Math 0 Precalculus Sstem of Equation Review Questions Multiple Choice. The sstem of equations A. 7 0 7 0 0 0 and can be solved using the quadratic equation. In solving the quadratic equation 0 ( ) intersection points. If one of the equations is A. Y Y Y Y. For the two functions ( ) q and is true? A. It is not possible for them to intersect. The must intersect in onl one location. The must interest in two locations The are the same function, so the coincide., a student could graph two equations and find the Y ( ), then the other is ( ) q, q 0, which of the following statements. A Math 0- student is attempting to find the intersection point(s) between two quadratic functions, Y and Y. After making Y Y the student has a quadratic equation to solve. Which of the following quadratics would indicate onl one intersection point? A. 0 0 0 0. Using the graph to the right, P ( ) 0 when A.,, 0 - - - -
. Which of the following is a solution to the inequalit 0 0? A.,, 7. Which of the following is the inequalit that represents the solution to the graph shown on the right? A.. The sstem of equations k and the line have solutions of when k A. - - 0 - - - - 9. Two equations are given b k and k. Regardless of the value of k, the solution to this sstem of equations will have A. 0 onl Both 0, Both 0, There are no solutions for. 0. Which of the following ordered pairs does not satisf the inequalit A. (-,-) (-,-) (,9) (0,-)?. Two quadratic functions given b and A. not intersect intersect at one location onl intersect at two locations intersect at more than two locations. a( ), a 0,
. Which of the following must be true in order for two quadratic functions to intersect in an infinite number of locations? A. The must be the same quadratic function The must be reflections of each other around a line The must share the same verte, but have different stretch factors The must have different stretch factors and a different verte. In the algebraic development of the solution to 0 7 a calculus student must A. Find the zeros, one of which is Find the zeros, one of which is Find the zeros, one of which is Find the zeros, one of which is. Which of the following number lines represents the solution to the inequalit 0 ( )( )? A. - - - - - 0 - - - - - 0 - - - - - 0 - - - - - 0. The sstem of equations ( ab, ). The value of b is A. - - - - and are graphed and ield a solution of (, 9) and. One -value in the solution to the sstem of equations value of k must be A. -0-0 k and is. The
7. Two sugar solutions, one that is 0% and the other 0% will be mied in order to make a 0 L solution that is less than %. If is the amount of 0% solution used, and is the amount of 0% solution used, which of the following is an inequalit representing this problem for the amount of 0% and 0% solution that should be used? A. 0. 0. 0. 0. 0. 0.. 00 0. 0. 0. The graph shown to the right represents the number of nickels and dimes that could be combined to total a value of less than $.00. The ais of the problem represents A. The number of dimes used in the total The number of nickels used in the total Both the number of dimes and nickels used in the total The value of the mone 0 0 0 0 9. Which of the following quadratic inequalities would have the origin among one of the solutions? A. 0 0 0 0 00 0. Georgia attempted to present a graphical solution of the inequalit to a group of her friends. Her attempt is shown on the right. Which of the following statements are correct? (7., 7.) A. She has correctl used a solid line and has the correct region shaded. She has incorrectl used a solid line but has the correct region shaded. She has correctl used a solid line, but has the incorrect region shaded. She has incorrectl used a solid line, and has the incorrect region shaded. 0 - - - -. Which of the following statements is true regarding the inequalities and A. The ordered pair (-,-) satisfies both inequalities The ordered pair (-,-) satisfies neither inequalit The ordered pair (-,-) satisfies onl The ordered pair (-,-) satisfies onl?
. A student attempts to solve the sstem of equation shown below. In order to solve the sstem, the student uses the method of substitution to correctl derive the equation. Therefore, a possible solution for is; A. - -. The region bounded b the and ais, along with the line 0, as illustrated in the graph shown to the right, has an area of; 0 A. 7 units 0 units units 00 units 0. As part of a homework assignment, a student graphs a sstem of two equations on her calculator to solve for the solution set. Her result is shown to the right. One equation was quadratic, and the other linear. She can be sure that the number of solutions in the solution set is; A. f g. A quadratic equation, written in the form a( p) q has an ais of smmetr at, and contains the ordered pairs (-,-) and (,). The value of q must be; A.
. A student uses the method of comparison to solve the sstem of equations and. Which of the following quadratic equations will assist in determining the value(s) in the solution set? A. 7. The graph of 0 0 0 0 is shown to the right. If a second equation in this sstem is q, the value of q ielding onl one single solution would be; A. - - f f 0. The graph shown to the right illustrates one of an infinite number of ordered pairs that satisfies a linear sstem of inequalities. In this case, the ordered pair (0, ) satisfies the sstem, consistent with the boundar lines shown, of; A. f b 0, a,
Numerical Response Questions How man solutions satisf the sstem of equations and? The solution to 0 is k. The value of k must be. The solution to k 0 is given b the number line below. The value of k must be. - -7 - - - - - - 0 A quadratic equation ( p) q passes through the points (-,) and (-9,0). The value of p must be. 0 The graph shown to the right is the solution to k. The value of k must be. - - 0 - - 0 How man of the ordered pairs shown on the right satisf both and 0 0? - - 0 - -
0 7 The sstem of equations illustrated b the graph to the right has solutions at. If the sstem is given b the two equations and k, the value of k must be. f g 0 0 A student graphs two quadratic functions. The minimum number of solution sets of this sstem, represented b the possible intersection points, must be. Written Response Show our work in providing a response to each of the following questions. Find the solutions sets to the following sstems of equations algebraicall. a) 0, b), 0 A student agrees to pick up garbage, and gets paid $0.0 for each non-food item, and $0.0 for each food item. a) If is the number of non-food items she must pick up, and is the number of food items she must pick up, what inequalit represents the requirement that she must pick up at least times as man non-food items as food items? b) The student must collect at least 70 pieces each da to keep this job. What inequalit, again, in terms of and represents this requirement? c) On an da, there is less than or equal to 000 pieces of garbage in the area the student must clean. Design a third inequalit representing this condition. d) Show, b graphical methods, the solution to this problem b shading in a region of all possible combinations of non-food items,, and food items,, this student could pick up. No marks will be given for graphs not labelled.
An electronics repair facilit fies stereo and video equipment. Below is a table illustrating the average time necessar to repair most pieces of stereo equipment and video equipment at the two facilities, and the maimum number of hours/week that is available to make those repairs. Location Stereo Video Hours Available Lethbridge h h 0 Red Deer h h 0 a. One week in Lethbridge, all available hours were used to repair stereos, with no time allotted to repairing video equipment. How man stereos were repaired? b. A second week in Lethbridge, all available hours were used to repair video equipment, with no time allotted to repairing stereo equipment. How man units of video equipment were repaired? c. Three equations are necessar to develop a sstem that would illustrate the number of stereos and video units that can be repaired in the Lethbridge facilit. Determine the three equations, in terms of s (stereo units repaired each week) and v (video units repaired each week). d. If the plant capacities of Lethbridge and Red Deer were combined, draw a graph illustrating the number of stereo and video units that could be repaired each week.. A student graphs two inequalities as shown to the right. a. Determine the boundar lines in the form a b c and m b. b. State the sstem of inequalities that satisfies the region shown in the graph on the right. - - - -0 -. Solve each of the following inequalities b an algebraic method, and represent our answer on a number line. a. 0 b. ( )( ) 0 c. d. 0