Question 6 - NUMBER PATTERNS 6.1 Complete the number pattern and describe it in words: 5; 9; 13; 17; PATTERN IN WORDS: 6.2 Consider the matchstick pattern below and complete the table.

Step 1: Fill in the correct relationship sign for $-9$ and $-3$ (from question 5.2.1). On a number line, $-9$ is to the left of $-3$, meaning $-9$ is smaller than $-3$. $-9 < -3$

Step 2: Calculate the expressions (from question 5.3).

• 5.3.1 Calculate $(-7) + (+5)$. $(-7) + (+5) = -7 + 5 = -2$ $(-7) + (+5) = -2$

• 5.3.2 Calculate $(+8) - (-4)$. Subtracting a negative number is equivalent to adding its positive counterpart. $(+8) - (-4) = 8 + 4 = 12$ $(+8) - (-4) = 12$

• 5.3.3 Calculate $(-5) + (-6) + (+14) + (-2)$. Combine the negative numbers first: $-5 - 6 - 2 = -13$ Then add the positive number: $-13 + 14 = 1$ $(-5) + (-6) + (+14) + (-2) = 1$

Step 3: Calculate the difference in temperature (from question 5.4). The temperature inside the freezer is $-18^\circ\text{C}$. The temperature outside is $16^\circ\text{C}$. To find the difference, subtract the lower temperature from the higher temperature. $Difference = 16^\circC - (-18^\circC)$ $Difference = 16^\circC + 18^\circC = 34^\circC$ The difference in temperature is $\boxed{34^\circC}$.

Step 4: Complete the number pattern and describe it (from question 6.1). The given pattern is $5; 9; 13; 17; \_ ; \_$. Find the common difference between consecutive terms: $9 - 5 = 4$ $13 - 9 = 4$ $17 - 13 = 4$ The pattern increases by $4$ each time. The next two terms are: $17 + 4 = 21$ $21 + 4 = 25$ The completed pattern is $5; 9; 13; 17; 21; \boxed{25}$. PATTERN IN WORDS: The pattern starts at $5$ and increases by $4$ for each subsequent term.

Step 5: Complete the matchstick pattern table and find the rule (from question 6.2). The number of matchsticks for patterns $1, 2, 3$ are $4, 7, 10$. Find the common difference: $7 - 4 = 3$ $10 - 7 = 3$ The number of matchsticks increases by $3$ for each subsequent pattern. The rule for the number of matchsticks ($M$) in terms of the pattern number ($n$) is $M = 3n + c$. Using $n=1, M=4$: $4 = 3(1) + c \implies 4 = 3 + c \implies c = 1$. So the rule is $M = 3n + 1$. Now, complete the table for $n=5$ and $n=10$:

• For $n=5$: $M = 3(5) + 1 = 15 + 1 = 16$.
• For $n=10$: $M = 3(10) + 1 = 30 + 1 = 31$.

The completed table is: | Pattern (n) | 1 | 2 | 3 | 5 | 10 | | :---------- | :-: | :-: | :-: | :-: | :--: | | Matchsticks | 4 | 7 | 10 | 16 | 31 |

Rule: $\boxed{M = 3n + 1}$

Step 6: Use the given rule to determine the missing values in the table (from question 7.1). The rule is $y = 4x - 3$.

• For $x=0$: $y = 4(0) - 3 = 0 - 3 = -3$.
• For $x=1$: $y = 4(1) - 3 = 4 - 3 = 1$.
• For $x=2$: $y = 4(2) - 3 = 8 - 3 = 5$.
• For $x=3$: $y = 4(3) - 3 = 12 - 3 = 9$.
• For $x=4$: $y = 4(4) - 3 = 16 - 3 = 13$.
• For $x=10$: $y = 4(10) - 3 = 40 - 3 = 37$.

The completed table is: | x | 0 | 1 | 2 | 3 | 4 | 10 | | :-: | :-: | :-: | :-: | :-: | :-: | :--: | | y | -3 | 1 | 5 | 9 | 13 | 37 |

Step 7: Determine the values of A, B, and C from the input-output diagram (from question 7.2). The operations are: first multiply by $5$, then subtract $2$.

• For input $3$: $3 \times 5 = 15$ $15 - 2 = 13$ So, $A = \boxed{13}$.

• For input $6$: $6 \times 5 = 30$ $30 - 2 = 28$ So, $B = \boxed{28}$.

• For input $11$: $11 \times 5 = 55$ $55 - 2 = 53$ So, $C = \boxed{53}$.

Drop the next question.