Students Currently in Algebra 2 Maine East Math Placement Exam Review Problems

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1 Students Currently in Algebra Maine East Math Placement Eam Review Problems The actual placement eam has 100 questions 3 hours. The placement eam is free response students must solve questions and write answer in space provided. No calculator is allowed everything is pencil and paper. All answers must be in eact simplified form. Linear Systems and Matrices 9 questions Quadratic Equations and Factoring 5 questions Polynomials and Polynomial Functions 3 questions Rational Eponents and Radical Functions 15 questions Eponential and Logarithmic Functions 1 questions Rational Functions 7 questions 1) Solve 4y = y = 8 ) Shade the region defined by y 3 y 3 4 3) A triangular has vertices of ( 0,0 ), ( 0,5 ), and (,0 ). Write a system of three linear inequalities to describe this triangular region. 4) Solve: 3y+ z = 10 y+ z = 13 z = 5

2 5) Solve: + y+ z = 9 + y z = 1 + y z = 0 6) Subtract: ) Perform the scalar multiplication: ) Perform the matri multiplication: ) Evaluate the determinant of ) Evaluate the determinant of

3 y = ) Identify the verte of the parabola ( ) 1) Identify the verte of the parabola y = ( 3)( + 1) 13) Identify the verte of the parabola y = ) Write the quadratic function y ( 4)( ) = + 9 in standard form. 15) Write the quadratic function ( ) y = in standard form. 16) Solve: = 0 by factoring. 17) Solve: 1 ( 5) = 9 by etracting square roots ) Solve: + = 5 by using the quadratic formula.

4 19) Given 8+ c A) Find the value of c that makes the epression a perfect square trinomial. B) Then write the epression as the square of a binomial. ( ) 0) Find the zeros of f = ) Plot ( 3+ i) in the comple plane. ) Find the absolute value of ( i) 3) Simplify ( 4+ 3i) ( + 4i) 4) Simplify 4i( 6 i) 5) Simplify ( 1+ i) ( 11 i) 3i 6) Simplify ( 1+ i )

5 7) Simplify i 1 i 8) Simplify ) Complete the square in order to convert y = into verte form. 30) Complete the square in order to convert y = into verte form. 31) Evaluate the discriminant of the following and then describe solutions (real/nonreal, different/same) A) 4+ 10= 0 B) + 3 6= 0 C) = 0 3) When an object is dropped, the model ( ) h t = 16t + h describes the height (feet) of the object as a function of time (seconds). The initial height is represented by. If an object is dropped from a height of 30 feet, in how many seconds will it hit the ground? 0 h 0 33) Use the quadratic formula to solve + =.

6 34) Solve the quadratic inequality ) Solve the quadratic inequality ) Write a quadratic function in verte form given verte ( 1, 4) and point (,) 37) Write a quadratic function in intercept form given -intercepts &1 and point ( 1, 6) 38) Write a quadratic form in standard form given points ( 0, 4 ), ( 1, 5 ), (,10) 39) Epand ( ) + y 40) Factor completely: ) Factor completely: 4 4 3

7 4) Factor completely: ) Factor completely: ) Factor completely: ) Factor completely: ) Factor completely: ) Factor completely: ) Evaluate 10 (hint: use fingers and count to 10 as you keep doubling, 4, 8, 16, etc.) 49) Simplify 50) Evaluate

8 51) Evaluate ( ) 5) Evaluate 53) Evaluate ( 5) ( 5) ) Evaluate ) Evaluate ( ) 56) Evaluate ) Simplify ( 3) 3 58) Simplify 9 y 7 y 5 0 y 1

9 59) Simplify ( mw 4 ) m + w ) Subtract ( ) ( 6 + 1) 61) Multiply ( + 5)( ) 6) Multiply ( )( 1)( + 3 ) 63) Solve = ) Divide ( ) by ( 4) 3 65) Divide ( ) by ( + ) 3 ( ) = + + given that ( ) 66) Factor f f 4 = 0

10 f = ) List all the possible rational zeros of ( ) ) State the degree of the following polynomial: f ( ) = ( + 3)( ) ( + 1) 69) A third degree polynomial function has zeros of nd ( 4i) List the other zero. 3 a. 70) Write a polynomial function of least degree that has a lead coefficient of 1, real coefficients, and zeros of 4 and. 5i y 71) Draw a rough sketch of the polynomial function 1 f ( ) = ( + 4)( + 1) ( 3 ) 1 7) The graph of a cubic polynomial function has -intercepts of 3,, and 5. The graph also passes through the point ( 0, 15). Write the cubic polynomial function in intercept form. 73) Simplify 3/ 9

11 74) Simplify 3 /5 75) Simplify 1/ 1/ ) Simplify ) Simplify ) Simplify y (assume all variables are positive) 79) Simplify 5 5a 5 bc 9 13 (assume all variables are positive) 80) Simplify (assume all variables are positive) 81) Simplify

12 8) Epand ( + 3) 83) Multiply ( 3)( 3+ ) 84) Simplify 1 85) Simplify ) Let f ( ) = 1 g( ) = 3 A) Find the composition f ( g( )) ( ) B) Find the composition g f ( ) ) If f ( ) = +, find the inverse f ( ). 88) Solve 3 4= 0

13 89) Solve 3/ = 50 90) Solve 4 7+ = 5 91) Solve 3+ = 0 9) Solve 4= 93) Simplify and write in radical form: 1/ 5/3 5 y (assume all variables are positive) 94) Simplify and write using rational eponents: y (assume all variables are positive) 95) State the domain and range of y ( ) = ln + 5

14 96) State the domain and range of y = ) A town has a population of 75,000 and the population increases % every year. Write an eponential growth model. 98) You purchase a car for $5,000 and the value decreases 15% every year. Write an eponential decay model. 99) Just set up the equation for the following do not evaluate. You deposit $500 in a bank that pays 0.8% annual interest, compounded quarterly. How much money will you have in 10 years? 100) Just set up the equation for the following do not evaluate. You deposit $1000 in a bank that pays.5% annual interest, compounded continuously. How much money will you have in 0 years? 101) Simplify 13 ( e ) e

15 10) Evaluate log ( 64 ) 103) Evaluate log ) Simplify log ) Find the inverse of y e + = 5 ( ) ( ) 106) Use log 0.4 and log to approimate 5 5 log ) Condense 1 ln 40 + ln + ln 108) Epand log 4 3y

16 109) Use the change of base formula to epress log3 7 in terms of common logarithms. 110) Solve 4 1 = 3 111) Solve ( ) 4ln + 3= 1 11) Solve 4 = 11 and report answer in terms of natural logs. 113) You take soup off the stove at 00 deg F. The kitchen is at 75 deg F F The cooling rate of the soup is r =. min In how many minutes will it take the soup to cool to 100 deg F?

17 114) Write an eponential function whose graph passes through ( ) ( ) 3,18 and 1,. 115) Write a power function whose graph passes through (,16 ) and ( 1, 4 ). 116) The intensity of light varies inversely as the square of the observers distance from the light source. The light intensity is 9 lumens when the observer is 10 meters from the light source. If the observer is 3 meters from the light source, what is the light intensity? 117) State the domain and range of y = ) Given y = + 8, find the following: A) Vertical Asymptotes B) Horizontal Asymptote

18 119) Given y = 3, find the following: 4 A) Vertical Asymptote B) Slant Asymptote 10) Simplify ) Add ) Simplify: ) Solve: + =

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