Question 1 Given the line whose equation is y = 3x + 5 (a) Write an equation for a line parallel to the given line (b) Write an equation for a line perpendicular to the given line Question 2 (a) Solve the following simultaneous equations graphically 2x - y = 5 y + 1.5x = 9 10 y+ 1.5x=9 2x - y=5 5 (b) Check your solution algebraicallyQuestion 10 Jason paints signs on buildings using the following letters: ABCDEFGHIJKLMNOPQRSTUVWXYZ He can paint the letters which contain all straight edges quite easily but the letters which contain a curved edge take longer Straight letters Curved letters AEFHIKLMNTVWXY Z BCDGJOPQRS U It takes Jason 25 minutes to paint the word CHEMIST and 29minutes to paint the word BUTCHER. Calculate how long would it take Jason to paint the word ACCOUNTANT.Question 3 Graph the following inequality on the number line below x > 12 Question 4 Solve the following inequality for x (2x-3) 2 2 5Question 5 ark Lee's soccer team played 38 games this season. Their results are shown in the two-waytable below. a) Complete the table by determining the missing values Win Draw Loss Total Home 11 6 3 Away 8 4 18 Total 17 7 b) Determine the probability that a randomly selected game was won. c) Calculate the probability that a randomly selected game was won, given that it was at home.Question 6 In a bag there are four balls: two green, one blue and one red. In a second bag, there are two balls, one yellow and one green. One ball is chosen from each bag. a) In the space below, complete a tree diagram to show all possible colour combinations that may be selected. Ensure you list the sample space. SAMPLE SPACE G G G G G R b) Determine the probability that two green balls are selected. c) Calculate the probability of at least one of the balls selected being green.Question 7 The admission fee at a small fair is $1.50 for kids and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended? (Mathematically justify your solution by showing all working.) a) Complete the following: i) Let A = Number of Adults and K = ii) A +K= b) Write an equation for the total cost of Adult and Children's tickets in terms of A and K c) Use this information to mathematically determine the number of adults and children to visit the fair. (Note: to get full marks you'll need to show a method other than guess and check)(CFIUF - 2% marks) Question 8 Solve the following equations simultaneously. (Be sure to Check your solution) 4x + ym 8 yEx-2 1 14x+) =8 Y=X - 2 = x-2 4(2 ) +0=8 4 x + (x-2) =8 1 = 2- 2 8=8 ( Tree ) y= 0 5 x-2=8 * = 2 and )= 0 2 ) y = V-Z 5X= 10 0=2- 2 X = 2 0=0 ( Tive ) The solution satisfies both equations, so it is correct. Question 9 (CF/UF - 4 marks) Solve the following equations using the elimination method. (Be sure to Check your solution) 2x + y = 8 3(24 + 1)= 3(8 ) 76X + 3*=24 4x - 3y = 6 2 ( 4x- 3x) = 2(61 8x-6y=12 19x - 3x = 36 6 * + 3y = 29 14 x = 36 + 3y 8x- 64 = 12 14* = 36+ 3 17 ( since we elm y ) 14% = 36 ( 6 * + 34 ) + ( 8x- 6y) = 24+12 x = 36/14 14 - 34 = 36 * = 18/7