y = 3^(x/2) / -3 | ## Graph each function. | Function | Answer | |---|---| | y = √x - 5 | A) | | f(x) = 1/(x+4) - 1 | C) |