# ACT Ch12

## 25 terms · Algebra

### Algebra is...

all about solving for an unknown quantity

### What is the Golden Rule of algebra?

Whatever you do to one side of an equation, you have to do to the other side.

### What order are numeric answers presented in?

From least to greatest.

### What are the three steps to Working Backward?

Start with the middle answer, if it's too big, go to the next smaller choice, if it's too small, go to the next larger choice.

### When can you work backward?

When you see numbers in the answer choices and when the question asked in the last line of the problem is relatively straightforward.

### When asked to find a particular value for x, you can..

solve for x or work backward.

### A cosmic equation is...

when x has no particular value.

any value of x.

### One method to solve a cosmic problem is..

Translation; where ACT english terms are converted into ACT math terms.

### Another method to solve a cosmic problem is...

Plugging In; where a number is plugged into the equation.

### What are the three steps involved in plugging in?

Pick numbers for the variables in the problem, using those numbers, find an answer to the problem, then plug in those numbers into the answer choices and see which equals the answer in step 2.

### What is the advantage of plugging in?

It makes difficult problems easier.

### How do you spot a cosmic problem?

If the problem has variables in the answer choices.

### Numbers to avoid when plugging into cosmic problems are..?

0, 1, and numbers already being used in the problem.

### What method can you use when factoring?

The FOIL method. (First, Outer, Inner, Last)

When a factorable expression is equal to zero.

two values that solve the solution.

### The two solutions in a quadratic equation are sometimes called...?

the roots or zeros of the equation.

### What is the difference of perfect squares equation?

x^2 -y^2=(x+y)(x-y)

### What is another commonly used quadratic equation used on the ACT?

x^2+2xy+y^2=(x+y)^2

### What is another commonly used quadratic equation used on the ACT?

x^2-2xy+y^2=(x-y)^2

### In a simultaneous equation...

you can never solve it because it has two variables.

### Simultaneous equations...

include systems of equations.

### When do you change the direction of an inequality sign?

When you multiply or divide both sides of an inequality by a negative number.

### Logarithms...

can be written in exponential form.