Math Placement

Multiplying fractions (e.g. !0/7 × 3/5)

Multiply numerator by denominator, then simplify if applicable

What is an integer?

A whole number

Adding fractions

Make the denominator the same number (what you do to bottom must also be done to top). You can usually do this by multiplying the denominators. However, do not add the denominators, only the new numerators.

Multiplying a fraction by a whole number. (E.g., 6 x -5/2)

Write the whole number as itself over 1. Then multiply. (6 x -5, and 1 by 2 (you don’t put the negative sign on denominator) to get -30/2.) If necessary, simplify. (-30/2 simplifies to -15 as the answer.)

Multiply binomials. (E.g., (w -1) x (w + 6)

Use FOIL (first, outer, inner, last) method.

So it is w x w = w²
Then, x x 6 = 6w
Then, -1 x w = -w
Then, -1 × 6 = -6

Put it together as w² + 5w - 6
(It is 5w at the end because the -w and 6w were combined.)

Multiply conjugate binomials (pairs of two-term expressions that have the same terms but opposite signs between them). (E.g., (a - 7) (a+ 7)

Use the proof: (a -b)(a + b) = A² + B². So it is a² - 49

Simplify - e.g. b^6 a³/b²a^4

Subtract b2 from top and bottom. b^4a³/a^4
Then subtract a³ from top and bottom
Answer is b^4/a

Graph the line y = x-2

Substitute numbers fro x. You only need 2 points to graph a line. You can do x = 0 to get the point (0, -2) (because 0 -2 = -2 y value). And then x = 1 to get (1, -1)

Graph the line x = -3.

You can choose any y values for this, but x will always be -3.

Find an ordered pair - e.g. that fits the equation 3x - y = 9

Set x to zero. Then solve. - y = 9. Therefore, y = -9. An ordered pair would then be (0, -9)

If you have an x intercept of 9, the y value is

zero

Find the slope of a graphed line.

Do y2 - y1/x2 - x1. Find the coordinates of two points and plug them into the equation

Setting up an equation to solve. E.g., Bob has a 30$ card. He both something that was .24$ per pound. His card no has 24.48$ left. How much did he buy?

30 - .24x = 24.48

To find the length of the sides of a square given its perimeter or area

Divide perimeter or area by 4

When a force 80 N acts on an object, its acceleration is 10. What about when the force is 48 N? What is the acceleration?

Do 80/10 =8. And then 48/8 = 6. 6 is the acceleration.

Find the area of a circle

Area = pi x r²

Find the circumference of a circle

Circumference = 2 x pi x r

The sum of the angle measures in a triangle must equal

180

Find the value of x

The angle here adds up to 180, so 39 can be subtracted from 180 to find the missing angle

Find the area and missing side of a rectilinear figure

Break the figure down into 2-3 rectangles (or however many is appropriate). Find their areas (L x W) and then add them. You can use existing angles to find missing ones.

Area of a triangle

½ x b x h

Area of a parallelogram

base x height

Horizontal translations: y = g(x - c)

Shift graph to the right c units

Horizontal translations: y = g(x + c)

Shift graph to the left c units

Horizontal translations: y = g(x) + c

Shift graph up c units

Horizontal translations: y = g(x) - c

Shift graph down c units