The document contains math problems and exercises involving square, cube, and triangle numbers. It begins with warm-up problems calculating expressions and listing the first few terms of each type of number sequence. The remainder of the document consists of diagnostic questions and multi-part exercises to identify properties of these number types and calculate terms in the sequences. It concludes with challenge problems involving writing sequences and calculating totals based on patterns of increasing terms.

1. Warm-up activity
Work out the following
42

32

23

53

1)
2)
3)
4)
Answer
Answer
Answer
Answer

2. Square, cube and triangle numbers
List the first few square numbers:
1, 4, 9, …
List the first few cube numbers.
1, 8, 27, …
List the first few triangle numbers:
1, 3, 6, …

3. Diagnostic
The number 25 is…
(a) a cube number
(b) a square number
(c) a triangle number
(d) none of the above

4. Diagnostic
The number 21 is…
(a) a cube number
(b) a square number
(c) a triangle number
(d) none of the above

5. Diagnostic
The number 7 is…
(a) a cube number
(b) a square number
(c) a triangle number
(d) none of the above

6. Diagnostic
The number 8 is…
(a) a cube number
(b) a square number
(c) a triangle number
(d) none of the above

7. Diagnostic
The number 36 is…
(a) a cube number
(b) a square number
(c) a triangle number
(d) both a square and a
triangle number

8. Alpha Exercise 1
1) List the first five square numbers.
2) What is the 10th square number?
3) What is the 11th square number?
4) List the first five cube numbers.
5) What is the 10th cube number?
6) What is the 11th square number? Answer
Answer
Answer
Answer
Answer
Answer

9. Alpha Exercise 2
1) Find two triangle numbers that are also square
numbers.
2) Find two triangle numbers with a difference of 7.
3) Find two triangle numbers with a sum of 25.
4) 231 and 253 are consecutive triangle numbers.
What is the next triangle number?
5) 378 and 406 are consecutive triangle numbers.
What is the next triangle number?
Answer
Answer
Answer
Answer
Answer
α

10. The nth square, cube and triangle
numbers
What is the nth square number?
What is the nth cube number?
What is the nth triangle number?

11. Beta Exercise
1) What is the 20th square number?
2) What is the 34th square number?
3) What is the 11th cube number?
4) What is the 50th cube number?
5) What is the 20th triangular number?
6) What is the 87th triangular number?
Answer
Answer
Answer
Answer
Answer
Answer
β

12. Gamma Exercise
1) Here is a sequence: 16, 25, 36, 49, 64, …
a) Write down the next term in the sequence.
b) Find the 40th term in this sequence.
2) Here is a sequence: 1001, 1008, 1027, 1064, 1125, …
a) Write down the next term in the sequence.
b) Find the 10th term in this sequence.
Answer
Answer
Answer
Answer
γ

13. Explain the mistake
Portia writes the following:
7 is a square number because 72 =49.
Explain why Portia is wrong.
Answer

14. Exam-style question 1
Here is a sequence:
a) Write down the next term in the sequence.
b) Find the 50th term in this sequence.
1 1 1 1
1 4 9 16
, , , ,...
Answer
Answer

15. Exam-style question 2
Here is a sequence:
8
,
27
,
64
,
125
,...
1 2 3 4
a) Write down the next term in the sequence.
b) Find and expression for the nth term of this sequence.
Answer
Answer

16. Challenge
A king was very pleased with his chef for preparing an
excellent banquet. The king decided to reward the chef
with gold coins for 100 days as follows:
On day 1, he would give the chef 1 gold coin.
On day 2, he would give the chef 2 gold coins.
On day 3, he would give the chef 3 gold coins.
Each day until day 100, the king would give the chef one
more gold coin than the previous day.
How many gold coins will the king give the chef in total?
Answer