Math SL 1 Chapter 2/3
Tell whether the following statement is true or false and justify your answer: It is possible for the graph of a cubic function to be tangent to the x-axis at x= -2. x=1. and x=6.
page 89 #5 (2.7)
Give a set of inequalities that defines the shaded regions.
page 106 Class Exercise #10 (3.3)
Give a set of inequalities that defines the shaded regions.
page 106 Class Exercise #8 (3.3)
Give a set of inequalities that defines the shaded regions.
page 106 Class Exercise #9 (3.3)
Graph the solution set of the given system of inequalities: x < 0 3x-2y ≤ -6
page 107 Written Exercise #19 (3.3)
Graph the solution set of the given system of inequalities: y ≥ x^2-2 y < x
page 107 Written Exercise #21 (3.3)
Graph the solution set of the given system of inequalities: y ≤ 6-x^2 2x-y ≤ -3
page 107 Written Exercise #22 (3.3)
Graph the solution set of the given system of inequalities: 0 ≤ x ≤ 3 0 ≤ y ≤ 2
page 107 Written Exercise #25 (3.3)
Graph the solution set of the given system of inequalities: |x| < 3 |x| < 1
page 107 Written Exercise #27 (3.3)
Find the remainder when x^5-2x^3+x^2-4 is divided by a. x-1 b. x+1 c. x-2 d. x+2
page 61 #1 (2.2)
Determine whether x-1 or x+1 is a factor of x^100-4x^99+3
page 61 #11 (2.2)
Determine which of the following are factors of P(x)= x^3-5x^2+3x+9. a. x-1 b. x+3 c. x-3
page 61 #13 (2.2)
Show that x-a is a factor of x^n-a^n for any positive integer n.
page 61 #15 (2.2)
With the given polynomial and one of its roots, find the remaining roots; 2x^3-5x^2-4x+3= 0; root: x=3
page 61 #19 (2.2)
With the given polynomial and one of its roots, find the remaining roots; 6x^3+11x^2-4x-4=0; root: x=-2
page 61 #20 (2.2)
Find the quotient and the remainder when x^3-2x^2+5x+1 is divided by (x-1)
page 61 #3 (2.2)
Find the quotient and the remainder when x^4-2x^3+5x+2 is divided by (x+1)
page 61 #5 (2.2)
Sketch a graph of the equation y= (x+1)(x-2)(x-4)
page 66 #1 (2.3)
Factor the polynomial function f(x)= x^3-4x and sketch its graph
page 66 #13 (2.3)
Factor the polynomial function f(x)= x^4-x^2 and sketch its graph
page 66 #15 (2.3)
Factor the polynomial function f(x)= x^4-2x^3+2x-1 and sketch its graph
page 66 #17 (2.3)
Factor the polynomial function f(x)= 4x^4-24x^3+35x^2+6x-9 and sketch its graph
page 66 #18 (2.3)
Give an equation for the polynomial graph shown.
page 66 #21 (2.3)
Give an equation for the polynomial graph shown.
page 66 #22 (2.3)
Sketch a graph of the equation y= -x(x+5)(x+3)
page 66 #3 (2.3)
Sketch a graph of the equation y= (x+1)^3(x-2)
page 66 #9 (2.3)
Give an equation for the polynomial graph shown.
page 67 #23 (2.3)
Give an equation for the polynomial graph shown.
page 67 #24 (2.3)
A cubic equation with integral coefficients has no quadratic term. Is one root is 2+ i√5, what are the other roots?
page 89 #17 (2.7)
Find a cubic equation with integral coefficients that has the given roots: 2 and 4 + i
page 89 #19 (2.7)
Find a cubic equation with integral coefficients that has the given roots: (4+ i√3)/2 and -1
page 89 #21 (2.7)
Find a quartic equation with integral coefficients that has roots 5-i√3 and i.
page 89 #23 (2.7)
Find integers c and d such that the equation x^3+cx+d=0 has 1+√3 as one of its roots.
page 89 #25 (2.7)
Tell whether the following statement is true or false and justify your answer: The roots of a certain quartic equation are ±1/2, 0. and 1+i.
page 89 #3 (2.7)
a^3+2a^2-4a-8 > 0
page 103 #15 (3.2)
2x^3+x^2-5x < -2
page 103 #19 (3.2)
(x-1)(x-2)(x-4) > 0
page 103 #3 (3.2)
x^2-2x-15 < 0
page 103 #7 (3.2)
Solve the inequality using a graphing calculator of computer. x^3+2x^2-3x-6 > 0
page 104 #31 (3.2)
Solve the inequality using a graphing calculator of computer. 2x^3-5x^2+1 ≥ 0
page 104 #33 (3.2)
(x-3)(x+4) > 0
page 103 #1 (3.2)
2x^2+5x-7 ≤ 0
page 103 #11 (3.2)
x^4- 3x^2-10 > 0
page 103 #13 (3.2)
As the diagram indicates, a manufacturer cuts squares from the corners of an 8 cm by 14 cm piece of sheet metal and then folds the metal to make an open-top box. a. Show that the volume of the box is: V(x)= x(8-2x)(14-2x) b. What is the domain of V? c. Find the approximate value of x that maximizes the volume. Then give the approximate maximum value.
page 71 #1 (2.4 Cubic)
A farmer wants to make a rectangular enclosure using a wall as one side and 120 m of fencing for the other three sides. a. Express the area in terms of x and state the domain of the area function. b. Find the value of x that gives the greatest area.
page 71 #1 (2.4 Quadratic)
The publisher of a magazine that has a circulation of 80,000 and sells for $1.60 a copy decides to raise the price of the magazine because of increased production and distribution costs. By surveying the readers of the magazine, the publisher finds that the magazine will lose 10,000 readers for each $.40 increase in price. What price per copy maximizes the income?
page 71 #11 (2.4 Quadratic)
Suppose you have 102 m of fencing to make two side-by-side rectangular enclosures, as shown. What is the maximum area that you can enclose?
page 71 #3 (2.4 Quadratic)
If a ball is thrown upward from a building 30 m tall and the ball has a vertical velocity of 25 m/s, then its approximate height above the ground t seconds later is given by h(t)= 30+25t-5t^2. a. After how many seconds does the ball hit the ground? b. What is the domain of h? c. How high does the ball go?
page 72 #10 (2.4 Quadratic)
In a rectangular piece of cardboard with perimeter 20 ft, three parallel and equally spaces creases are made, as shown at the left below. The cardboard is then folded to make a rectangular box with open square ends. a. Show that the volume of the box is V(x)= x^2(10-4x) b. What is the domain of V? c. Find the approximate value of x that maximizes the volume. Then give the approximate maximum volume.
page 72 #3 (2.4 Cubic)
In a rectangular piece of cardboard with perimeter 30 in., two parallel and equally spaces creases are made, as shown at the right above. The cardboard is then folded to make a prism with open ends that are equilateral triangles. a. Show that the volume of the prism iix V(x)= ((√3/4)x^2)(15-3x). b. What is the domain of V? c. Find the approximate value of x that maximizes the volume. Then give the approximate maximum volume.
page 72 #4 (2.4 Cubic)
A rectangular piece of sheet metal with perimeter 50 cm is rolled into a cylinder with open ends, as shown at the right. a. Express the volume of the cylinder as a function of x. Then give the domain of this function. b. Find the approximate value of x that maximizes the volume. Then give the approximate maximum value.
page 72 #5 (2.4 Cubic)
A cylinder is generated by rotating a rectangle with perimeter 12 in. about one of its sides, as shown at the right. a. Express the volume of the cylinder as a function of x. Then give the domain of this function. b. Find the approximate value of x that maximizes the volume. Then give the approximate maximum value.
page 72 #6 (2.4 Cubic)
A cylinder is inscribed in a sphere with radius 5, as shown at the right. a. Express the volume of the cylinder as a function of x. Then give the domain of this function. b. Find the approximate value of x that maximizes the volume. Then give the appropriate maximum value.
page 72 #7 (2.4 Cubic)
A cone is inscribed in a sphere of radius 6, as shown at the right. a. Express the volume of the cone as a function of x. Then give the domain of this function. b. Find the approximate value of x that maximizes the volume. Then give the approximate maximum value.
page 72 #8 (2.4 Cubic)
Find the real roots to the nearest tenth of x^3-5x^2-3x-7=0 using a GDC.
page 78 #7 (2.5)
Find the real roots to the nearest tenth of 1.2x^4-0.7x^2=3.6x using a GDC.
page 78 #9 (2.5)
Tell whether the equation is: (a) a polynomial equation that can be solved by grouping terms, or (b) a polynomial equation that has a quadratic form. Then solve the equation x^4-4x^2-12=0
page 83 #1 (2.6)
Tell whether the equation is: (a) a polynomial equation that can be solved by grouping terms, or (b) a polynomial equation that has a quadratic form. Then solve the equation x^3+6x^2-4x-24=0
page 83 #2 (2.6)
Tell whether the equation is: (a) a polynomial equation that can be solved by grouping terms, or (b) a polynomial equation that has a quadratic form. Then solve the equation 3x^3-16x^2-12x+64=0
page 83 #3 (2.6)
Tell whether the equation is: (a) a polynomial equation that can be solved by grouping terms, or (b) a polynomial equation that has a quadratic form. Then solve the equation x^4-7x^2-8=0
page 83 #4 (2.6)
Tell whether the equation is: (a) a polynomial equation that can be solved by grouping terms, or (b) a polynomial equation that has a quadratic form. Then solve the equation 2x^4= -7x^2+15
page 83 #5 (2.6)
Use the rational root theorem to solve each equation, giving all real and imaginary roots. x^3-x^2-x+1=0
page 84 #13 (2.6)
Use the rational root theorem to solve each equation, giving all real and imaginary roots. 3x^3-4x^2-5x+2=0
page 84 #17 (2.6)
Use the rational root theorem to solve each equation, giving all real and imaginary roots. x^4+2x^3-2x^2-6x-3=0
page 84 #19 (2.6)
Show that the equation x^3+x^2-3=0 has no rational roots, but that it does have an irrational root between x=1 and x=2.
page 84 #29 (2.6)
Tell whether the following statement is true or false and justify your answer: Some cubic equations have no real roots.
page 89 #1 (2.7)
Find the sum and product of the roots of the given equation: 3x^3+5x^2-x-2=0
page 89 #11 (2.7)
Find a quartic equation with integral coefficients that has the given roots: 1±i
page 89 #13 (2.7)
Find a quartic equation with integral coefficients that has the given roots: 3± √2
page 89 #15 (2.7)
Tell whether the following statement is true or false and justify your answer: Suppose P(x) is a polynomial with rational coefficients, and b is rational but the square root of b is irrational. If the square root of b is a root of the equation P(x)=0, then the negative square root of b is also a root.
page 89 #7 (2.7)
Find the sum and product of the roots of the given equation: 4x^2-3x+6=0
page 89 #9 (2.7)
Solve the given equation or inequality and graph its solution. |x| < -8
page 98 #13 (3.1)
Solve the given equation or inequality and graph its solution. (15-6x)/3 > 5
page 98 #3 (3.1)
Solve the given equation or inequality and graph its solution. (x+2)/(4) - (2-x)/(3) + (4x-5)/(6) < 4
page 98 #9 (3.1)
|x-4| < 3
page 99 #15 (3.1)
|x+7| ≥ 3
page 99 #17 (3.1)
|x-8| = 4
page 99 #19 (3.1)
|2x-4| ≤ 5
page 99 #21 (3.1)
|4x+8| ≤ 9
page 99 #23 (3.1)
Plant experts advise that gardenias kept indoors must have high humidity, plenty of sunlight during the day, and cool temperatures at night. The recommended nighttime temperature range in degreed Fahrenheit is 60 degrees ≤ F ≤ 65. Given that C = (5/9)(F-32), express the corresponding temperature range in degrees Celsius.
page 99 #25 (3.1)
