Math Team

Expressions and Equations

100

x^2 – 4 = 12

x=+/- 4

200

Solve for x: 3(x + 2) -13 = 8

x=5

300

(-3)^2+2[4(1-6)-3(2-5)]

-13

400

I have a number x in mind. When I increase half of a half of x by 8 I get 12. Find x.

x=16

500

If the average of 2, 5, 6, 8, and x is 7, find x.

x=14

Geometry

200

A man has a 10m x 10m square garden. In the center is a 2m x 2m square patch of ground he cannot use. He divides his usable space into four congruent rectangular patches. Find the dimensions (length and width) of each patch.

4x6

300

One leg of a right triangle is 16 and its hypotenuse is 20, find the length of the other leg.

x=12

400

The coordinates of the vertices of a triangle are (0,0), (a,0), (0,b), where a and b are both integers. If the area of this triangle is 1, what are all possible values of a?

1, 2, -1, -2

500

Find the area of the triangle that lies at the given coordinates. A (2,5) B (6,4) C (4,7)

5

Random Challenge

200

There is a pair of whole numbers a, and b, each greater than 1 and less than 10 for which a^b = b^a + 7. Find the value of (a + b)^2.

49

300

If p-2, p, and p+2 are all primes, find the only possible value of p.

5

400

If x + y = 5 and x – y =1, what is the value of 2^(x^2-y^2)?

32

500

There is only one set of four consecutive positive integers such that the sum of the cubes of three of them is equal to the cube of the remaining one. What is the largest of these four integers?

6