advertisement

GRADE 8 MATHEMATICS TERM 4 FORMAL ASSESSMENT TASK 4.1 ASSIGNMENT: Graphs MEMORANDUM Total: 70 Marks Time: 1½ hour Instructions: 1) 2) 3) 4) 5) 6) 7) Write your name and surname in the spaces above. All questions must be answered on the question paper. Show all calculations. You may use an approved calculator. You must do your own work. Check your answers. All answers must be rounded to one decimal place unless stated otherwise. QUESTION 1 1.1. Complete the sentences below by using the following vocabulary: Origin; X-coordinate; Y-coordinate; X-axis; Y-axis; Ordered pair; quadrants 1.1.1. 1.1.2. 1.1.3. 1.1.4. 1.1.5. 1.1.6. 1.1.7. The four regions on the coordinate plane are called quadrants. The Y-coordinate corresponds to a number on the y-axis. The X-coordinate corresponds to a number on the x – axis. The vertical number line is called the Y-axis. The point where the number lines intersect is called the origin. The horizontal number line is called the X-axis. A(n) ordered pair is the set of numbers used to locate a point on the coordinate plane. (7) 1.2 Plot each point on the coordinate plane. Label with the corresponding letter. 1.2.1 A (-4, -5) 1.2.2 B (6, -5) B F E 1.2.3 C (-2, 0) D 1.2.4 D (6, 5) 1.2.5 E (-4, 5) C 1.2.6 F (0, 5) A (6) 1.3 A Write the ordered pair for each point: (6; 8) B (-6; 2) C (4; -4) (3) [16] 2 QUESTION 2 2.1 The graph below shows the attendance of learners in a Gr 8 Mathematics class at a high school. Use the graph to answer the questions that follow. Attendance over 10 days in a Math class at a high school 45 Number of learners 40 35 30 25 20 1 2 3 4 5 6 7 8 9 10 Days 2.1.1 Complete the following table to show the learner attendance on certain days. No learners were absent on days 2, 6 and 9. Day 3 5 8 10 Learners present 2.1.2 39 36 38 37 (4) How many learners are in the Mathematics class? 40 learners 2.1.3 (1) How many learners were absent on day 7? 1 Method 40 – 28 = 12 learners 1A (2) 2.1.4 Do you think that the attendance of the Mathematics learners over the 10 days 1A was good? Give a reason for your answer. A Reason Yes. The average number of learners that attended the school during this 10 day period is: 𝟑𝟕𝟐 𝟏𝟎 = 37,2 (2) 3 The graph shows a journey that Denver and his father made to Johannesburg. They arrived in Johannesburg at 12:00. Journey to Johannesburg 250 200 Distance in km 2.2 150 100 50 0 7:00 8:00 9:00 10:00 11:00 12:00 13:00 Time in hours 2.2.1 2.2.2 At what time did they start their journey? 07:00 How many times did they stop along the road? 3 times 2.2.3 (1) (1) At what time between 9:00 and 12:00 did they stop? 10:30 – 11:00 (1) 2.2.4 How far did they travel to Johannesburg? 200km (1) 2.2.5 Calculate the average speed at which they travelled between 9:00 and 10:30? 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 [Hint: Speed = 𝑡𝑖𝑚𝑒 ] Speed = 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒊𝒎𝒆 Kilometres travelled: 50km Total hrs travelled: 1½hrs 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 Speed = 𝒕𝒊𝒎𝒆 𝟓𝟎𝒌𝒎 = 𝟏,𝟓𝒉𝒓𝒔 = 33,3km/h 1 Subst 1 Subst 1 CA in km/h (3) [16] 4 QUESTION 3 Four glasses are filled with water from a tap that flows at a constant rate. Match the glass with the graph that best shows the water level at a certain time. Only write down the question number together with the letter of the graph. B distance distance A time time C D distance distance 3.1 time time No. 3.1.1 GRAPH Matches Graph A, B, C or D B 3.1.2 A 3.1.3 D 3.1.4 C (4) 5 3.2 Choose for every graph below a word from each of the two categories indicated in the table to describe the graph in the best way. Complete the table by writing the corresponding word(s) in the column provided. Graph A B C D E Represents a linear or non-linear relation Linear Linear Linear non-linear non-linear Constant; Increasing; Decreasing constant constant constant increase & decrease varying decrease 1X answer each (11) [15] 6 QUESTION 4 To raise money to pay for her son’s school fees, Maria decided to sell hamburgers at R9 each. Copy and complete the table below to show the amount collected for selling a certain number of hamburgers. 4.1 4.2 Hamburgers (n) 1 5 7 11 Amount (R) 9 45 63 99 (2) Use the grid on the attached Annexure to draw a graph to show the amount collected for selling a certain number of hamburgers. Use the following information to assist you: 110 Show the Amount in rand on the vertical axis. Show the number of Hamburgers on the horizontal axis. Give a relevant title to the graph. Plot the points on the system of axes. (8) AMOUNT COLLECTED FROM SELLING HAMBURGERS (in Rand) 100 90 80 Amount in Rand B 70 60 50 40 30 20 10 0 1 2 3 4 5 6 7 Number of Hamburgers 4.2.1 4.2.2 8 9 10 11 Is the graph increasing or decreasing? Increasing How much will Maria have collected if she sold 8 hamburgers? Use dotted lines and show with the letter B where you will read this value from the graph. R72 (1) (1) 7 4.2.3 4.2.4 Write down a formula to determine the amount (R) collected for n hamburgers in the form: R = 9n (1) Maria’s expenses to buy ingredients for the hamburgers were R99. How much hamburgers must she sell before she will show a profit? 99 Number of hamburgers for R99 ingredients = 9 =11 burgers to play even 12 hamburgers (2) (for profit) [15] QUESTION 5 Study the following table: x y 1 2 2 4 3 6 4 8 5.1 What is the relationship between x and y? x is the half of y or y is double the value of x 5.2 5.3 (1) Write it down as a rule. y = 2x Plot the points this Cartesian plane and connect them. points correct (1) 8 7 6 points joined correctly 5 4 3 2 1 0 1 5.4 5.5 5.6 2 (3) 3 4 5 Is the graph linear or non-linear? Linear (3) Is the graph continuous or discrete? Continuous (1) Is the graph ascending or descending? Ascending (1) [8] TOTAL: 70 8