NOTE: Answers to all questions are given at the end of this exercise.

__Question No. 1:
__

**Consider the pattern:**

1 + 3 = 4 = 2 = (1 + 1)

1 + 3 + 5 = 9 = 3 = (2 + 1)

1 + 3 + 5 + 7 = 16 = 4 = (3 + 1)

1 + 3 + 5 + 7 + 9= 25 = 5 = (4 + 1)

1 + 3 + 5 + … + a = b = c = (d + 1)

(a) Write down the fifth and sixth lines in the pattern.

(b) write down the 11th line in the pattern.

(c) given that b = 169, find the values of a, c and d.

1 + 3 = 4 = 2 = (1 + 1)

1 + 3 + 5 = 9 = 3 = (2 + 1)

1 + 3 + 5 + 7 = 16 = 4 = (3 + 1)

1 + 3 + 5 + 7 + 9= 25 = 5 = (4 + 1)

1 + 3 + 5 + … + a = b = c = (d + 1)

(a) Write down the fifth and sixth lines in the pattern.

(b) write down the 11th line in the pattern.

(c) given that b = 169, find the values of a, c and d.

NOTE: Answers to all questions are given at the end of this exercise.

__Question No. 2:
__

**Consider the pattern:**

2 + 1 = 3

2 + 2 = 6

2 + 3 = 11

2 + 4 = 18

2 + x = 66

(a) write down the 6th line in the pattern.

(b) find the value of x.

2 + 1 = 3

2 + 2 = 6

2 + 3 = 11

2 + 4 = 18

2 + x = 66

(a) write down the 6th line in the pattern.

(b) find the value of x.

NOTE: Answers to all questions are given at the end of this exercise.

__Question No. 3:
__

**Consider the pattern:**

1 – 0 = 1 = 1 + 0

2 – 1 = 3 = 2 + 1

3 – 2 = 5 = 3 + 2

4 – 3 = 7 = 4 + 3

(a) write down the 10th line in the pattern,

(b) find the value of 598 – 597.

(c) Find the values of m and n.

1 – 0 = 1 = 1 + 0

2 – 1 = 3 = 2 + 1

3 – 2 = 5 = 3 + 2

4 – 3 = 7 = 4 + 3

(a) write down the 10th line in the pattern,

(b) find the value of 598 – 597.

(c) Find the values of m and n.

NOTE: Answers to all questions are given at the end of this exercise.

__Question No. 4:
__

**Consider the pattern:**

(a) write down the 11th line in the pattern

(b) find the values of p and q.

(a) write down the 11th line in the pattern

(b) find the values of p and q.

NOTE: Answers to all questions are given at the end of this exercise.

__Question No. 5:
__

**A sequence of diagrams consisting of shaded and unshaded small triangles is shown above. Diagram 1 and 2 contains 3 and 6 shaded triangles respectively. The sequence continues as shown in diagram 3 and 4 and so on. Let n denote the diagram number and t the corresponding number of shaded triangles.**

(a) by counting the number of shaded triangles in each of the diagram 3 and 4, write down the next 2 terms of the number sequence 3, 6, ….

(b) find a formula that connects n and t.

(c) using the formula in (b), find

(i) the number of shaded triangles there will be in diagram 50;

(ii) the numbering of the diagram that has 87 shaded triangles.

(a) by counting the number of shaded triangles in each of the diagram 3 and 4, write down the next 2 terms of the number sequence 3, 6, ….

(b) find a formula that connects n and t.

(c) using the formula in (b), find

(i) the number of shaded triangles there will be in diagram 50;

(ii) the numbering of the diagram that has 87 shaded triangles.

NOTE: Answers to all questions are given at the end of this exercise.

__Question No. 6:
__

**The above shows the first four of a sequence of figures. Figures 1 and 2 contain 4 and 9 small triangles respectively. The sequence continues as shown in figure 3 and 4 and so on. Let N denote the figure number and T the corresponding number of small triangles.**

(a) by counting the number of small triangles in figure 3 and 4, write down next 2 terms of the number sequence 4, 9, …

(b) find a formula that connects N and T.

(c) using the formula in (b), find

(i) the number of small triangles there will be in figure 9;

(ii) the numbering of the figure that has 121 small triangles.

(a) by counting the number of small triangles in figure 3 and 4, write down next 2 terms of the number sequence 4, 9, …

(b) find a formula that connects N and T.

(c) using the formula in (b), find

(i) the number of small triangles there will be in figure 9;

(ii) the numbering of the figure that has 121 small triangles.

**Answers**

**(from left to right)**

April 12, 2017

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