Number Theory
7+7-7 =
7
-52=
-25
A 3D figure has 6 faces and contains a pentagon. What is this figure?
A pentagonal pyramid
Write an expression:
Six less than a number.
x-6
-|-|||-|-||-|||||-5|||||||||||=
-5
1/2, 3, -5, 0.11111... : These are what kind of numbers? Be specific.
Rational
Will (-3)2x be negative or positive, if x is a positive integer? Explain.
Positive, because 2x will be even.
A triangular prism has base 8 cm, height 4 cm, and width 3 cm. Find its volume.
48 cm3
12 decreased by a number is -3. What is that number?
15
A cube has side length y cm. What is its surface area?
6y2 cm2
How many different pairs of integers multiply to 12?
8
(5-1)15/(13-11)27 =
8
A cube's surface area is 384 cm2. Find half of its volume.
256 cm3
Winnie can run twice as fast as Grogg. If they ran a total of 684 m combined, how far did Winnie run?
456 m
5 consecutive integers have a sum of 65. Find the middle integer.
13
Is 1 a prime number? Explain why.
No. It only has one factor, which is 1.
Solve for x: 33x+4 = 9x+12
x=20
A rectangle's length is 6 m longer than its width. Its perimeter is 52 m. Find its area.
160 m2
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
50!/48!=
2450
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)
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
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
Solve the following system of equations:
y = 2x-3
3x + 2y = 15
x=3, y=3
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)