Year 10 Linear relations test 2024.pdf

ST. JOSEPH’S COLLEGE YEAR 10 GENERAL MATHEMATICS 2024 LINEAR RELATIONS TEST Name: _________________________________ Mark: ______ / 35 Percentage: ________ Grade: __________ SECTION Possib...

ST. JOSEPH’S COLLEGE YEAR 10 GENERAL MATHEMATICS 2024 LINEAR RELATIONS TEST Name: _________________________________ Mark: ______ / 35 Percentage: ________ Grade: __________ SECTION Possible Marks Marks gained SECTION A: Multiple Choice Questions 10 SECTION B: Short Answer Questions 25 Writing Time: 70 minutes Materials allowed: One bound reference of notes which meets the VCAA guidelines Approved scientific calculator and/or graphics calculator Instructions: The task is to be completed under test conditions All questions are to be answered in the spaces provided For questions with more than one-mark available, appropriate working must be shown Unless otherwise indicated diagrams are not drawn to scale Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic devices into the examination room. Section A: Multiple choice (10 marks) Question 1 Solve for 𝑥 in the equation 2𝑥 − 3 = 7 A. 5 B. −5 C. 2 D. −2 Question 2 Simplify 5𝑥𝑦 − 2𝑦 + 3𝑥𝑦 + 𝑦 A. 3𝑥𝑦 + 4𝑦 B. 3𝑥𝑦 − 𝑦 C. 8𝑥𝑦 − 𝑦 D. 8𝑥𝑦 + 𝑦 Question 3 Evaluate 𝑎! − 4𝑏𝑐 if 𝑎 = −3, 𝑏 = 2 𝑎𝑛𝑑 𝑐 = −5. A. 31 B. 49 C. -49 D. 46 Question 4 "$% "&! The solution of the equation ! = ' % A. ( B. −7 C. 3 D. 7 Question 5 Which point lies on the line 𝑦 = 4𝑥 − 6 ? A. (1, −2) B. (2, − 2) C. (−3, 6) D. (0, 6) E. (−1, 10) Question 6 The 𝑥 and the 𝑦-intercept, respectively of the equation 4𝑥 − 2𝑦 = 8, are: A. 2, −4 B. −2, 4 C. −4, −2 D. 2, −4 Question 7 The equation of the line shown below is: A. 𝑦 =𝑥−1 B. 𝑦 = −𝑥 − 1 C. 𝑦 = 2𝑥 + 1 D. 𝑦 = −𝑥 + 1 Question 8 The gradient of the line joining the points (−2, 3)and (4, 1) is A. -3 B. 3 % C. -' % D. ' Question 9 When solving the equation shown below to find the value of b, the correct order of working out the solution is: 2𝑏 − 1 =5 3 A. Multiply 5 by 3, add 1 to the answer, then divide by 2. B. Multiply 5 by 3, subtract 1 from the answer, then divide by 2. C. Divide 5 by 3, add 1 to the answer, then divide by 3. D. Multiply 5 by 3, add 1 to the answer, then multiply by 2. Question 10 At The Port Ice Creamery, one group of friends ordered 2 small servings of ice cream and 4 large servings of ice cream at $18. Another group of friends ordered 4 small servings of ice cream and 3 large servings of ice cream at $16. If 𝑠 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑚𝑎𝑙𝑙 𝑠𝑒𝑟𝑣𝑖𝑛𝑔𝑠 and 𝑙 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑎𝑟𝑔𝑒 𝑠𝑒𝑟𝑣𝑖𝑛𝑔𝑠 , then the two equations that represent this are: A. 2𝑠 + 4𝑙 = 18 and 4𝑠 − 3𝑙 = 16 B. 2𝑠 + 4𝑙 = 16 and 4𝑠 + 3𝑙 = 18 C. 2𝑠 + 4𝑙 = 18 and 4𝑠 + 3𝑙 = 16 D. 2𝑠 − 4𝑙 = 18 and 4𝑠 − 3𝑙 = 16 Section B: Short Answers (25 marks) Question 1 (3 marks) Simplify the following: a. 3𝑑 x 4𝑒 1 mark b. −2𝑎𝑏 + 3𝑎𝑏 1 mark c. −5𝑥 + 2𝑦 + 6𝑥 − 4𝑦 1 mark Question 2 (4 marks) a. Expand 4(𝑥 − 3). Show working 1 mark b. Expand and simplify 3(2𝑡 + 1) − 4(2 − 𝑡) 2 marks c. Solve 3(2𝑡 + 1) − 4(2 − 𝑡) = 0 1 mark Question 3 (2 marks) Twice a certain number is added to 5 and the result is 19. a) Write an equation to represent this equation. 1 mark b) Solve your equation from (a) to find the number. 1 mark Question 4 (3marks) Sketch the lines shown below. a. 𝑦 = −1 b. 𝑥 = 3 c. y = −2𝑥 1 mark 1 mark 1 mark Question 5 (2 marks) The graph of a line is shown below. a). Show that the gradient of this line is 2. 1 mark b) Hence, state the equation of the line. 1 mark Question 6 (3 marks) Find the gradient and y-intercept for this linear relation 𝑦 = −2𝑥 + 4 and sketch the graph. gradient = ____________ 1 mark y-intercept = ____________ 1 mark 1 mark Question 7 (3 marks) Sketch the graph 3𝑦 − 2𝑥 = 6 by finding the x and y-intercepts. x-intercept: ___________ 1 mark y-intercept: ____________ 1 mark 1 mark Question 8 (2 marks) When comparing the semester one results, Axel noticed that the sum of his English test score and Mathematics test score was 172. Axel wrote the following equation to represent this: 𝑒 + 𝑚 = 172 Axel then subtracted his English score from his Maths score and the result was 18. a) Write a second equation to represent this information. 1 mark b) Solve Axel’s two equations to find his English and Mathematics test scores? 1 mark Question 9 (3 marks) The graph below represents the costs per week of producing t-shirts by hand (graph A) or by machine (graph B). The equations for both lines are shown below: A: 𝑐𝑜𝑠𝑡 = 60𝑛 + 400 B: 𝑐𝑜𝑠𝑡 = 30𝑛 + 1000 where 𝑛 is the number of t-shirts produced each week. (B) (A) a) How many t-shirts must be produced for the cost of each method to be equal? 1 mark b) If the company receives an order for 15 t-shirts, will it be cheaper to produce the order by hand or by machine? 1 mark c) Which method has a smaller cost per t-shirt? Explain your answer. 1 mark END OF TEST