Question

Hi can you please show how you get the answers using the long way just so I can see how you worked it out even if you can label which properties you've used Thank you

1. (a) (i) A student claims that if p and q are odd integers then the evaluation of the expression (p 1)(g2 - 1) will always be a multiple of 8. Give 3 numerical examples you would 2 marks) 3 marks) use to check this claim (ii) Either prove, or disprove this claim (i) Work out a method that you can use to determine the last digit of the (b) 3 marks] (ii) Use your method to confirm that the evaluation of 7123454322 ends with 9. 1 marks] numerical value of 7" where p EN 2. (a) Calculate v23+8 12+2V(-3)2) x 4x 2 marks] (b) If a, b and c are real numbers and-a-c, simplify 2a2-b2 + c2-2ac. [2 marks] where r is not equal to 0,-1, or 2. 3 marks] [4 marks 2 marks) [2 marks] 9 marks (c) Simplify (d) Simplify (e) Expand the expression (p2)(p4q) (p-2q) (f) Solve the equation 3272 r+1 - 2 r+1 /432 , where x R, and x>1 3. (a) Solve the following inequalities, showing your working r 15 3r 1 (ii) 20 > 8x -22-5(iii 2 4 (b) The sum of 3 consecutive odd numbers (positive integers) is between 63 and 81. Using algebraic methods, find all possible sets of numbers that satisfy these conditions HINT:] form an inequality first. This will mean that you will need to think about how you will represent the sum of 3 odd numbers algebraically. 3 marks) 4. (a) A data company buys a computer system valued at S20 000 to begin work on the 1st January 2019. The budget used to purchase it is based on an 8 year obsolesence plan. That is, after 8 years the computer system will have no value (i) Find a linear function that expresses the value (v) of the computer system in terms of the number of years (t) that it has been used, O t S 8. That is, write a formula 2 marks beginning with v -.... (ii) Determine the value of the computer system after 3 years 1 marks (iii) The company plans to renew the system when its value decreases to $4000. After 2 marks how many years and months of use should this occur? (b) For each of the following find the equation of the indicated line 3 marks) (ii) The line passing through (-2,1) and perpindicular to 3x - 5y-11.3 marks] 3 marks (i) The line passing through (2,-1) and parallel to z+y 10 (ii The line passing through the points and 4' 5

Answer 1

As (a-b) to4b) 3 12 6x 3 u) (b) (i) un, paalw to And ry.ty=lo ra-) lui u

and passes through (-4) ク◆ 3.