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13 Find the next three terms for the following number patterns that have a common difference.

14 Find the next three terms for the following number patterns that have a common ratio.

a 35, 70, 140, b 24 300, 8100, 2700, c 64, 160, 400, a 21, 66, 42, 61, 84, 56, … b 22, 41, 79, 136, … b Copy and complete this table. of sticks required c Describe the pattern by stating how many sticks are required to make the first rhombus and how many sticks must be added to make the next rhombus in the pattern. d List the input values that represent the domain. e List the output values that represent the range.

15 Find the next six terms for each of these number patterns.

16 a Draw the next two shapes in this spatial pattern of sticks.

17 A rule to describe a special window spatial pattern is:

Number of sticks = 3 × number of windows + 2 a How many sticks are required to make 1 window? b How many sticks are required to make 10 windows? c How many sticks are required to make g windows? d How many windows can be made from 65 sticks? b State the coordinates on this grid of a point C so that ABCD is a square. c State the coordinates on this grid of a point E on the x-axis so that ABED is a trapezium (i.e. has only one pair of parallel sides).

18 Copy and complete each table for the given rule.

19 Find the rule for each of these tables of values.

20 a State the coordinates of each point plotted on this number plane.

21 Determine the next three terms in each of these sequences and explain how each is generated.

Multiple-choice questions

1 Which number is the incorrect multiple for the following sequence?

30

2 Which group of numbers contains every factor of 60?

3 Which of the following numbers is not divisible only by prime numbers, itself

4 Which of the following groups of numbers include one prime and two points is in a horizontal line?

Extended-response questions

1 For the following questions, write the answers in index notation (i.e. bx) and simplify where possible.

a A rectangle has breadth 27 cm and length 125 cm i Write the breadth and the length as powers. ii Write power expressions for the perimeter and for the area. b A square’s side length is equal to 43 i Write the side length as a power in a different way. ii Write power expressions in three different ways for the perimeter and for the area. c 5 × 5 × 5 × 5 × 7 × 7 × 7 d 43 + 43 + 43 + 43 one desk two desks three desks four desks five desks a How many rhombuses are contained between: i four desks that are in two rows (as shown in the diagram above)? ii six desks in two rows? b Draw 12 desks in three rows arranged this way. c Rule up a table with columns for the number of:

2 A class arranges its square desks so that the space between their desks creates rhombuses of identical size, as shown in this diagram.

• rows

• desks per row

• total number of desks d If there are four desks per row, write a rule for the number of rhombuses in n rows of square desks. e Using a computer spreadsheet, complete several more tables, varying the number of desks per row. f Explain how the rule for the number of rhombuses changes when the number of desks, d, per row varies and also the number of rows, n, varies. g If the number of rows of desks equals the number of desks per row, how many desks would be required to make 10 000 rhombuses?

• total number of rhombuses.

If there are four desks per row, complete your table for up to 24 desks.