University:
California Institute of Technology
Course:
ACM 206 | Topics in Computational Mathematics
Academic year:

2019
Views:

435

Pages:

4
Author:

Leilani Contreras

Math 2 Final Exam Review Name: Key Block: 1. Determine whether each expression is equal to 36 ^ (3/2) 10.9 Equal Not Equal 63 X root(36 ^ 2, 3) X: 216 X sqrt^2 36 X root(36 ^ 3, 2) X X (5) ^ 2 - 10(5) + 21 = - 4 2. Identify the coordinates of the vertex defined by f(x) = x ^ 2 - 10x + 21 Farm: ADS: x = (- b)/(2a) = 10/(2(1)) = 10/2 = 5 Vertex: (5, - 4) y = (x - 5) ^ 2 - 4 14.7 3. Consider f(x) = 1 + sqrt(m + 1) For which value of x does f(x) = 8' *4. Match each equation to an equivalent equation with a perfect square on one side. 3,1 1 + sqrt(x + 1) = 8 x ^ 2 - 18x + 60 = - 21 (x - 9) ^ 2 = 0 x + 1 = 49 (sqrt(x + 1)) ^ 2 = (7) ^ 2 5 = z ^ 2 - 14z (x - 7) ^ 2 = 54 x ^ 2 + 10x = - 13 (x + 5) ^ 8 =(2 x ^ 2 - 6pi + 5 = 12 (x - 3) = 16 x = 48 8 = x ^ 2 - 2x (x - 1) ^ 2 = 9 x ^ 2 + 4x - 5 = 0 (x + 9) ^ 2 = 9 exists (x - 1) ^ 2 = 0 Pi * (x - 7) ^ 2 = 54 11 * (x + 2) ^ 2 = 9 pi * (x - 9) ^ 2 = 0 \mathfrak{I} * (sigma - 3) ^ 2 = 16 Xi * (x + 5) ^ 2 = 12 Add to packet Simplify 5-29 Answer, sqrt(29) Solve use quadratic 3x ^ 2 + 12x + 27 = 0 formula b ^ 2 - 4ac = 180 (12) = 4(3)(27) = X = - (b plus/minus sqrt(b ^ 2 * 4a) * c)/(2a) = (- 12 plus/minus sqrt(- 188))/(2(a)) = (- 12 plus/minus 6 * i * sqrt(s))/6 - 2 plus/minus i * sqrt(5) 5. The following expressions all define the same quadratic function: y + - i * nf / (0, c) x ^ 2 - 6x + 5 (0,5) Sketch a graph of the quadratic function. What key feature does each expression show us? Make sure the x-intercepts, y-intercepts, and vertex are plotted accurately. x + - i * ht / (r, 0) * (xi, 0) Vertex ( h_{y} |<) (x - 5)(x - 1) (5, 0)(1, 0) (x - 3) ^ 2 - 4 ( 6. Consider the false statement: "An irrational number multiplied by an irrational number always makes an irrational product." Determine whether each example below explains why the statement is false. Put an X in the correct column for each statement. Explains why the statement is false Does NOT explain why the statement is false. sqrt(9) * sqrt(3) \approx sqrt(21) X sqrt(9) * sqrt(9) = 9 X sqrt(2) * sqrt(2) = 2 X X sqrt(0) * sqrt(2) = 0 X - sqrt(3) * sqrt(3) * epsilon * sqrt(1) sqrt(3) * sqrt(2) = sqrt(w) X 1/(sqrt(3)) * sqrt(3) = 1 7. * Lin uses the expression n²+n+1 to represent the total number of squares for each figure, based on the figure number, n. Figure 1 Figure 2 Figure 3 Which parts of Lin's expression represent the shaded squares in the pictures? Figure 2 Figure 3 +1 Figure 1 Figure 1 Figure 2 [Stem 2] Figure 3 2 n Figure 1 Figure 2 Figure 3