SEKOLAH BUKIT SION – HIGH SCHOOL AY 2020-2021 MATHEMATICS (EXTENDED) 0580 CHAPTER TEST LINEAR PROGRAMMING NAME: ___________________________ CLASS: ________ DATE: _______________ ===================================================================== INSTRUCTIONS: 1. Answer all questions by choosing one of the four methods below:

(a) in the Class Notebook, for full features of drawing tools/menu, click Open in App button (b) by printing the pdf file and answer on the printed material (c) by downloading the pdf and annotate on it using a pdf annotating app on your device (d) by doing on an actual graphing paper [for graphing] and file paper [for working and final

answer statements].

2. For those doing (b), (c) and (d) methods, send your working and answers by inserting a pdf as file printout into the Chapter Test page in the Assignment Tab/Class Notebook. *Do not “Add work” as it becomes a different file. Your work should be found inside/within the the Chapter Test page that I sent. 3. For graphing questions, use an appropriate graph/grid paper and pencil for accuracy. Those that are not done on a grid paper may be given deduction marks. *For those who are annotating, use appropriate drawing tools for accuracy i.e. straight lines, broken lines. 4. You may not use highlighter or correction tape in any of the methods specified in item #1. ===========================================================================

Question 1. Encircle the points which are solutions of x – 4y < 7. [3] (3, 5) (–5, –3) (–3, –5) (5, 3) Question 2. Complete the table below as whether the given point is a solution or not to the following inequalities. [4]

Inequalities (0, –5) (–5, 0) (5, 1) (1, 5)

5x – y > 5

5x – 3y < 15

Question 3. Find all the points that satisfy the inequality y < 2x – 6. [3]

Question 4. Archie wants to find out the region of solutions of the system of inequalities below.

–3x – y < –10 and 4x – 4y > 8. He started by drawing the boundary lines and by finding out where the boundaries intersect.

(i) Which of the following graphs show the boundaries of the two inequalities above with their corresponding point of intersection?

Answer: _____________________________ [2]

a.

Point of Intersection: (–1, 3)

c.

Point of Intersection: (1, 3)

b.

Point of Intersection: (3, –1)

d.

Point of Intersection: (3, 1)

(ii) After identifying the correct graph in part (i), complete Archie’s work in finding the region of solutions by shading the unwanted regions of the selected graph. [2]

O 2 4–2–4 x

2

4

–2

–4

y

O 2 4–2–4 x

2

4

–2

–4

y

O 2 4–2–4 x

2

4

–2

–4

y

O 2 4–2–4 x

2

4

–2

–4

y

Question 5. Given the system of linear inequalities below: x > 0 y > 0 4x + 5y < 40 y < –x + 9

(a) Show the graph of the 4 inequalities in one Cartesian plane and by shading the unwanted, determine the region R where all points satisfy all the linear inequalities given. [5]

(b) Find the values of x and y that maximize the objective function P = 3x + 2y for the graph.

Answer: _____________________________ [3]

(c) Write down the maximum value.

Answer: ______________________________ [1]

Candidate Name CandidateCentre Number Number

Question 6. One of the lines in the diagram shown below is labelled y = mx + c.

(a) Find the value of m and of c.

Answer: ______________________________ [2]

(b) Show, by shading the unwanted regions of the diagram, the region defined by the inequalities

x > 1 y < mx + c y > x + 2 y > 4. Label the region with R. [3] Question 7. Write down the 4 inequalities that describe the UNSHADED region below. Answers: [4 marks] ____________________ ____________________ ____________________ ____________________

Question 8. A new school has x day students and y boarding students. (a) It can accommodate at most 900 students. Write this inequality in x and y to represent this information.

Answer:______________________________ [1] (b) The fees for a day student are $600 per term. The fees for a boarding student are $1200 per term. The school needs at least $720 000 per term. Write an inequality in x and y to represent this information and show that it simplifies to x + 2y > 1200.

Answer:______________________________ [2] (c) Draw the two lines on the grid and by shading the unwanted, determine the region R. [4]

(d) Each day student consumes 7 litres of water while each boarding student consumes 10 litres of water daily. What is the number of day students and the corresponding boarding students at the school with the least daily water consumption?

Answer:______________________________ [3]