COORDINATE GEOMETRY, EQUATIONS AND PROBLEM SOLVING TEST
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1 Year 8 Maths TEST A 2017 Name: COORDINATE GEOMETRY, EQUATIONS AND PROBLEM SOLVING TEST PART A: COORDINATE GEOMETRY [22 marks] Question 1: Use the set of axes below to answer the following questions. a) i. On same set of axes (provided below), plot the following points: A(1,3), B(-4,0), C(3, -2), D(0,5) ii. What quadrant do Points A and C lie in? [3 marks] b) On the axes above, plot any point P which has a negative x and y coordinate. Question 2: For each of the following equations fill in the provided table of values and draw the graph of the equation. a) y = 2x + 1. x y
2 Year 8 Maths TEST A 2017 Name: [3 marks] b) y =! x + 2.! x y [3 marks]
3 Year 8 Maths TEST A 2017 Name: Question 3: Sarah is eating a block of chocolate over the weekend. On Saturday morning, she ate 4 squares from the block, and will eat 2 more squares of chocolate every hour over the weekend (she really likes chocolate). Let C be the total number of chocolate squares Sarah eats over the weekend. Let h be the number of hours Sarah has spent eating chocolate. a) What are the independent and dependent variables? b) Complete the following table: Time, h Number of chocolate squares, C c) Plot the graph of C against h. d) Is the relationship between C and h linear?
4 Year 8 Maths TEST A 2017 Name: e) How many squares of chocolate would Sarah have eaten after 8 hours? f) How many hours would it take Sarah to eat an entire block of chocolate (48 squares)? Question 4: a) Show that the point (2,4) lies on the line y = 3x 2. b) Determine whether the point (2,4) lies on the line y = x + 6. c) Plot the point (2,4) on the graph below. Explain your reasoning. y = 3x 2 y = x + 6
5 Year 8 Maths TEST A 2017 Name: COORDINATE GEOMETRY, EQUATIONS AND PROBLEM SOLVING TEST PART B: EQUATIONS AND PROBLEM SOLVING [21 marks] Question 5: Solve the following equations for x: a) x 4 = 12. d)!!!!!! = 5. b) 2x + 3 = 11. e) 7 2x + 4 = 21. c) 45 3x = 3. f) 3x 2 = x + 4. [3 marks]
6 Year 8 Maths TEST A 2017 Name: g) 2 x + 6 = 4x + 3(x + 1). [3 marks] Question 6: William is counting the number of Maths textbooks he owns. He has 3 suitcases full of textbooks and 2 textbooks on his desk. William has 38 Maths textbooks in total. a) How many textbooks are in each suitcase? Assume each suitcase has the same number of textbooks. b) William decided to measure one of these textbooks. Maths Textbook Length Width (x cm) i. Let the width of the textbook be x cm. The length of the textbook is 4cm more than its width. What is the length of the book in terms of x?
7 Year 8 Maths TEST A 2017 Name: ii. The perimeter of the book is 44cm. Use this information to make an equation and solve it to find the dimensions of the book. [3 mark]
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15 Year 8 Maths TEST B 2017 Name: COORDINATE GEOMETRY, EQUATIONS AND PROBLEM SOLVING TEST PART A: COORDINATE GEOMETRY [22 marks] Question 1: Use the set of axes below to answer the following questions. a) i. On same set of axes (provided below), plot the following points: A(2,1), B(-6,0), C(5, -1), D(0,7) ii. What quadrant do Points A and C lie in? [3 marks] b) On the axes above, plot any point P which has a negative x and y coordinate. Question 2: For each of the following equations fill in the provided table of values and draw the graph of the equation. a) y = 2x 1. x y
16 Year 8 Maths TEST B 2017 Name: [3 marks] b) y =! x 1.! x y [3 marks]
17 Year 8 Maths TEST B 2017 Name: Question 3: Emily is eating a block of chocolate over the weekend. On Saturday morning, she ate 2 squares from the block, and will eat 3 more squares of chocolate every hour over the weekend (she really likes chocolate). Let C be the total number of chocolate squares Emily eats over the weekend. Let h be the number of hours Emily has spent eating chocolate. a) What are the independent and dependent variables? b) Complete the following table: Time, h Number of chocolate squares, C c) Plot the graph of C against h. d) Is the relationship between C and h linear?
18 Year 8 Maths TEST B 2017 Name: e) How many squares of chocolate would Emily have eaten after 7 hours? f) How many hours would it take Emily to eat an entire block of chocolate (48 squares)? Question 4: a) Show that the point (1,3) lies on the line y = 2x + 1. b) Determine whether the point (1,3) lies on the line y = 2x + 5. c) Plot the point (1,3) on the graph below. Explain your reasoning. y = 2x + 1 y = 2x + 5
19 Year 8 Maths TEST B 2017 Name: COORDINATE GEOMETRY, EQUATIONS AND PROBLEM SOLVING TEST PART B: EQUATIONS AND PROBLEM SOLVING [21 marks] Question 5: Solve the following equations for x: a) x 3 = 15. d)!!!!!! = 7. b) 3x + 2 = 14. e) 8 3x + 2 = 45. c) 46 4x = 6. f) 2x 4 = 4x + 3. [3 marks]
20 Year 8 Maths TEST B 2017 Name: g) 3 x + 4 = 6x + 4(x + 5). [3 marks] Question 6: Simon is counting the number of Maths textbooks he owns. He has 2 suitcases full of textbooks and 4 textbooks on his desk. Simon has 40 Maths textbooks in total. a) How many textbooks are in each suitcase? Assume each suitcase has the same number of textbooks. b) Simon decided to measure one of these textbooks. Maths Textbook Length Width (x cm) i. Let the width of the textbook be x cm. The length of the textbook is 6cm more than its width. What is the length of the book in terms of x?
21 Year 8 Maths TEST B 2017 Name: ii. The perimeter of the book is 48cm. Use this information to make an equation and solve it to find the dimensions of the book. [3 mark]
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