Praxis Core Math Domain 3: Algebra and Geometry Welcome to your Praxis Core Math Domain 3: Algebra and Geometry 1. Praxis Core Math: Algebra and Geometry Given the quadratic equation \( x^2 - 4x + 4 = 0 \), what are the roots? A. 0 and 4 B. 2 and -2 C. 2 and 2 D. -2 and -2 None 2. Praxis Core Math: Algebra and Geometry If the sides of a square are lengthened by 40%, by what percent does the area increase? A. 40\% B. 60\% C. 80\% D. 96\% None 3. Praxis Core Math: Algebra and Geometry What is the slope of the line perpendicular to the line with the equation \( 3x - 4y = 12 \)? A. \(\frac{3}{4}\) B. \(-\frac{3}{4}\) C. \(\frac{4}{3}\) D. \(-\frac{4}{3}\) None 4. Praxis Core Math: Algebra and Geometry The sum of the interior angles of a polygon is 1080 degrees. How many sides does the polygon have? A. 6 B. 7 C. 8 D. 9 None 5. Praxis Core Math: Algebra and Geometry If \( f(x) = x^2 - 5x + 6 \), what are the x-intercepts of the graph of \( f \)? A. 2 and 3 B. -2 and -3 C. 2 and -3 D. -2 and 3 None 6. Praxis Core Math: Algebra and Geometry What is the equation of the circle with a center at \( (3,-4) \) and a radius of 5? A. \( (x-3)^2 + (y+4)^2 = 25 \) B. \( (x+3)^2 + (y-4)^2 = 25 \) C. \( (x-3)^2 + (y-4)^2 = 5 \) D. \( (x+3)^2 + (y+4)^2 = 5 \) None 7. Praxis Core Math: Algebra and Geometry If \( \sin \theta = \frac{1}{2} \) and \( 0 \leq \theta \leq \frac{\pi}{2} \), what is \( \cos \theta \)? A. \( \frac{\sqrt{3}}{2} \) B. \( \frac{1}{2} \) C. \( \frac{\sqrt{2}}{2} \) D. \( \frac{1}{\sqrt{2}} \) None 8. Praxis Core Math: Algebra and Geometry Solve for \( x \) in the equation \( \log_2(x-1) + \log_2(x+1) = 3 \). A. 2 B. 3 C. 4 D. 5 None 9. Praxis Core Math: Algebra and Geometry Find the vertex of the parabola given by \( y = 2x^2 - 4x + 3 \). A. (1, 1) B. (-1, -1) C. (1, -1) D. (-1, 1) None 10. Praxis Core Math: Algebra and Geometry Which equation represents a line parallel to the line given by \( y = -2x + 3 \)? A. \( y = -2x - 3 \) B. \( y = 2x + 3 \) C. \( y = -\frac{1}{2}x + 3 \) D. \( y = -2x + 5 \) None 11. Praxis Core Math: Algebra and Geometry What is the volume of a cylinder with radius 3 and height 4? A. 36\(\pi\) B. 48\(\pi\) C. 72\(\pi\) D. 144\(\pi\) None 12. Praxis Core Math: Algebra and Geometry If \( f(x) = 3x^2 - 2x + 1 \), what is \( f(-2) \)? A. 15 B. 17 C. 19 D. 21 None 13. Praxis Core Math: Algebra and Geometry The line \( y = mx + b \) passes through the points (1, 2) and (3, 8). What is the value of \( m \)? A. 2 B. 3 C. 4 D. 6 None 14. Praxis Core Math: Algebra and Geometry Solve for \( x \): \( 2x^2 - 5x - 3 = 0 \) A. -1 and 3/2 B. -3/2 and 1 C. 3/2 and -1 D. 1 and -3/2 None 15. Praxis Core Math: Algebra and Geometry What is the length of the hypotenuse of a right triangle with legs of lengths 7 and 24? A. 25 B. 28 C. 31 D. 35 None 16. Praxis Core Math: Algebra and Geometry What are the solutions to the inequality \( 3x - 7 < 2(x + 4) \)? A. \( x < 15 \) B. \( x < 11 \) C. \( x > 15 \) D. \( x > 11 \) None 17. Praxis Core Math: Algebra and Geometry If the area of a trapezoid is 60 square units and the lengths of the bases are 5 units and 15 units, what is the height? A. 6 units B. 8 units C. 10 units D. 12 units None 18. Praxis Core Math: Algebra and Geometry What is the sum of the solutions to the equation \( \frac{1}{x} + \frac{1}{x-2} = \frac{1}{2} \)? A. 2 B. 4 C. 3 D. 5 None 19. Praxis Core Math: Algebra and Geometry In the equation \( ax^2 + bx + c = 0 \), if \( a + b + c = 0 \), what is one of the roots? A. -1 B. 0 C. 1 D. 2 None 20. Praxis Core Math: Algebra and Geometry If \( \tan \theta = \sqrt{3} \) and \( 0 \leq \theta \leq \frac{\pi}{2} \), what is \( \sin \theta \)? A. \( \frac{\sqrt{3}}{2} \) B. \( \frac{1}{2} \) C. \( \frac{\sqrt{2}}{2} \) D. \( 1 \) None 1 out of 20 Time is Up! Time's up
