Part A: Multiple Choice (1 mark each) 1. An expression that is equivalent to * +x -, x * 0 is: A. x , x*0 B. 2x,x #0 C. x+1,x #0 D. x2 + 1, x # 0 Use the following information to answer the next question. Consider the following statements. I. x2 -16 2x +2 x+1 2x-8 ;x#-1,4 II. x +16 2x +2. x+1 2x+8' ;x * -1, 4 III. x2 - 16 2x +2. x-1 2x -8 ;x #-1,4 IV. x2 -16 2x - 2. x+1 2x-8 ;x#-1,4 2. The statement that simplifies to x + 4 is: A. I B. II C. III D. IV1-x" 5. Identify the rational expression that is equivalent to 6 3-3x A. 2 X - X B. 6x C. 2 -x 12 X-x D. 6xUse the following information to answer the next question. The simplified product of 2n p 6m 3m 3n2p2. m #0. n # 0. p # 0, can be represented by 3p where A, B, and C represent single-digit numbers. Numerical Response 1. In the simplified product And , the value of 3p A is (Record in the first column) B is (Record in the second column) Cis (Record in the third column) (Record your answer in the numerical-response section on the answer sheet.)Use the following information to answer the next question. Ken made an error in the simplification of the rational expression 2x + 10 212-50 x#-5, 5. His simplification of the expression is shown below. Step 1 12(x +5) 12(17- 25) Step 2 1 (x + 5) 1 (x + 5) (x - 5) Step 3 1( *+5 ) 1(1+5) ( x - 5) Step 4 (x- 5), x #-5,5 9. The step in which Ken made his error is A. Step 1 B. Step 2 C. Step 3 D. Step 4Use the following information to answer the next question. Over a distance of 800 km, the average speed of a small airplane is 6 times faster than the average speed of a train. This information is shown in the table below. Distance (km) | Speed (km/h) Time (h) 800 Train 800 x x 800 Airplane 800 6x 6x To travel 800 km, the train requires 8 h more than the airplane. The equation shown below represents this relationship. 800 800 = 8 6x Numerical Response 2. The average speed of the train, to the nearest tenth of a kilometre per hour, is _km/h. (Record your answer in the numerical-response section on the answer sheet.)Written Response: (6 marks) **SHOW ALL OF YOUR WORK!!!** 4x 5x+3 1. Consider the rational expression- . [3 marks] x+2 x +2 . Explain why the non-permissible value for this expression is x = -2 . Subtract the expressions 2. Competing in an endurance race, Shannon cycled for 120km and then swam for 12km. Her average cycling speed was eight times faster than her average swimming speed. Shannon took nine hours to complete the race. Solve to calculate her average cycling and swimming speed. (5 marks) Distance Speed Time km km/h h Cycle Swim3. Alma tried to simplify an expression, as shown below. 12t - 1623 2(21) ( 3-423 I started by factoring the numerator and the 18t - 242* 3 ( 21 ) ( 3 - 41 ) denominator. 2(21) (3- 42 ? I cancelled the common factors. 3(2t ) (3-41) 2, 1 = 0,1# The numerator and the denominator have no more = common factors, so the expression cannot be simplified any further. Identify Alma's error, and correct her solution. (2 marks)