ASPIRE Study Guide
Algebraic Expressionscontain a combination of variables, constants, and at least one operation.
(Variable = a, x, y; contants = 1, 2, 56, 24; operation = +, -, ×, ÷)
To Evaluate an Expression follow these steps:
- Write the algebraic expression
- Substitute the values given for the variables
- Simplify the expressions, following correct order of operations
Equations:
When solving one step equations always use inverse operations. Remember you must always keep the equationbalanced. (Draw the balance if you get stuck).
The inverse of multiplication is division and the inverse of division is multiplication and
When multiplying by a fraction, multiply both sides by its reciprocal
When writing an equation from a word problem. Look for key words that hint at what operation to do. If the problem is abstract, then make up some numbers to check your thinking.
To write an equation from a table or graph, identify values for x and y and figure out a rule that would work for each set of numbers. Make sure to work out several to test the equation. To do this, evaluate the equations with each set of x and y values and see which equation is true for all numbers in the table.
Numbers and Operations:
Factors are numbers that can go into another number. Multiples are numbers you get when skip counting.
Multiplying Fractions:Dividing Fractions:
1. Change mixed numbers to improper1. Change mixed numbers to improper
2. Multiply across the top and bottom2. Flip 2nd fraction, then multiply straight across
3. Simplify (divide top and bottom by same number)(or cross multiply instead)
3. Simplify
An ordered pair is the location of a point on the coordinate grid. Example: (4, 5)
The first number (x-coordinate) is the location of the point along the x-axis. You must move right or left along the x-axis to locate the x-coordinate.
*The second number (y-coordinate) is the location of the point along the y-axis. You must move up or down along the y-axis to locate the y-coordinate.
The coordinate grid has 4 quadrants. Each quadrant is labeled using a Roman Numeral.
II I
III IV
Points in quadrant I have positive x- and y-coordinates.
Points in quadrant II have a negative x-coordinate and a positive y-coordinate.
Points in quadrant III have negative x- and y- coordinates.
Points in quadrant IV have a positive x-coordinate and a negative y-coordinate.
RATIOS and PROPORTIONS
Percent means a number out of 100. To solve percent problems, set up a proportion.
A ratio is a comparison of 2 numbers.
A ratio can be shown as a fraction, colon, or with the word “to”
2 equal ratios form a proportion. You can tell if two ratios are equal if you cross multiply.
A ratio table is comparing several equivalent ratios. Set up proportions to solve.
GEOMETRY
Area = length x width ***For a triangle do length x width then divide by 2
Surface area: Find the area of each surface then add for total. For rectangular prisms: 2( lw + wh + hl)
Volume = length x width x height
STATISTICS
A statistical question is one that can have many different answers.
Mean :average - add all values then divide by the number of items you added
Median: middle - put numbers in order least to greatest then find the middle; 1st quartile is median of lower half; 3rd quartile is median of upper half of numbers.
Mode: the number that appears the most often
Range: highest value minus lowest value
Box and Whisker plot: Plot minimum, 1stquartile(median of 1st half of numbers), median, 3rd quartile(median of last half of numbers), maximum above a number line. Draw a box around 1st quartile and 3rd quartile, then “whiskers” to the lowest and highest value.