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•   Algebra
•   Objective: Exploring patterns and relationships
•   Level 3

The keywords for each question in this search are:

Question 1: Spatial pattern; rule
Question 2: number sequences; rule
Question 3: number sequences; rule
Question 4: number sequences; rule
Question 5: Co-ordinates; grid interpretation
Question 6: Co-ordinates; grid interpretation
Question 7: Spatial pattern; number sequences; rule
Question 8: Spatial pattern; number sequences; rule

 

QUESTION 1

Here is the beginning of a pattern of tiles.

Figure 1 Figure 2 Figure 3

If the pattern continues, how many tiles will be in Figure 6?

(A)   12
(B)   15
(C)   18
(D)   21

 

QUESTION 2

These numbers are part of a pattern.

50, 46, 42, 38, 34, ...

What do you have to do to get the next number? ____________________________________

 

QUESTION 3

What do you have to do to each number in Column A to get the number next to it in Column B?

Column A

Column B

10

2

15

3

25

5

50

10

(A)   Add 8 to the number in Column A.
(B)   Subtract 8 from the number in Column A.
(C)   Multiply the number in Column A by 5.
(D)   Divide the number in Column A by 5.

 

QUESTION 4

Which pair of numbers follow the rule "Multiply the first number by 5 to get the second number"?

(A)

 15

3
(B) 6 11
(C) 11 6
(D) 3 15

 

QUESTION 5

This is a game board.

Which object is located at (2,D)?

(A)   The plane  

(B)   The truck   

(C)   The bus     

(D)   The boat 

 
   

QUESTION 6

On this grid, find the dot with the circle around it. We can describe where the dot is by saying it is at First Number 1, Second Number 3.

Now find the dot with the triangle around it. Describe where the dot is on the grid in the same way. Fill in the numbers we would use:

First Number __________           Second Number __________

 
   

QUESTION 7

Here is a sequence of three similar triangles. All of the small triangles are congruent.
  

Figure 1 Figure 2 Figure 3

a)
Complete the chart by finding how many small triangles make up each figure.
  

Figure

Number of small triangles

1

1

2

   

3

   

b)
The sequence of similar triangles is extended to the 8th figure. How many small triangles would be needed for Figure 8?

__________

 
   

QUESTION 8

The figures show four sets consisting of circles.
  
Figure 1 Figure 2 Figure 3 Figure 4

a)
Complete the table below. First, fill in how many circles make up figure 4. Then, find the number of circles that would be needed for the 5th figure if the sequence of figures extended.
 

Figure

Number of circles

1

1

2

3

3

6

4

  

5

  


b)
The sequence of figures is extended to the 7th figure. How many circles would be needed for Figure 7?

Answer: __________

c)
The 50th figure in the sequence contains 1275 circles. Determine the number of circles in the 51st figure. Without drawing the 51st figure, explain or show how you arrived at your answer.