9th Grade Math

Exponent Law

Who did it?

Pattens in number sequence

Word problem

Finding Numbers

100

(x² ⋅ x^-⁴) / (x^-1 ⋅ x⁰)

1/x

100

Amy: “Brian did it.”

Brian: “Carl did it.”

Carl: “I didn’t do it.”

Only one is telling the truth. Who stole the test paper?

Carl stole the test paper.

If Brian is telling the truth, then Carl did it, which makes Amy and Carl’s statements false. Only Brian tells the truth.

100

Find the next numbers:
3, 6, 18, 72, 360, ___

2160
(Multiply by 2, then 3, then 4, then 5, next multiply by 6)

100

Three consecutive numbers have a sum of 75. What is the smallest number?

The smallest number is 24.

100

I am a three-digit number.

My tens digit is four more than my ones digit.
My hundreds digit is three less than my tens digit.
The sum of my digits is 14.

What number am I?

473

150

(2x³y)² / (4x⁴y)

x²y

150

Four people—Dan, Eva, Frank, and Gina—each make a statement about who took a cookie:

Dan: “Eva took it.”

Eva: “Frank took it.”

Frank: “Gina took it.”

Gina: “I didn’t take it.”

Only one person is telling the truth. Who took the cookie?

Gina took the cookie.

If Gina’s statement is true (“I didn’t take it”), then someone else did. But only one is telling the truth. Testing others shows only if Gina is lying and the others are false does it fit for Gina to have taken it.

150

Find the next two numbers:
2, 3, 5, 9, 17, 33, ___, ___

65, 129
(Each term is previous term × 2 – 1:

150

If Austin scores a 78 and 85 on his first two tests, what does he need to score on his third test to average an 87 for all three?

Austin needs to score a 98.

150

I am a three-digit number.

My hundreds digit is twice my ones digit.
My tens digit is three less than my hundreds digit.
The sum of my digits is 17.
What number am I?

854

200

(3a²b/6a^-1b³)²

a⁶/4b⁴

200

At a contest, three contestants made these statements:

Helen: “I didn’t win.”

Ian: “Helen won.”

Jack: “Ian is lying.”

Only one of them is telling the truth. Who won?

Ian won.

If Ian tells the truth, Helen won, contradicting Ian winning. Testing possibilities shows Ian won fits only if Helen and Jack are lying.

200

Find the next number in the sequence:
2, 5, 10, 17, 26, ___

37

The pattern is adding consecutive odd numbers:

2+3=5

5+5=10

10+7=17

...

200

If the side lengths of a triangle are three consecutive odd numbers, and the perimeter is 51 cm, what is the length of the longest side?

The longest side is 19 cm.

200

My hundreds digit is half my tens digit plus 1.
My ones digit is 2 less than my hundreds digit.
The sum of my digits is 12.
What number am I?

462

250

See picture attached

b⁷/16a⁴

250

Find the next number in the sequence:
2, 4, 3, 6, 4, 8, ___

The sequence alternates between two simple rules:

Odd positions (1st, 3rd, 5th): increase by 1
2 → 3 → 4 → 5
Even positions (2nd, 4th, 6th): increase by 2
4 → 6 → 8

So, the 7th term follows the odd-position pattern: 4 → 5

250

Neal, Austin, and Claire play ball. Austin scores eight more points than Claire, and Claire scores five less than three the number of points as Neal.If they score 89 points total, how many points does Austin score?

42 points

250

I am a three-digit number.

My hundreds digit is half my tens digit plus 2.
My ones digit is 3 less than my hundreds digit.
The sum of my digits is 17.
What number am I?

683

300

See picture attached

5xy¹¹

300

Four friends — Nora, Owen, Paul, and Quinn — are suspects in a prank. They say:

Nora: “Paul did it.”

Owen: “Quinn did it.”

Paul: “Owen didn’t do it.”

Quinn: “Nora is lying.”

Exactly one of these statements is true. Who did the prank?

Owen did it.

If Owen did it, then Nora’s statement “Paul did it” is false, Owen’s “Quinn did it” is false, Paul’s “Owen didn’t do it” is false, and Quinn’s “Nora is lying” is true — exactly one truth.

300

Find the next number in the sequence:
1, 11, 21, 1211, 111221, ___

312211

This is the famous “Look-and-say” sequence. Each term describes the digits of the previous term:

1 → "one 1" → 11
11 → "two 1s" → 21
21 → "one 2, one 1" → 1211
1211 → "one 1, one 2, two 1s" → 111221
111221 → "three 1s, two 2s, one 1" → 312211

300

Spencer, Neal, and Claire go lastertagging. Neal gets five more than two times the number of kills as Spencer. Claire gets twice as many kills as Neal. If the three of us had 92 kills altogether, how many kills did Claire get?

Claire got 54 kills.

300

I am a three-digit number.

My hundreds digit is one-third of the sum of my tens and ones digits.
My tens digit is two more than my ones digit.
The sum of my digits is 16.
What number am I?

475