Pre-Calc Chapter 1 Sample Test - Weebly



Pre-Calc Chapter 1 Sample Test

|1. |Use the graphs of f and g to evaluate the function. |

| |[pic] [pic] |

| |(f o g)(-0.5) |

| |A) 2 B) 1 C) –1 D) 0 E) 4 |

|2. |Plot the points and find the slope of the line passing through the pair of points. |

| | |

| |(2, –3), (–4, 5) |

| |[pic] |

| |A) slope: [pic] B) slope: [pic] C) slope: [pic] D) slope: [pic] E) slope: [pic] |

|3. |Evaluate the indicated function for f (x) = x2 + 4 and g (x) = x + 3. |

| | |

| |( f − g )(t + 2) |

| |A) t2 + 3t + 9 B) t2 + 5t + 3 C) t2 − t + 3 D) t2 + 3t + 3 E) t2 + 5t + 9 |

|4. |Given x2 + y2 = 15, use the algebraic tests to determine symmetry with respect to both axes and the origin. |

|A) |x-axis, y-axis, and origin symmetry |D) |origin symmetry only |

|B) |no symmetry |E) |y-axis symmetry only |

|C) |x-axis symmetry only | | |

|5. |Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. |

| | |

| |L1 : (9, 6), (–5, –4) |

| |L2 : (0, 9), (–7, 4) |

| |A) parallel B) perpendicular C) neither |

|6. |Find all real values of x such that f (x) = 0. |

| | |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

|7. |Assume that y is directly proportional to x. If [pic]and[pic], determine a linear model that relates y and x. |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

|8. |Which function does the graph represent? |

| |[pic] |

|A) | |

| |[pic] |

|B) | |

| |[pic] |

|C) | |

| |[pic] |

|D) | |

| |[pic] |

|E) | |

| |[pic] |

|9. |Use the graph of |

| |[pic] |

| |to write an equation for the function whose graph is shown. |

| |[pic] |

|A) | |

| |[pic] B) [pic] |

|C) | |

| |[pic] D) [pic] |

|E) | |

| |[pic] |

|10. |During math class, a fly lands on your graph paper. It lands at a point seven units from the left side of the paper and two units from the bottom of |

| |the paper. Before it flies away, it walks in a straight line to a point three units from the left side of the paper and ten units from the bottom of |

| |the paper. How far did the fly walk? Round to the nearest unit. |

| |[pic] A) 11 units B) 12 units C) 10 units D) 81 units E) 9 units |

|11. |Find a mathematical model for the verbal statement: |

| |"[pic] varies directly as the square of [pic] and inversely as [pic]." |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

|12. |Use the graph of the function to find the domain and range of f. |

| | |

| |[pic] |

|A) | |

| |[pic] B) [pic] |

|C) | |

| |[pic] D) [pic] |

|E) | |

| |[pic] |

|13. |Write the height h of the rectangle as a function of x. |

| |[pic] |

|A) | |

| |[pic] B) [pic] |

|C) | |

| |[pic] D) [pic] |

|E) | |

| |[pic] |

|14. |The polygon is shifted to a new position in the plane. Find the coordinates of the vertices of the polygon in its new position. |

| |[pic] |

|A) | |

| |[pic] B) [pic] |

|C) | |

| |[pic] D) [pic] |

|E) |none of these |

|15. |Find the domain of the function. |

| | |

| |[pic] |

|A) |all real numbers |D) |all real numbers [pic] |

|B) |all real numbers [pic], [pic] |E) |w = 6 |

|C) |w = 6, w = 0 | | |

|16. |The graph shows the net profit (in thousands) for Deepti's landscaping business for the past year. |

| |[pic] |

| |Use slopes to determine the month in which the net profit showed the greatest increase. |

| |A) February B) July C) September D) June E) January |

|17. |Find the inverse function of [pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

|18. |Find ( f / g )(x). |

| | |

| |[pic] [pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

|19. |Which equation does not represent y as a function of x? |

| |A) [pic] B) x = –y – 4 C) y = –x + 4 D) y = |6 + 8x2| E) x = –3 |

|20. |After determining whether the variation model below is of the form [pic] or [pic], find the value of [pic]. |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| | |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| | |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

|21. |Determine whether the function has an inverse function. If it does, find the inverse function. |

| | |

| |[pic] |

|A) |[pic] |D) |No inverse function exists. |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

|22. |Use the position equation s = −16t2 + v0t + s0 to write a function that represents the situation and give the average velocity of the object from |

| |time t1 to time t2. |

| | |

| |An object is thrown upward from a height of 100 feet at a velocity of 37 feet per second. |

| | |

| |t1 = 1, t2 = 5 |

|A) |[pic]; avg. velocity = –236 ft/s |

|B) |[pic]; avg. velocity = 64 ft/s |

|C) |[pic]; avg. velocity = –59 ft/s |

|D) |[pic]; avg. velocity = 1 ft/s |

|E) |[pic]; avg. velocity = 4 ft/s |

|23. |Find the distance between the points. Round to the nearest hundredth, if necessary. |

| | |

| |(–5, –9), (–4, 3) |

| |A) 6.08 B) 8.06 C) 15 D) 12.04 E) 10.82 |

|24. |Which graph represents the function? |

| | |

| |[pic] |

|A) | |

| |[pic] B) [pic] |

|C) | |

| |[pic] D) [pic] |

|E) | |

| |[pic] |

|25. |Use the functions given by [pic] and [pic] to find the indicated value. |

| | |

| |[pic] |

| |A) [pic] B) undefined C) [pic] D) [pic] E) [pic] |

|26. |Find ( f − g )(x). |

| | |

| |[pic] [pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

|27. |Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. |

| | |

| |f (x) = x3 + 3x2 + 2x + 3 |

|A) |relative maximum: (–1.58, 3.38) |

| |relative minimum: (–0.42, 2.62) |

|B) |relative maximum: (–0.42, 2.62) |

| |relative minimum: (–1.58, 3.38) |

|C) |relative maximum: (2.62, 46.63) |

| |relative minimum: (3.38, 82.93) |

|D) |relative maximum: (3.38, –1.58) |

| |relative minimum: (2.62, –0.42) |

|E) |relative maximum: (2.62, –0.42) |

| |relative minimum: (3.38, –1.58) |

|28. |Find the midpoint of the line segment joining the points. |

| | |

| |(9, –2), (–9, 8) |

| |A) (0, 3) B) (3, 0) C) (0, –3) D) (9, –5) E) (–5, 9) |

|29. |Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope. |

| | |

| |point: (–9, –8) slope: m = 5 |

| |A) y = 5x – 9 B) y = 5x – 1 C) y = 5x + 31 D) y = 5x + 37 E) y = 5x – 8 |

|30. |Determine the quadrant(s) in which (x, y) is located so that the condition is satisfied. |

| | |

| |xy > 0 |

|A) |quadrant IV |D) |quadrant III |

|B) |quadrants II and IV |E) |quadrants I and III |

|C) |quadrant I | | |

|31. |Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. |

| | |

| |point: (6, –1) line: 8x – 40y = 6 |

| |A) y = –5x + 29 B) [pic] C) y = 8x + 47 D) [pic] E) [pic] |

|32. |Determine the intervals over which the function is increasing, decreasing, or constant. |

| |[pic] |

| | |

| |[pic] |

|A) | |

| |[pic] B) [pic] |

|C) | |

| |[pic] D) [pic] |

|E) | |

| |[pic] |

|33. |Find the zeroes of the functions algebraically. |

| | |

| |[pic] |

|A) | x = 9, x = –2 |D) | x = –9, x = 2 |

|B) | x = –9, x = 2, [pic] |E) | x = 9, x = –2, [pic] |

|C) |[pic] | | |

|34. |Describe the sequence of transformations from the related common function[pic] to g. |

| | |

| |[pic] |

|A) |reflection in the x-axis; then vertical shift 8 units down |

|B) |reflection in the y-axis; then horizontal shift 8 units right |

|C) |reflection in the y-axis; then vertical shift 8 units up |

|D) |reflection in the y-axis; then horizontal shift 8 units left |

|E) |reflection in the x-axis; then vertical shift 8 units up |

|35. |Find [pic] when f (x) = x + 5 g (x) = x2 |

|A) | [pic]x2 + 10x + 25 |D) | [pic]x2 + 5x + 25 |

|B) | [pic]x2 – 25 |E) | [pic]x2 + 25 |

|C) | [pic]x2 + 5 | | |

|36. |Find the x- and y-intercepts of the graph of the equation[pic]. |

| | |

| |[pic] |

|A) |x-intercepts: [pic]; y-intercept: [pic] |

|B) |x-intercepts: [pic]; y-intercept: [pic] |

|C) |x-intercepts: [pic]; y-intercept: [pic] |

|D) |x-intercepts: [pic]; y-intercepts: none |

|E) |x-intercepts: [pic]; y-intercept: [pic] |

|37. |Determine the center and radius of the circle represented by the equation [pic]. |

|A) |center: [pic]; radius: [pic] |D) |center: [pic]; radius: [pic] |

|B) |center: [pic]; radius: [pic] |E) |center: [pic]; radius: [pic] |

|C) |center: [pic]; radius: [pic] | | |

|38. |The electrical resistance, [pic], of a wire is directly proportional to its length, [pic], and inversely proportional to the square of its diameter, |

| |[pic]. A wire 100 meters long of diameter 5 millimeters has a resistance of 8 ohms. Find the resistance of a wire made of the same material that has|

| |a diameter of 1 millimeter and is 4 meters long. |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

|39. |Write the standard form of the equation of the circle whose radius is [pic] and whose center is the point [pic]. |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

|40. |Assuming that the graph shown has y-axis symmetry, sketch the complete graph. |

| | |

| |[pic] |

|A) | |

| |[pic] B) [pic] |

|C) | |

| |[pic] D) [pic] |

|E) | |

| |[pic] |

Answer Key

|1. |D |

|2. |E |

|3. |D |

|4. |A |

|5. |A |

|6. |E |

|7. |E |

|8. |C |

|9. |E |

|10. |E |

|11. |A |

|12. |A |

|13. |E |

|14. |B |

|15. |D |

|16. |D |

|17. |A |

|18. |B |

|19. |E |

|20. |B |

|21. |D |

|22. |C |

|23. |D |

|24. |D |

|25. |C |

|26. |C |

|27. |A |

|28. |A |

|29. |D |

|30. |E |

|31. |A |

|32. |D |

|33. |A |

|34. |E |

|35. |A |

|36. |A |

|37. |A |

|38. |E |

|39. |E |

|40. |B |

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