Algebra Questions

1 Find the exact value of the following logarithmic expression

For y f x 6x 5 x 3 and Ax 4 find a Ay for the given x and Ax values b dy f x dx c dy for the given x and Ax values a Ay Round to four decimal places as needed

Let C and C be two biased coins such that the probabilities of getting head in a single toss are and 13 respectively Suppose a is the number of heads that appear when C is tossed twice independently and suppose is the number of heads that appear when C is tossed twice independently Then probability that the roots of the quadratic polynomial x ax are real and equal is C 1 1 2 A 40 81 B 20 81 WIN 1 D 4

A polynomial has the following real zeros 2 crossing 3 touching and 7 crossing What is the smallest degree that the function can have 3 02 05

2x x 3x 3x x is equivalent to A 5x 3 5x 2x C 6x 3x D 4x 3x 3x E 7

11a Write an expression and combine like terms the sum of twice x and 5 times y is added to the difference of 5x and 4y 11b Evaluate your expression for x 2 and y 4

a 3x 4 5x

b Find the sum of 3x 4 and 2x 10

9 Combine like terms in the expression 3x4 2x8 5x

c 4x 10x 8y 6y

10 Combine like terms below 3x4x2 2x 4x2 2x 5x 8

Use the parent function f x b to graph h 1 11 The domain of h is The range of his The equation of the

3 a 8 pts If a and b are positive numbers find the maximum value of f x x 1 x 0 x 1 b 8 pts Find the maximum and minimum values of f x x cot x 2 on the interval T 3 5 3

1 Approximate the following value using a calculator Round the solution to four decimal places if necessary 2 Note No work needed this question ensures a student is using a calculator properly

4 It is known for a quadratic function f that f 11 f 7 55 Find the axis of symmetry of f x

10 15 n m On m 1 10 n m 3 10 Given the following graph what is the relationship between the degree of the numerator n and the degree of the denominator m 15 Activate Wine Go to Settings to

In Problems 11 and 12 evaluate each expression using the graphs of y f x and y g x shown in the figure 11 y g x a gof 1 b gof 0 c fog 1 d fog 4 1 3 1 1 2 YA 6 4 2 2 1 4 2 2 2 5 4 3 1 1 1 4 2 2 6 5 7 5 4 2 7 3 6 2 8 4 5 1 1 6 y f x 8 X

Match each function with its graph Ay 1 0 14 TO X T Q y cos 2x AY 2 1 0 1 2 TO 2T Drag each graph above to match the function below y sinx y cos x y 2 sin x 1 0 1 2 4 X y sin 2x y 2 cos x Ay 2 1 0 1 2 T 2 Q Ay 1 0 1 R x Q 2x 1 0 14

Find a calculator approximation of the following Be sure your calculator is in radian mode csc 6 7464 This question 4 point s pc csc 6 7464 Round to four decimal places

The function graphed is of the form y a sin bx or y a cos bx where b 0 Determine the equation of the graph y Type an expression using x as the variable 4 NON 2 0 2 4 6 R XA 3x 2 o 5

3 Selected values of a quadratic function g are given in the table Write the function g in the most appropriate form using the given information 2 8 0 5 6 1 0 2 15

1 y sin x 6 1 What is the period of the function y sinx Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression 1 What is the amplitude of the function y sinx Type an integer or a simplified fraction Which of the following is the correct graph of the function y sinx O A 121 2 2 V 12x OB Ay 2 2 X CO tx O C 12T 2 A 12n Ly OD A 2 i

Graph the following function over the interval 2 2n Give the amplitude y 4sin x Which of the following is the correct graph of the function y 4sin x A 21 OB What is the amplitude of the function y 4sin x Type an integer or a simplified fraction 27 8 y 12T O C 2 Ay 2x

Solve the system of equations using the inverse of the coefficient matrix of the equivalent matrix equation x y z 0 2y z 1 6 2x 3y The solution is Type an ordered thple Type an integer or a simplified fraction XX

Find the measure in radians of the central angle The area of a sector is 12 sq units Q Picture is not drawn to scale The measure is radian s Type an integer or decimal rounded to the nearest tenth as needed

K Find the exact function value CSC CSC T T BOXED Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

Find the exact value of tan Choose the correct answer below O A 1 OB 0 OC 3 OD Undefined OE 3 3 3 20 O F

Convert the radian measure to degrees 16 15 This que 16T 15 Type an integer or 0

Use the following information to determine cos 2x Answer cos x and sin x is positive 4

Solve the system of equations by using the inverse of the coefficient matrix of the equivalent matrix equation x 4y 23 7x 5y 4 The inverse of matrix A A is

Solve the system of equations using the inverse of the coefficient matrix of the equivalent matrix equation x y z 0 2y z 1 5 4x 3y The solution is D Type an ordered triple Type an integer or a simplified fraction

11b Evaluate your expression for x 2 and y 4

6 Write an expression and combine like terms in the expression 4 times y de creased by triple y increased by double y

11a Write an expression and combine like terms the sum of twice x and 5 times v is added to the difference of 5x and 4y

4 Simplify by combining like terms 3x 4x 10 2x 5x 2

3 Combine like terms x y 5x 5y

4s 37 19x 3r is equivalen to F 148 11 G 108 21 H 25 22 J 14 11 K 40 24

Which of the following expressions is equivalent to the one shown below 5m 120 14r 9r A 14m 2 R 14m 27 C 14m 3 D 14M 28 E 45w 168

5 Find the sum of 3x 2 and 2x 4

2 Combine like terms in the following 2 4a 6 3a 10a

1 Combine like terms in the expression 3x 4 2x 6

3 Evaluate 3 2x y if x 3 and y 3 3 x 7 3

D 5 5 8x 4X6x x 4 A 21 38 41x 6 B 7x14x 4x 3 C 20x 34x 26x 4 D 48x 32x 28x 16 6 6 8k 7X4 2k 2 A 428 78 60k 24 B 16 34 35 C 11 238 3 D 324 124 30 14

8 10 8 8b 3 8b 5b 8 A 6b 56 246 7 B 216 3462 26 8 C 86 33b2 3b 4 D 64b 64b 49b 24 10 7b 6b 7 6b 8b 5 A 16b 546 92b 54b 40 B 16b 18b 40 C 426 92b 125b 86b 35 D 16b 42b 56b 6b 40

7 7 2k 8 6k 5k 8 A 12k 38k 24k 64 B 12k 34k2 30k 8 C 10k 44k 12k 16 D 25k 48 34k 9 7b b 4 3b 4b 1 A 2164 25b b 17b 4 B 216 46 4 C 1664 206 346 8b 5 D 126 326 7b 36b 15

2 4 2 2n 5 8n 2 A 16n 36n 10 B 28n 45n 18 C 28n 3n 18 D 28n 18 4 n 4 2n 7 A 2n n 28 B 2n 28 C 2n 15n 28 D 2n 15n 28

How much interest will you have to pay for a credit card balance of 986 that is 1 month overdue if a 16 annual rate is charged You will have to pay V CAN V MER Wh ALAND TE PANTA M A in interest Round to two decimal places

Listen Write an equation of the line that passes through 2 7 and is perpendicular to the line y x 9 An equation of the perpendicular line is

Write an equation of the line that passes through 7 1 and is parallel to the line y x 9 An equation of the parallel line is

Write in point slope form an equation of the line that passes through the point 5 8 with slope 2 0 0 0