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QUESTION 3 For the sequence 4 2 0 —2 —4 ... the common difference is (A) 4 B) 2 C) =2 (D) -4
QUESTION 18 (4 marks) Exhibition organisers believe that the number of attendees increases each day as an arithmetic sequence. The organisers know that 353 people attended the first day and 439 people attended the third day. a) Determine the common difference. [2 marks] b) Use the result from 18a) to predict the number of people who will attend the sixth day. [2 marks]
QUESTION 1 (5 marks) A water tank contains 12 500 L of water. The tap is accidently left on and the tank loses 135 L per minute. The tap 1s turned off when the tank has 5000 L of water left. Use a mathematical model to determine how long the tap was left on to the nearest minute.
QUESTION 9 A staircase is to be extended by installing » additional stairs. Each stair is 25 cm high. If the existing staircase reaches 1.2 m off the ground which rule models the total height the stairs will reach in centimetres? (A) t =25+(n-1)x1.45 B) 1 =12+(n-1)x25 (C) t =145+(n-1)x25 (D) 1 =25+(n-1)x120
QUESTION 4 A swimmer has a weekly training routine to improve their fitness as modelled by the recursive function T =T +2 where T is the number of laps they swim in week n and 7} = 4. Which graph best represents the swimmer’s routine? (A) (B) 16 0 % 14 —o 0 - 2 = 12 o s g 38 o 5 5 . 5 2 Z s 4 zZ 2 0 0 2 4 6 8 10 12 14 16 2 3 -+ 5 6 Number of laps per week Number of weeks © 6 » (D) s 24 5 d § Gy 5 & o & < 5 O ; = o S S g 2 s = = / o Z = 3 1 /! > 0 ® 0 2 4 6 8 10 12 14 16 0 1 2 3 4 5 6 Number of laps per week Number of weeks
QUESTION 5 The table lists the number of books sold per month by an online bookstore. If the simple 3-point moving average in October is 54 what is the simple 3-point moving average in May? o [ weo [ v [ aor [y [ [ [ e [ sep [ o [ [ e 5w e 6w e 5w 0] 0w (A) 69 (B) 73 (C) 74 (D) 89
QUESTION 18 (4 marks) The number of songs on a person’s playlist n in each week since joining a music streaming service ¢ forms an arithmetic sequence as shown by the graph. 700 % 600 575 > % 500 = 0453 o 2 400 S ®33] «w 300 o _qné 200 e209 Z 100 eR7 0 0 1 2 3 4 5 6 Time (weeks) Use the arithmetic sequence to predict the number of songs on this person’s playlist 25 weeks after joining the streaming service.
QUESTION 6 (7 marks) The first three lines in a pattern have the equations given. Their slopes form the terms of one sequence and their y-intercepts form the terms of another sequence. Each sequence is either arithmetic or geometric. Line 1: y=-0.8x + 1.2 Line2: y=0.4x+2.7 Line3: y=-0.2x+ 4.2 Determine the coordinates of the point where Line 5 in the pattern intersects Line 1.
QUESTION 9 Determine the 6th term of the arithmetic sequence that begins 3 9 ... (A) 21 (B) 33 (C) 45 (D) 729
QUESTION 5 (7 marks) At 9:00 am a security guard begins their patrol of the eight work sites represented in the network diagram starting and ending at site A. They drive at 40 km/h on the roads between sites and check every site once for 15 minutes. The length (km) of each road corresponds to the terms of the arithmetic sequence ¢ = ¢ + 2(n — 1) where ¢ = 1. Determine the earliest possible time the security guard can finish their patrol and identify the route they must follow. B ty C
QUESTION 4 A sequence is defined by aAn =0a -1 + 14 Given that as = 56 the value of a is A) 14 (B) 28 ©) 42 (D) 70
QUESTION 22 (7 marks) A sequence has been defined as t 4 =t +4 t =5 a) Sketch the first six terms of the sequence in graphical form using the grid below. [3 marks] b) Use the rule t = t; + (n — 1)d to model the sequence in simplified form. [2 marks] c) Use the results from 22b) to calculate the 27th term. [2 marks]
QUESTION 7 (7 marks) In 2011 Chris was earning a salary of $67 500. Chris receives the same pay increase each year and in 2018 was earning a salary of $84 300. In 2015 Sam was earning a salary of $79 500. Sam receives the same pay increase each year and in 2019 was earning a salary of $87 900. Determine when Chris will earn more than Sam.
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