Patterns — Practice

Question 1

What is the square of 9?

Accepted Answer

9 x 9 = 81.

Question 2

64 is the square of which number?

Accepted Answer

8, because 8 x 8 = 64.

Question 3

Write the first five triangular numbers.

Accepted Answer

1, 3, 6, 10, 15.

Question 4

Circle the square numbers: 4, 6, 9, 12, 16, 20, 25.

Accepted Answer

4, 9, 16 and 25.

Question 5

Is 24 a square number? Explain your answer.

Accepted Answer

No. 4 x 4 = 16 and 5 x 5 = 25, so no whole number multiplied by itself gives 24. Laid out as dots it would leave gaps in the square.

Question 6

What is the next triangular number after 21, and how did you find it?

Accepted Answer

28. Each new triangular number adds a row one dot longer than the last, and the row after 21 has 7 dots, so 21 + 7 = 28.

Question 7

Find 1 + 3 + 5 + 7 + 9 without adding the terms one by one.

Accepted Answer

There are 5 odd numbers, and the sum of the first n odd numbers is n x n. So the total is 5 x 5 = 25.

Question 8

Add the consecutive triangular numbers 6 and 10. What kind of number do you get?

Accepted Answer

6 + 10 = 16, which is a square number, 4 x 4.

Question 9

Find 1 + 3 + 5 + 7 + 9 + 11 + 13 and explain the rule you used.

Accepted Answer

There are 7 odd numbers, so the total is 7 x 7 = 49. The sum of the first n odd numbers starting from 1 is always n squared.

Question 10

What is the difference between 36 and 25, and what does this tell you about consecutive square numbers?

Accepted Answer

36 - 25 = 11, which is an odd number. The gap between any two consecutive square numbers is always odd, which is exactly why adding successive odd numbers builds the squares.

Question 11

Show that adding two consecutive triangular numbers always gives a square number, using three examples.

Accepted Answer

1 + 3 = 4, 3 + 6 = 9 and 6 + 10 = 16, all squares. Picture two triangles of dots, one turned upside down; they fit together exactly into a square.

Practice — Patterns

Sign in to save attempts to your dashboard and track your accuracy over time

Find a verified tutor

Join a live course

Browse coaching centres

About

Categories

Support

Documentation

Get Study Tips & Updates

Download Our App

Download for iOS

Download for Android

Popular Cities