Grade 11 · Math · Algebra 2

11th grade Systems of inequalities with absolute value, and linear programming worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Systems of inequalities with absolute value, and linear programming

Grade 11 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

1.
Noah shades the graph of y ≥ |x − 2| + 1 together with y < −x + 9. Which point is in the shaded region?
- (4, 5)
- (6, 6)
- (0, 2)
- (3, 4)
2.
Pia shades the graph of y ≤ −|x + 1| + 6 together with y > x − 2. Which point is in the shaded region?
- (0, 3)
- (2, 0)
- (−1, 7)
- (3, 0)
3.
Ren shades the graph of y ≥ |x − 3| − 2 together with y < 4. Which point is in the shaded region?
- (8, 6)
- (3, −4)
- (7, 4)
- (3, 0)
4.
Zee shades the graph of y > |x + 2| together with y ≤ 6 − x. Which point is in the shaded region?
- (4, 7)
- (−6, 3)
- (1, 3)
- (−2, 3)
5.
Time 2x + 3y ≤ 24; paper x + y ≤ 9; at least 4 posters, x ≥ 4. Jun makes x posters and y banners. The figure lists the limits. Which limit does the plan (3, 5) break?
- 2x + 3y ≤ 24
- x + y ≤ 9
- The plan is allowed: it meets the limits
- x ≥ 4
6.
Soil x + 4y ≤ 24; pots x + y ≤ 9; at least 2 large plants, y ≥ 2. Luz sells x small and y large plants. The figure lists the limits. Which limit does the plan (3, 1) break?
- x + 4y ≤ 24
- y ≥ 2
- x + y ≤ 9
- The plan is allowed: it meets the limits
Lines x + y = 10 and 2x + y = 14 meet at a corner of Noah's bracelet-sale region. Profit is P = 3x + 2y dollars. What is P at that corner?
Lines x + y = 12 and 3x + y = 20 meet at a corner of Pia's bake-sale region. Profit is P = 5x + 2y dollars. What is P at that corner?
Lines x + 2y = 14 and x + y = 9 meet at a corner of Ren's kite-sale region. Profit is P = 4x + 3y dollars. What is P at that corner?
Lines 2x + y = 16 and x + y = 11 meet at a corner of Zee's poster-sale region. Profit is P = 6x + 2y dollars. What is P at that corner?

11th grade Systems of inequalities with absolute value, and linear programming worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Systems of inequalities with absolute value, and linear programming. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can tell whether a point is in a region bounded by a V and a line, and see why a strict boundary is left out.
I can write the limits of a story as a system and find every corner of the allowed region, including where two limits cross.
I can test every corner to find the best profit or least cost, and redo it when a price changes.

Standard: A-REI.D.12, A-CED.A.3

Words to know

region: All the points that pass every inequality.

corner: A point where two boundary lines meet.

constraint: A limit from the story, written as an inequality.

objective: The rule to make as big or as small as possible, like P = 4x + 3y.

Common mistakes

Checked a point in the first inequality only. A point must pass every inequality, so test it in each one together.

Checked a point in the second inequality only. A point must pass every inequality, so test it in each one together.

Counted a point on the boundary of a strict inequality (< or >). A strict inequality leaves its boundary out.

Questions parents ask

What is the most common mistake with systems of inequalities with absolute value, and linear programming?

Checked a point in the first inequality only. A point must pass every inequality, so test it in each one together.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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