Math Challenge

Real Numbers

100

Name the number property that the following question belongs in:

4 × 2 = 2 × 4

commutative

200

Name the number property that the following question belongs in:

6+(-6)=0

additive inverse

300

Name the number property that the following question belongs in:

1290+0=1290

identity

400

Name the number property that the following question belongs in:

(1+6)+3=1+(6+3)

associative

500

Name the number property that the following question belongs in:

3x(6+2)=3x6+3x2

distributive

Functions

100

evaluate the function:

f(x)=1x+1 for x=7

f(7)=8

200

evaluate the function:

f(x) = 2x+4 for x=5

f(5)=14

300

evaluate the function:

h(x) = x2 + 2 for x = −3

h(-3)=11

400

evaluate the function:

f(x)=-10x-5 for x=3

f(x)=-35

500

evaluate the function:

f(x)=1/2x-25 for x=5

f(x)= -22.5

TRY

100

Solve the system of equations.

−5x+13y=−7

5x+4y=24

​ 

y=1 and x=4

200

Solve the following system of equations:

x + y = 6

−3x + y = 2

x = 1 and y = 5

300

Solve the following system of equations:

y + 4x = 8  

5x + 2y = 13  

(x, y) = (1, 4)

400

Two times a number added to another number is 25. Three times the first number minus the other number is 20. Find the numbers. 

x=9, y=7

500

Solve the following system of equations:

10x + 7y = 49  

10y - x = 70  

(x, y) = (0, 7)

Equations and Inequalities

100

Find the answer to the inequality:

2x-5<1

x<3

200

Find the answer to the inequality:

y+12≤22

y≤10

300

Find the answer to the inequality:

2-6y<-10

y>2

400

Find the answer to the following inequality:

 x/5>3

x>15

500

Find the answer to the following inequality:

2/3p+4>10

p>9

Factoring

100

Factor:

x⁴-16

(x²+4)(x²-4)

200

Factor:

x²+5x+6

(x+2)(x+3)

300

Factor:

x²+11x+24

(x-3)(x-8)

400

Factor:

2x²-5x-3

(2x+1)(x-3)

500

Factor:

6x²+17x-14

(3x-2)(2x+7)