(a) (i) Use a factor tree to write 5544 as a product of prime factors. Display your factor tree in your answer. [4] (ii) Calculate

5 9

1 5

+

13 15

,

leaving your answer as a fraction in its simplest form, showing all your working. [4] (iii) Simplify the surd 53 15 +80

by writing it as a surd in its simplest form, showing your working. [3]

(b) A group of 330 students are required to take a test. Of these, 285 actually take the test, and 45 are absent that day. (i) Write down the ratio of the number of students who take the test to the number of students who are absent. Simplify this as far as possible. [3] (ii) Of the 285 students who take the test, the numbers of students obtaining grades A, B, C and D are in the ratio 3 : 10 : 5 : 1, respectively. Calculate the number of students obtaining each grade. Explain how you could check that your answers are plausible. [4]

(c) Novak Djokovic played in tennis matches for a total of 14 hours and 3 minutes to win the 2019 Australian Open men's singles title. He won 2.56 million in prize money. (i) Calculate how long Novak played (in minutes) for each pound that he won in this tournament. Give your answer to three signicant gures in both ordinary notation and scientic notation. [4] (ii) Calculate how much Novak won (in pounds) for each hour that he played in this tournament. Give your answer to three signicant gures in both ordinary notation and scientic notation. [3]

Question 3 - 30 marks

This question is based on your work on MU123 up to and including Unit 5.

(a) Simplify each of the following expressions as far as possible; multiply out any brackets, expand any algebraic fractions, and collect like terms together. Show your working. (i) 7x133x + 21 [2] (ii) 7(53t) [2] (iii) 9 + n(114n)11n [3] (iv) 10t5(9s7t) [3] (v) 5p(7 + 2p2)7(3p6 + 2p3) [5] (vi) 3x2 + 12x24 3x [4] (b) Solve the following equations. Show your working and check that your answers are correct. (i) 9a5 = 3 + 5a [5] (ii) y 4 1 = 3(y4) [6]

Question 4 - 10 marks

This question is based on your work on MU123 up to and including Unit 5.

In this question, you are asked to comment critically on a student's incorrect attempt at solving the equation

5 9(x7) = 10. The attempt is shown below. The equation is (x 7) 5 9 Clear the fraction 5(x 7) Multiply out by 5 5x 35 Subtract 35 5x= 415 Divide by 5 x = 83 = 10 = 90 = 450 The solution is x = 83

(a) Substitute the student's solution x = 83 into the left-hand side of the equation 5 9(x7) = 10. Explain why this shows that the student's solution is incorrect. [2]

(b) Write out your own full and correct attempt at solving the equation and checking your solution. [4]

(c) Identify the two lines in the student's attempt where a mistake has been made. Explain, as if directly to the student, why their working is incorrect. [4]