MATH U2

Which of the following inequalities is the same as 3w2−w−4<0? Correct (4−3w)(1+w)<0 (4−3w)(1+w)>0 (3w+4)(w−1)>0 (3w+4)(w−1)<0

(4−3w)(1+w)>0

If one test interval is −2<x<6−2<x<6, which of the following numbers can be test numbers in that interval? Correct −1 −3 8 4

-1 4

The base of a triangle is 2 cm more than its height. Its area does not exceed 84 cm2. If h is the height of the triangle, what are the critical numbers of the quadratic inequality that represents the problem? Correct 12 and 14 -14 and 12 -14 and -12 -12 and 14

-14 and 12

What is the solution of 6s2+11s≤−3? Correct 13≤s≤32 -3/2 ≤ s ≤ -1/3 s≤−13−32 −13

-3/2 ≤ s ≤ -1/3

Which of the following numbers satisfy the quadratic inequality (x+2)2<25? Correct −8 0 3 254

0

The leg of a right triangle is 1 unit less than thrice its other leg. Its area should not be greater than 210 square units. What is the interval of possible values for the shorter leg? Let x be the shorter leg. Correct −353≤x≤12 0<x≤12 12≤ x≤ 35 x>12

0<x≤12

Which of the following numbers is part of the solution set of x2−x−2<0? Correct 2 3 1 −4

1

Categorize the following.

12x2<0.5x2+x Not Quadratic Inequality x2(x−3)+2x(x−4)=0 Not Quadratic Inequality (x−√2)(x+√2)≥0 Quadratic Inequality 4x(x+17)≤13 Quadratic Inequality 8x2−4x(2x+3)>17 Not Quadratic Inequality

What is the degree of a quadratic inequality?

2

The sum of two positive integers is 86 while their product is at most 1800. Which of the following pairs of numbers is not part of the solutions of the problem? Correct 40 and 46 35 and 51 36 and 50 20 and 66

40 and 46

The area of a rectangle is at least 560 square inches. The length is 3 inches more than twice the width. If w represents the width of the rectangle, which of the following expressions represent its length? Incorrect 2w+3 2w−3 3w−2 3w+2

2w+3

Which of the following numbers satisfy the quadratic inequality x2+3x−10>0? Correct 2 −2 3.4 −5

3.4

What are the critical numbers of the quadratic inequality 5a2+a≤a2+5a+3? Correct 3/2 −1/2 −3/2 1/2

3/2 −1/2

A businessman is looking for a rectangular lot that is at least 1500 m2 and he only has fencing material for 160m. Find the possible the values of the length of the lot. Correct l≤30∪l≥50 l=30 30 ≤ l ≤ 50 l=50

30 ≤ l ≤ 50

A businessman is looking for a rectangular lot that is at least 1500 m2 and he only has fencing material for 160m. Find the possible the values of the width of the lot. Correct w≤30 or w≥50 w=30 30 ≤ w ≤ 50 w=50

30 ≤ w ≤ 50

Which of the following is not a quadratic inequality? Correct 4x+3x−5>0 x2+3x−40≥0 5x(x−3)<0 3x2−3x+3≤49

4x+3x−5>0

For what numbers does the inequality x2<0 hold true? Correct Positive numbers Negative numbers No solution. All real numbers except 0.

No solution.

The sum of two positive integers is 86 while their product is at most 1800. If x is one of the integers, which quadratic inequality represents the problem? Correct x(86−x)≥1800 x(86−x)≤1800 x(86−x)>1800 x(86−x)<1800

x(86−x)≤1800

Which of the following quadratic inequalities has a solution of x<−3x or x>4 ? Correct x2−x−12>0 x2−x−12≤0 x2−x−12≥0 x2−x−12<0

x2−x−12>0

If −3 and 4 are the critical numbers of the inequality, which of the following are the possible test intervals? Incorrect x>4 −3 x<4 x<−3

x>4 x<−3

Which of the following is not a quadratic inequality? Incorrect x2≥1 5x(x−3)−3(x+4)>27 x2−3x+4=0 (x+15)(x−7)>5

x^2 - 3x + 4 = 0

What is the solution set of the quadratic inequality 2x2−3x−14<0? Correct −2<x<7/2 x<−2 x<−2or x>7/2 x>7/2

−2 < x < 7/2

The sum of two positive integers is 86 while their product is at most 1800. Which symbol will you use to represent the inequality? Correct > < ≤ ≥

≤

The area of a rectangle is at least 560 square inches. The length is 3 inches more than twice the width. What symbol will you use to represent the inequality? Correct < ≥ ≤ >

≥

Which of the following are the critical numbers of the quadratic inequality 2y2+5y+1≥4? Correct 3 1/2 −3 −12

1/2 -3

Which value of k will not make 0.25w2+2w>kw2−4 a quadratic inequality? Correct 1/4 −1/4 2 1/2

1/4

Which symbol is not used to describe a quadratic inequality? Correct ≤ > < =

=

For what numbers does the inequality x2>0 hold true? Correct Negative numbers Positive numbers All real numbers except 0 No solution

All real numbers except 0

To solve a quadratic inequality, which of the following should you find first? Correct test intervals critical numbers test numbers inequality symbol

critical numbers

The base of a triangle is 2 cm more than its height. Its area does not exceed 84 cm2. Which quadratic inequality models the given problem? Correct h2+2h−168≤0 h2+2h−168<0 h2+2h−168≥0 h2+2h−168>0

h2+2h−168≤0