Math

Number Theory

100

7+7-7 = 

7

200

1/2, 3, -5, 0.11111... : These are what kind of numbers? Be specific.

Rational

300

How many different pairs of integers multiply to 12?

8

400

Is 1 a prime number? Explain why.

No. It only has one factor, which is 1.

500

a, b, and c are prime numbers with a < b < c. The sum of a+b+c is equal to 34. Find all possible combinations of a, b, and c.

(2, 3, 29), and (2, 13, 19)

Exponents

100

-5²=

-25

200

Will (-3)^2x be negative or positive, if x is a positive integer? Explain.

Positive, because 2x will be even.

300

(5-1)¹⁵/(13-11)²⁷ =

8

400

Solve for x: 3^3x+4 = 9^x+12

x=20

500

Alex thinks of two integers. Winnie tries to guess them. Alex gives two hints:
- One number raised to the exponent of the other equals 64.

- The sum of the two numbers is less than 0.

What are the integers that Alex is thinking of?

-8 and 2

Geometry

100

A 3D figure has 6 faces and contains a pentagon. What is this figure?

A pentagonal pyramid

200

A triangular prism has base 8 cm, height 4 cm, and width 3 cm. Find its volume.

48 cm³

300

A cube's surface area is 384 cm². Find half of its volume.

256 cm³

400

A rectangle's length is 6 m longer than its width. Its perimeter is 52 m. Find its area.

160 m²

500

A cube's surface area is equal to its volume based off the number (without the units). Find its side length (in units).

6 units

Algebra

100

Write an expression:

Six less than a number.

x-6

200

12 decreased by a number is -3. What is that number?

15

300

Winnie can run twice as fast as Grogg. If they ran a total of 684 m combined, how far did Winnie run?

456 m

400

Alex, Grogg, and Lizzie each took some marbles from a bag. The bag ended up being empty.

- Grogg took 3 less than twice of how many marbles Alex took.

- Lizzie took 5 more marbles than Alex.

- There are 50 marbles in the bag.

How many marbles did each monster take?

Alex: 12 marbles

Lizzie: 17 marbles

Grogg: 21 marbles

500

Solve the following system of equations:

y = 2x-3

3x + 2y = 15

x=3, y=3

Random

100

-|-|||-|-||-|||||-5|||||||||||=

-5

200

A cube has side length y cm. What is its surface area?

6y² cm²

300

5 consecutive integers have a sum of 65. Find the middle integer.

13

400

50!/48!=

2450

500

Winnie thinks of three positive integers, a, b, and c, where a<b<c. Grogg tries to guess them. Winnie gives three hints:

- They multiply to 72.

- The largest is a perfect square.

- Another integer (not the same one) is even.

Grogg says, "I don't have enough information." What are all the possible combinations of Winnie's integers?

(1, 2, 36), (1, 8, 9), and (2, 4, 9)