Show all our work so that: Math 9 Practice Eam Part 1: No Calculator someone who wanted to know how ou found our answer can clearl see how. if ou make a mistake, I can see where it happened and determine how much partial credit ou should be awarded. You ma use scratch paper, but all necessar work must be written on this eam. Simplif all fractions as much as possible. The entire eam is closed-note, closed-book. You ma not use our calculator or an other electronic device on this part of the eam. Take our time, because ou have plent to spare. Check our answers. 1. Use the graph of the quadratic function shown in Figure 1 to complete the following. Approimating an values with a decimal that is reasonabl close is OK. Figure 1. Graph of = f() State the -intercept(s). g) State the -intercept. State the verte. Write the verte form for the function f. graph, a = 9.) What is the domain of f? What is the range of f? Solve f() = 3. (In this 6. Use the graph of the quadratic function shown in Figure to complete the following. Approimating an values with a decimal that is reasonabl close is OK. Figure. Graph of = g() State the -intercept(s). State the -intercept. State the verte. Write the verte form for the function g. (In this graph, a = 1.) What is the domain of g? What is the range of g? g) Solve g() = 10. 10 10 8 6 10 1
Math 9 Practice Eam 3. Let H() = 1.8( 9) +. What is the verte? Does this graph open upward or downward? State the domain in interval notation. State the range in interval notation.. Let H() = 3 ( + 1) 9. What is the verte? Does this graph open upward or downward? State the domain in interval notation. State the range in interval notation.. Solve the quadratic equation Q 8Q + 3 = 0 b completing the square. Clearl state the solution set. 6. Solve the quadratic equation + 3 7 set. = 0 b completing the square. Clearl state the solution 7. Let p() = ++. Find the ke features Let p() = 7. Find the ke of the graph of this function (-intercepts, - intercept, and verte) and sketch the graph of = p() in Figure 3. Figure 3. Graph of = p() features of the graph of this function (intercepts, -intercept, and verte) and sketch the graph of = p() in Figure. Figure. Graph of = p() 8. Solve each quadratic equation using the quadratic formula. Clearl state the solution set of comple solutions. + + 10 = 0 1 = 0 + 6 + = 0 Part 1: No Calculator Page of 6
Math 9 Practice Eam 9. Simplif each of the following epressions and state each comple number in standard form. (1 + 3i) + ( + i) ( 6i) + ( + i) (1 + 3i) ( + i) ( 6i) ( + i) 3i( + i) (1 + 3i)( + i) 6i 1 + 3i g) ( 6i)( + i) h) i) i + i 6i j) + i 10. Use the graph of = B() in Figure to answer the following. Reasonable decimal approimations are acceptable. Figure. Graph of = B() Find B(3). Solve B() =. Solve B() =. Solve B(). State the domain of B using interval notation. State the range of B using interval notation. 6 6 6 11. Use the graph of = C() in Figure 6 to answer the following. Reasonable decimal approimations are acceptable. Figure 6. Graph of = C() Find C(). Solve C() =. Solve C() =. Solve C() >. State the domain of C using interval notation. State the range of C using interval notation. 6 = 1 6 6 6 = Part 1: No Calculator Page 3 of 6
6 1. Let H() = + 17 + 7. Find and state the domain of H using the notation of our choice. Simplif H(), making sure to state an restrictions. 13. Let v() = + 3 + 17 18. Find and state the domain of v using the notation of our choice. Simplif v(), making sure to state an restrictions. 1. Simplif each epression. If applicable, include an restrictions. 7 18 + 6 Q + 13Q + 9 Q 3 Q + 3 + + + + 9 + 0 Name: Q + Q + 13 Z + 3 Z + 13Z + 30 Z + 3Z Z 100 Part : Calculator Permitted You ma use a calculator (basic, scientific, or graphing), but ma not use an other electronic device. Show all our work so that: someone who wanted to know how ou found our answer can clearl see how. if ou make a mistake, I can see where it happened and determine how much partial credit ou should be awarded. The calculator should onl be used at the end of our problem-solving process, to calculate some decimal value. Round where appropriate. 1. A microbe colon has a population (measured in thousands of individuals) that can be modeled b P (t) = t3 t + 1, where t is in das since the microbes first colonized the location. Find and t + t + interpret P (.). 16. A patient ingests a pill, and the concentration of the drug in that person s bloodstream (in 1t mg/ml) after t hours is given b C(t) =. Find and interpret C(0.). t + t + 1 17. An object is thrown upward. It s height above ground level, h(t) (in meters), after t seconds can be modeled b h(t) =.9t + 31.t + 6.. What is the maimum height? When does this occur? When does the object hit the ground? Solve and interpret h(t) = 0. Solve and interpret h(t) = 80. Part : Calculator Permitted Page of 6
Answers 1. ( 1, 0) and (, 0) about (0,.) (, ) f() = ( 9 ) + (, ) (, ] g) is about 0. or about 3... ( 7, 0) and ( 1, 0) (0, 7). (, 9) g() = ( + ) 9 (, ) [ 9, ) g) There are no solutions to this equation. 3. (9, ) downward (, ) (, ]. ( 1, 9) upward (, ) [ 9, ). Q 8Q + 3 = 0 Q 8Q = 3 Q 8Q + 16 = 3 + 16 (Q ) = 13 Q = 13 or Q = 13 Q = + 13 or Q = 13 The solution set is { + 13, 13}. 6. + 3 7 = 0 + 3 = 7 + 3 + 9 16 = 7 + 9 16 ( + 3 ) = 8 16 + 9 16 ( + 3 ) = 16 + 3 = 16 + 3 = or + 3 = 16 or + 3 = = 3 + or = 3 { The solution set is 3 +, 3 }. 7. 10 10 (0, ) (, 0) ( 1, 0) ( 1, 0) (3., 0) 10 10 (, ) 9 10 10 10 (, 10 81 8 (0, 7) ) 8. Answers Page of 6
= ± (1)(10) (1) = = ± 1. The solution set is { i 1, +i 1 }. = 1± 196 ( 1)( 0) ( 1) same as { 1+i, 1 i }. = = 1±. The solution set is { 1 i = 6± 36 ()() () = = 3± 1. The solution set is { 3 i, 3+i }. 9. 1 + i 1 i i g) 10 9i 10. B(3) 1. = 1 or = This equation has no solutions. [ 1, ] [ 3, ) About [0, 6.], 1+i }, which is the 3 + i 9 11i 3 6i 6 + i 1 7i 0 + i h) i) j) 1 11. C() 1.. 3...3 or 6.6. About (,.). (, ) (, ) (, 1) (1, ) 1. (, 9) ( 9, 8) ( 8, ) H() = 8 13. (, 18) ( 18, 1) (1, ), where 8 v() = + + 9 + 18, where 1 1. + 6, where and 9 ( + 1)( + ), where and and, where Q 13 and Q and Q Q 0 Z 10, where Z 3 and Z 10 Z(Z + 3) 1. P (.) 1.31. After. das, there are about 1.31 thousand microbes (about 1310). 16. C(0.) =.8. After half an hour, the drug concentration in the patient s blood is.8 mg/ml. 17. After about 3.0 seconds, the object reaches its maimum height of 6.8 meters. The object hit the ground after about 6.61 seconds. t 1.3 and t.06. After about 1.3 seconds the object reaches a height of 0 meters in the air. Later, at about.06 seconds after launch, the object returns to being 0 meters high on its wa down. This equation has no solutions. The object never reaches 80 meters high. Answers Page 6 of 6