PSLE
Rael uses toothpicks to form figures that follow a pattern. The first four figures are shown.

1. The table shows the number of toothpicks used for each figure. Complete the table for Figure 10 and Figure 11. Give your answers in numbers. (Eg 1, 2)
2. What is the difference in the number of toothpicks that Rael would use for Figure 12 and Figure 16?
3. How many toothpicks would he use for Figure 31?

; (c) 134
(a)
Number of toothpicks used:
Figure 1: 15 = 11 + 4 x 1
Figure 2: 18 = 10 + 4 x 2
Figure 3: 23 = 11 + 4 x 3
Figure 4: 26 = 10 + 4 x 4

The formula for the total number of toothpicks used is different for odd-numbered patterns and even-numbered patterns.
Number of toothpicks for odd-numbered figure = 11 + 4 x Figure number
Number of toothpicks for even-numbered figure = 10 + 4 x Figure number

Number of toothpicks used for Figure 10
= 10 + 4 x 10 
= 10 + 40
= 50

Number of toothpicks used for Figure 11
= 11 + 4 x 11
= 11 + 44
= 55

(b)
Since every 2 jumps has the same increase,
difference in the number of toothpicks for Figure 12 and 16
= 2 x 8
= 16

(c)
Figure 31 is an odd number.

Number of toothpicks that Rael would use for Figure 31
= 11 + 4 x Figure number
= 11 + 4 x 31
= 11 + 124
= 135

Answer(s): (a) 50, 55; (b) 16; (c) 135