Math 521B Chapter 4 Test (33 marks) Name: Multiple Choice Identify the choice that best completes the statement or answers the question. (10 marks) 1. What are the x-intercepts of the quadratic function graphed here? y 12 10 8 6 4 2 6 5 4 3 2 1 1 2 3 4 5 6 x 2 4 6 8 10 12 A 4.6 C 2.2 B there are none D 9.0 2. Factor completely. A B C D 3. Determine the roots of the quadratic equation. A x = 4 9 and x = 4 9 C x = 9 4 and x = 9 4 B x = 3 2 and x = 3 2 D x = 2 3 and x = 2 3
4. A rectangle has dimensions and, where x is in centimetres. If the area of the rectangle is 72 cm 2, what is the value of x, to the nearest tenth of a centimetre? x + 10 5x 4 A B C D 5. The value of k that makes the expression a perfect square trinomial is A 1296 C 0 B 144 D 72 6. The vertex form of is A B C D 7. Solve. A 1 + 43 and 1 43 C 2 11 B 1 + 43 and 1 43 D 42 8. The roots, to the nearest hundredth, of are A 7.91 and 1.29 C 3.95 and 0.64 B 1.98 and 0.32 D 3.95 and 0.64
9. The number of real roots for the equation is A 2 C 1 B 0 D impossible to tell 10. For a science experiment, a projectile is launched. Its path is given by, where h is the height of the projectile above the ground and d is the horizontal distance of the projectile from the launch pad, both in metres. How far away from the launch pad is the projectile when it begins to fall, to the nearest tenth of a metre? A 255.8 m B 7.7 m C 0.3 m D 15.7 m Short Answer (5 marks) 1. Find the x-intercepts of the quadratic function y = 3x 2 10x + 6. Express your answers as exact values.
Problem (6 marks each) 1. A baseball batter hits a line drive. The height, h, in metres, of the baseball after t seconds is approximately modelled by the function h(t) = 5t 2 + 45t + 1. a) Graph the function. b) State the domain and range of the function. c) How long does it take for the ball to hit the ground?
2. The Parthenon, in Athens, is a temple to the Greek goddess Athena, and was built in about 447 B.C.E. It has a rectangular base with a perimeter of approximately 202 m and an area of 2170 m 2. Find the dimensions of the base, to the nearest metre.
3. A car travelling at v kilometres per hour will need a stopping distance, d, in metres, without skidding that can be modelled by the function. What is the speed, to the nearest kilometre per hour, at which a car can be travelling to be able to stop in 75 m?
Math 521B Chapter 4 Test Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: Average OBJ: Section 4.1 NAT: RF 5 TOP: Graphical Solutions of Quadratic Equations KEY: x-intercepts no real roots 2. ANS: D PTS: 1 DIF: Easy OBJ: Section 4.2 NAT: RF 5 TOP: Factoring Quadratic Equations KEY: factor trinomial 3. ANS: B PTS: 1 DIF: Average OBJ: Section 4.2 NAT: RF 5 TOP: Factoring Quadratic Equations KEY: difference of squares 4. ANS: A PTS: 1 DIF: Average OBJ: Section 4.2 NAT: RF 5 TOP: Factoring Quadratic Equations KEY: area problem solve trinomial 5. ANS: A PTS: 1 DIF: Easy OBJ: Section 4.3 NAT: RF 5 TOP: Solving Quadratic Equations by Completing the Square KEY: perfect square trinomial 6. ANS: C PTS: 1 DIF: Average OBJ: Section 4.3 NAT: RF 5 TOP: Solving Quadratic Equations by Completing the Square KEY: vertext form 7. ANS: B PTS: 1 DIF: Easy OBJ: Section 4.3 NAT: RF 5 TOP: Solving Quadratic Equations by Completing the Square KEY: square root 8. ANS: C PTS: 1 DIF: Average OBJ: Section 4.2 NAT: RF 5 TOP: The Quadratic Formula KEY: quadratic formula 9. ANS: B PTS: 1 DIF: Average OBJ: Section 4.3 NAT: RF 5 TOP: Factoring Quadratic Equations KEY: real roots 10. ANS: B PTS: 1 DIF: Difficult + OBJ: Section 4.4 NAT: RF 5 TOP: The Quadratic Formula KEY: vertex coordinates SHORT ANSWER 1. ANS:
PTS: 1 DIF: Average OBJ: Section 4.4 NAT: RF 5 TOP: The Quadratic Formula KEY: roots of quadratic equation quadratic formula PROBLEM 1. ANS:
a) h 96 80 64 48 32 16 4 8 12 t b) From the graph, the t-values go from t = 0 to approximately t = 9. Thus, the domain is. From the graph, the maximum value is approximately 106. Thus, the range is. c) It takes approximatley 9 s for the ball to hit the ground. PTS: 1 DIF: Easy OBJ: Section 4.1 NAT: RF 5 TOP: Graphical Solutions of Quadratic Equations KEY: x-intercepts zeros domain range 2. ANS: Draw a diagram to visualize the problem. width (w) Area (A) = 2170 square metres length (l) Perimeter (P) = 202 m
Thus, l = 70 or l = 31. The dimensions of the base are 70 m by 31 m. PTS: 1 DIF: Average OBJ: Section 4.2 NAT: RF 5 TOP: Factoring Quadratic Equations KEY: factor trinomial 3. ANS: Set d = 75 and solve for v. Use the quadratic formula: A negative speed does not make sense in this context. To stop within 75 m without skidding, the speed of the vehicle must be 95 km/h. PTS: 1 DIF: Average OBJ: Section 4.4 NAT: RF 5 TOP: The Quadratic Formula KEY: quadratic formula