Graphical Inequalities

Transcription

1 Graphical Inequalities Question Paper 5 Level IGCSE Subject Maths (0580) Exam Board Cambridge International Examinations (CIE) Paper Type Extended Topic Algebra and graphs Sub-Topic Graphical Inequalities Booklet Question Paper 5 Time Allowed: 62 minutes Score: /51 Percentage: /100 Grade Boundaries: A* A B C D E U >85% 75% 60% 45% 35% 25% <25%

2 1 8 y y = mx + c x (a) One of the lines in the diagram is labelled y = mx + c. Find the values of m and c. Answer(a) m= c= (b) Show, by shading all the unwanted regions on the diagram, the region defined by the inequalities x 1, y mx + c, y x+2 and y 4. Write the letter R in the region required. [2]

3 2 Answer the whole of this question on a sheet of graph paper. A taxi company has SUPER taxis and MINI taxis. One morning a group of 45 people needs taxis. For this group the taxi company uses x SUPER taxis and y MINI taxis. A SUPER taxi can carry 5 passengers and a MINI taxi can carry 3 passengers. So 5x + 3y 45. (a) The taxi company has 12 taxis. Write down another inequality in x and y to show this information. (b) The taxi company always uses at least 4 MINI taxis. Write down an inequality in y to show this information. (c) Draw x and y axes from 0 to 15 using 1 cm to represent 1 unit on each axis. (d) Draw three lines on your graph to show the inequality 5x + 3y 45 and the inequalities from parts (a) and. Shade the unwanted regions. [6] (e) (f) The cost to the taxi company of using a SUPER taxi is $20 and the cost of using a MINI taxi is $10. The taxi company wants to find the cheapest way of providing SUPER and MINI taxis for this group of people. Find the two ways in which this can be done. [3] The taxi company decides to use 11 taxis for this group. (i) The taxi company charges $30 for the use of each SUPER taxi and $16 for the use of each MINI taxi. Find the two possible total charges. [3] (ii) Find the largest possible profit the company can make, using 11 taxis.

4 3 Answer all of this question on a sheet of graph paper. A shop buys x pencils and y pens. Pencils cost 15 cents each and pens cost 25 cents each. (a) There is a maximum of $20 to spend. Show that 3x 5y 400. (b) The number of pens must not be greater than the number of pencils. Write down an inequality, in terms of x and y, to show this information. [2] (c) There must be at least 35 pens. Write down an inequality to show this information. (d) (i) Using a scale of 1 cm to represent 10 units on each axis, draw an x-axis for 0 x 150 and a y-axis for 0 y 100. (ii) Draw three lines on your graph to show the inequalities in parts (a), (b) and (c). Shade the unwanted regions. [5] (e) When 70 pencils are bought, what is the largest possible number of pens? (f) The profit on each pencil is 5 cents and the profit on each pen is 7 cents. Find the largest possible profit. [3]

5 4 Marina goes to the shop to buy loaves of bread and cakes. One loaf of bread costs 60 cents and one cake costs 80 cents. She buys x loaves of bread and y cakes. (a) She must not spend more than $12. Show that 3x! 4y 60. Answer (a) (b) The number of loaves of bread must be greater than or equal to the number of cakes. Write down an inequality in x and y to show this information. Answer (b)... (c) On the grid below show the two inequalities by shading the unwanted regions. Write R in the required region. y x [4] (d) The total number of loaves of bread and cakes is x! y. Find the largest possible value of x! y. Answer (d)...

6 5 A ferry has a deck area of 3600 m 2 for parking cars and trucks. Each car takes up 20 m 2 of deck area and each truck takes up 80 m 2. On one trip, the ferry carries x cars and y trucks. (a) Show that this information leads to the inequality x! 4y 180. [2] (b) The charge for the trip is $25 for a car and $50 for a truck. The total amount of money taken is $3000. Write down an equation to represent this information and simplify it. Answer (b)... [2]

7 (c) The line x! 4y # 180 is drawn on the grid below. (i) Draw, on the grid, the graph of your equation in part (b). y x (ii) Write down a possible number of cars and a possible number of trucks on the trip, which together satisfy both conditions. Answer (c)(ii)... cars,... trucks

8 6 y x (a) On the grid, draw the lines x = 1, y = 2 and x + y = 5. [3] (b) Write R in the region where x 1, y 2 and x + y 5.