# Lesson Worksheet: Pascal’s Triangle Mathematics

In this worksheet, we will learn how to solve problems on Pascal’s triangle.

Q1:

In the picture of Pascal’s triangle shown, what type of numbers appear in the diagonal indicated by the arrow? • AThe Fibonacci numbers
• BThe cube numbers
• CThe square numbers
• DThe triangular numbers

Q2:

What is the sum of the terms in the 30th row of Pascal’s triangle?

• A
• B
• C
• D
• E

Q3:

The figure shows a section of Pascal’s triangle. Without using a calculator, find the sum of the highlighted elements. Q4:

What is the second element in the 500th row of Pascal’s triangle?

Q5:

The figure shows 7 adjacent elements in Pascal’s triangle. Given that 5,985 is the 18th element on the 22nd row, find , , , , , and .

• A, , , , ,
• B, , , , ,
• C, , , , ,
• D, , , , ,
• E, , , , ,

Q6:

What is sum of every other element in the 1,000th row of Pascal’s triangle?

• A
• B
• C
• D
• E

Q7:

James is playing a game where a ball is dropped onto an array of pegs, from vertically above the top peg, and it bounces down to numbered buckets at the bottom. He only gets a prize if it falls into buckets 3 or 7. Find the probability that he gets a prize given that there is an even probability it will fall to the left or the right of any given peg.

• A
• B
• C
• D
• E

Q8:

You have 7 pool balls. Find, using Pascal’s triangle, how many different ways you could choose just 3 of them, ignoring the order that you select them in. Q9:

In Pascal’s triangle, each entry is the sum of the two entries above it. In which row of Pascal’s triangle do three consecutive entries occur that are in the ratio ?

Q10:

Use Pascal’s triangle to find the binomial expansion of . • A
• B
• C
• D
• E