Algebra Practice Test 1

puremath

New member
Algebra Practice Test 1

1. Devon owns a house cleaning company and has to give price quotes to potential customers. He figures out his price by assuming a $25 base charge and then adding $8 for each bathroom and $4 for each other room. If he uses P to represent the price, B for bathroom, and R for other rooms, create a formula describing the situation.

2. Given f(x) = 2x^2 − 3x + 7, find f(2.5)

3. Solve 5x + 8 < 3(x + 2)

4. Simplify (x^6)(x^5)

5. The area of a circle is 100π. Find the radius and diameter.

6. Graph y = 2x + 1 and y = 2x - 1 on the same xy-plane. What observation can you make regarding the two graphs?

7. Solve for m: y = mx + b

8. Solve for b: y = mx + b

9. Given f(x) = 2x^2 − 3x + 7, find f(f(x)).

10. Given f(x) = 2x^2 − 3x + 7, find f(1/f(x)).
 
Last edited:

Jason

Well-known member
4. Simplify \(\displaystyle (x)^{6}(x)^{5}\)

\(\displaystyle x^{6 + 5} = x^{11}\)

6. What's the observation of the graphs of the two equations?

It's obvious that equation with the +1 has a positive slope, and the one with the -1 has a negative slope. This is cause the sign on the number in that part of the equation designates the direction.

7. Solve for m:

\(\displaystyle y = mx + b\)

\(\displaystyle y - b = mx + b - b\)

\(\displaystyle y - b = mx\)

\(\displaystyle \dfrac{y - b}{x} = \dfrac{mx}{x}\)

\(\displaystyle \dfrac{y - b}{x} = m\)
 

puremath

New member
4. Simplify \(\displaystyle (x)^{6}(x)^{5}\)

\(\displaystyle x^{6 + 5} = x^{11}\)

6. What's the observation of the graphs of the two equations?

It's obvious that equation with the +1 has a positive slope, and the one with the -1 has a negative slope. This is cause the sign on the number in that part of the equation designates the direction.

7. Solve for m:

\(\displaystyle y = mx + b\)

\(\displaystyle y - b = mx + b - b\)

\(\displaystyle y - b = mx\)

\(\displaystyle \dfrac{y - b}{x} = \dfrac{mx}{x}\)

\(\displaystyle \dfrac{y - b}{x} = m\)
Sorry but not doing math until I move. Taking a break.
 
Top