Question 1

Solve the equation   = 4.

Accepted Answer

A)  x = -   or x =   
B)  x = -   
C)  x =   
D)  x =   
E)  x = -   or x =   
A)  x = -   or x =   
B)  x = -   
C)  x =   
D)  x =   
E)  x = -   or x =   A

Question 2

Write an equation for the line through P (0,a) with slope m = -1.

Accepted Answer

A)  x + y = a 
B)  x - y = v 
C)  x + y = 2a 
D)  x + y + a = 0 
E)  y - x = a 
A)  x + y = a 
B)  x - y = v 
C)  x + y = 2a 
D)  x + y + a = 0 
E)  y - x = a A

Question 3

Determine the intercepts and sketch the graph of the line   -   = 1.

Accepted Answer

The x-intercept is 3 and the y-intercept is -4.

Question 4

Simplify the expression csc x -   .

Accepted Answer

A)  cot x 
B)  cos x 
C)  sin x 
D)  tan x 
E)  1 
A)  cot x 
B)  cos x 
C)  sin x 
D)  tan x 
E)  1

Question 5

Sketch the graph of the function f(x) =   .

Accepted Answer

The answer of Sketch the graph of the function f(x)...

Question 6

Find the points of intersection of the pair of curves xy = 3 and y = x2. Give your answer in decimal form rounded to two decimal places.

Accepted Answer

A)  (1.44, 2.08) 
B)  (1.44, 2.08) and (-1.44, -2.08) 
C)  (1.44, 2.08) and (-1.44, 2.08) 
D)  (-1.44, -2.08), (1.44, -2.08), (1.44, 2.08), and (-1.44, 2.08) 
E)  These curves do not intersect. 
A)  (1.44, 2.08) 
B)  (1.44, 2.08) and (-1.44, -2.08) 
C)  (1.44, 2.08) and (-1.44, 2.08) 
D)  (-1.44, -2.08), (1.44, -2.08), (1.44, 2.08), and (-1.44, 2.08) 
E)  These curves do not intersect.

Question 7

What is the remainder if x3 + 2 is divided by x2 - 1?

Accepted Answer

A)  x + 2 
B)  x + 1 
C)  2 
D)  1 
E)  x 
A)  x + 2 
B)  x + 1 
C)  2 
D)  1 
E)  x

Question 8

What happens to the line y = mx + b when it is reflected in the origin?

Accepted Answer

A)  y-intercept changes sign, slope remains unchanged 
B)  y-intercept remains unchanged, slope changes sign 
C)  y-intercept and slope both change sign 
D)  y-intercept and slope both remain unchanged 
A)  y-intercept changes sign, slope remains unchanged 
B)  y-intercept remains unchanged, slope changes sign 
C)  y-intercept and slope both change sign 
D)  y-intercept and slope both remain unchanged

Question 9

Solve the inequality x3 < 9x, giving the solution set as an interval or union of intervals.

Accepted Answer

A)  (-   , -3)   (0, 3) 
B)  (-   , 3)   (3, 9) 
C)  (-   ,3) 
D)  (-   ,-3) 
E)  (9,    ) 
A)  (-   , -3)   (0, 3) 
B)  (-   , 3)   (3, 9) 
C)  (-   ,3) 
D)  (-   ,-3) 
E)  (9,    )

Question 10

Write an equation for the line through P (2, -1) with slope m = 4.

Accepted Answer

A)  4x - y - 9 = 0 
B)  y = 4x + 9 
C)  4x + y = 7 
D)  y = 2x - 5 
E)  y = 2x + 5 
A)  4x - y - 9 = 0 
B)  y = 4x + 9 
C)  4x + y = 7 
D)  y = 2x - 5 
E)  y = 2x + 5

Question 11

Find the points of intersection of the pairs of curves y = x2 - 4 and y = 2x -1.

Accepted Answer

A)  (-1,-3) and (3, 5) 
B)  (-1,-3) 
C)  (3, 5) 
D)  (-1,-3), (0, -1), and (3, 5) 
E)  These curves do not intersect. 
A)  (-1,-3) and (3, 5) 
B)  (-1,-3) 
C)  (3, 5) 
D)  (-1,-3), (0, -1), and (3, 5) 
E)  These curves do not intersect.

Question 12

Sketch the graph of the function f(x) =   .

Accepted Answer

The answer of Sketch the graph of the function f(x)...

Question 13

Determine whether the function f(x) =   + 1 - 3 cos(5x) is even, odd, or neither.

Accepted Answer

A)  even 
B)  odd 
C)  both even and odd 
D)  neither even nor odd 
A)  even 
B)  odd 
C)  both even and odd 
D)  neither even nor odd

Question 14

Find the roots of the polynomial x4 - 1. Give the multiplicity of each.

Accepted Answer

A)  Roots are x = 1, x = -1, x = i, x = -i, each with multiplicity 1. 
B)  Roots are x = 1, x = -1, each with multiplicity 2. 
C)  Root is x = 1 with multiplicity 4. 
D)  Roots are x = 1, x = i, each with multiplicity 2. 
E)  Roots are x = i, x = -i, each with multiplicity 2. 
A)  Roots are x = 1, x = -1, x = i, x = -i, each with multiplicity 1. 
B)  Roots are x = 1, x = -1, each with multiplicity 2. 
C)  Root is x = 1 with multiplicity 4. 
D)  Roots are x = 1, x = i, each with multiplicity 2. 
E)  Roots are x = i, x = -i, each with multiplicity 2.

Question 15

For what value(s) of k is x + 1 a factor of the polynomial x6 + 2x4 + kx + 3?

Accepted Answer

A)  k = 6 
B)  k = -1 
C)  k = 0 
D)  k = 2 
E)  k = 1 and k = 0 
A)  k = 6 
B)  k = -1 
C)  k = 0 
D)  k = 2 
E)  k = 1 and k = 0

Question 16

Sketch the graph of the function f(x) =   + x - 1.

Accepted Answer

The answer of Sketch the graph of the function f(x)...

Question 17

How does the graph of y = - 4 -   relate to that of y = 4 +   ?

Accepted Answer

A)  It is rotated   about the origin. 
B)  It is reflected in the y-axis. 
C)  It is reflected in the x-axis. 
D)  They represent the same graph. 
E)  These graphs are not related. 
A)  It is rotated   about the origin. 
B)  It is reflected in the y-axis. 
C)  It is reflected in the x-axis. 
D)  They represent the same graph. 
E)  These graphs are not related.

Question 18

Sketch the graph of the function f(x) = x - 2 +   .

Accepted Answer

The answer of Sketch the graph of the function f(x)...

Question 19

Factor the polynomial   + 8 completely into linear factors.

Accepted Answer

A)  (x + 2)(x - 1 -   i)(x - 1 +   i) 
B)  (x + 2)(x2 - 2x + 4) 
C)  x3 + 8 
D)  (x + 2)(x - 2)2 
E)  (x + 2)(x + 1 -   i)(x + 1 +   i) 
A)  (x + 2)(x - 1 -   i)(x - 1 +   i) 
B)  (x + 2)(x2 - 2x + 4) 
C)  x3 + 8 
D)  (x + 2)(x - 2)2 
E)  (x + 2)(x + 1 -   i)(x + 1 +   i)

Question 20

Describe the graph of the equation x2 + y2 = 3.

Accepted Answer

A)  circle centred at the origin with radius   
B)  circle centred at the origin with radius 3 
C)  circle centred at the origin with radius 9 
D)  line passing through the point (3, 0) 
E)  line passing through the point (0, 3) 
A)  circle centred at the origin with radius   
B)  circle centred at the origin with radius 3 
C)  circle centred at the origin with radius 9 
D)  line passing through the point (3, 0) 
E)  line passing through the point (0, 3)

Solve the equation = 4.

Write an equation for the line through P (0,a) with slope m = -1.

Determine the intercepts and sketch the graph of the line - = 1.

Simplify the expression csc x - .

Sketch the graph of the function f(x) = .

Find the points of intersection of the pair of curves xy = 3 and y = x². Give your answer in decimal form rounded to two decimal places.

What is the remainder if x³ + 2 is divided by x² - 1?

What happens to the line y = mx + b when it is reflected in the origin?

Solve the inequality x³ < 9x, giving the solution set as an interval or union of intervals.

Write an equation for the line through P (2, -1) with slope m = 4.

Find the points of intersection of the pairs of curves y = x² - 4 and y = 2x -1.

Sketch the graph of the function f(x) = .

Determine whether the function f(x) = + 1 - 3 cos(5x) is even, odd, or neither.

Find the roots of the polynomial x⁴ - 1. Give the multiplicity of each.

For what value(s) of k is x + 1 a factor of the polynomial x⁶ + 2x⁴ + kx + 3?

Sketch the graph of the function f(x) = + x - 1.

How does the graph of y = - 4 - relate to that of y = 4 + ?

Sketch the graph of the function f(x) = x - 2 + .

Factor the polynomial + 8 completely into linear factors.

Describe the graph of the equation x² + y² = 3.

Limits and Continuity

Differentiation

Transcendental Functions

More Applications of Differentiation

Integration

Techniques of Integration

Applications of Integration

Conics, Parametric Curves, and Polar Curves

Sequences, Series, and Power Series

Vectors and Coordinate Geometry in 3-Space

Vector Functions and Curves

Partial Differentiation

Applications of Partial Derivatives

Multiple Integration

Vector Fields

Vector Calculus

Differential Forms and Exterior Calculus

Ordinary Differential Equations

Filters

Exam 1: Preliminaries

Solve the equation = 4.

Write an equation for the line through P (0,a) with slope m = -1.

Determine the intercepts and sketch the graph of the line - = 1.

Simplify the expression csc x - .

Sketch the graph of the function f(x) = .

Find the points of intersection of the pair of curves xy = 3 and y = x2. Give your answer in decimal form rounded to two decimal places.

What is the remainder if x3 + 2 is divided by x2 - 1?

What happens to the line y = mx + b when it is reflected in the origin?

Solve the inequality x3 < 9x, giving the solution set as an interval or union of intervals.

Write an equation for the line through P (2, -1) with slope m = 4.

Find the points of intersection of the pairs of curves y = x2 - 4 and y = 2x -1.

Sketch the graph of the function f(x) = .

Determine whether the function f(x) = + 1 - 3 cos(5x) is even, odd, or neither.

Find the roots of the polynomial x4 - 1. Give the multiplicity of each.

For what value(s) of k is x + 1 a factor of the polynomial x6 + 2x4 + kx + 3?

Sketch the graph of the function f(x) = + x - 1.

How does the graph of y = - 4 - relate to that of y = 4 + ?

Sketch the graph of the function f(x) = x - 2 + .

Factor the polynomial + 8 completely into linear factors.

Describe the graph of the equation x2 + y2 = 3.

Limits and Continuity

Differentiation

Transcendental Functions

More Applications of Differentiation

Integration

Techniques of Integration

Applications of Integration

Conics, Parametric Curves, and Polar Curves

Sequences, Series, and Power Series

Vectors and Coordinate Geometry in 3-Space

Vector Functions and Curves

Partial Differentiation

Applications of Partial Derivatives

Multiple Integration

Vector Fields

Vector Calculus

Differential Forms and Exterior Calculus

Ordinary Differential Equations

Filters

Find the points of intersection of the pair of curves xy = 3 and y = x². Give your answer in decimal form rounded to two decimal places.

What is the remainder if x³ + 2 is divided by x² - 1?

Solve the inequality x³ < 9x, giving the solution set as an interval or union of intervals.

Find the points of intersection of the pairs of curves y = x² - 4 and y = 2x -1.

Find the roots of the polynomial x⁴ - 1. Give the multiplicity of each.

For what value(s) of k is x + 1 a factor of the polynomial x⁶ + 2x⁴ + kx + 3?

Describe the graph of the equation x² + y² = 3.