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Test your basic knowledge 
SAT Math: Concepts And Tricks
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Subjects
:
sat
,
math
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
study here
.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.
This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it reenforces your understanding as you take the test each time.
1. The largest factor that two or more numbers have in common.
Counting the Possibilities
Reciprocal
Raising Powers to Powers
Greatest Common Factor
2. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Multiplying and Dividing Powers
Multiplying/Dividing Signed Numbers
Length of an Arc
3. To predict whether the sum  difference  or product will be even or odd  just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd'  but there's no need to memorize them
Pythagorean Theorem
Comparing Fractions
Even/Odd
Union of Sets
4. If a right triangle's legtoleg ratio is 5:12  or if the legtohypotenuse ratio is 5:13 or 12:13  it's a 51213 triangle
Volume of a Rectangular Solid
Union of Sets
The 51213 Triangle
Solving a Quadratic Equation
5. (average of the x coordinates  average of the y coordinates)
Finding the midpoint
Multiplying Monomials
Percent Formula
Even/Odd
6. Example: If the ratio of males to females is 1 to 2  then what is the ratio of males to people?  work: 1/(1+2) answer: 1/3
Adding and Subtracting monomials
Domain and Range of a Function
Median and Mode
ParttoPart Ratios and ParttoWhole Ratios
7. To reduce a fraction to lowest terms  factor out and cancel all factors the numerator and denominator have in common
Similar Triangles
Reducing Fractions
Circumference of a Circle
Average Formula 
8. you can add/subtract when the part under the radical is the same
Finding the midpoint
Adding and Subtracting Roots
Percent Formula
Adding and Subtraction Polynomials
9. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal  an equaliteral is a triangle where all 3 sides are equal  thus the angles are equal  regardless of side length the angle is always 60 deg
Counting the Possibilities
Counting Consecutive Integers
Negative Exponent and Rational Exponent
Isosceles and Equilateral triangles
10. To multiply or divide integers  firstly ignore the sign and compute the problem  given 2 negatives make a positive  2 positives make a positive  and one negative  and one positive make a negative attach the correct sign
Triangle Inequality Theorem
Intersecting Lines
Factor/Multiple
Multiplying/Dividing Signed Numbers
11. When two lines intersect  adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Similar Triangles
Intersecting Lines
Direct and Inverse Variation
Repeating Decimal
12. pr^2
Reducing Fractions
Area of a Circle
Average of Evenly Spaced Numbers
Direct and Inverse Variation
13. Divisible by 2 if: last digit is even  divisible by 4 if: last two digits form a multiple of 4
Multiples of 2 and 4
Direct and Inverse Variation
Adding and Subtracting monomials
Volume of a Rectangular Solid
14. Add up numbers and divide by the number of numbers  Average=(sum of terms)/(# of terms)
Counting the Possibilities
Counting Consecutive Integers
Average of Evenly Spaced Numbers
Average Formula 
15. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Pythagorean Theorem
Repeating Decimal
Tangency
Prime Factorization
16. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4)  replace x with 4 everywhere in the equation
PEMDAS
Rate
Function  Notation  and Evaulation
Greatest Common Factor
17. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Characteristics of a Parallelogram
Relative Primes
Multiplying Fractions
Similar Triangles
18. Integers that have no common factor other than 1  to determine whether two integers are relative primes break them both down to their prime factorizations
Setting up a Ratio
Solving a System of Equations
Relative Primes
Area of a Circle
19. Add the exponents and keep the same base
Adding and Subtracting Roots
Characteristics of a Rectangle
Multiplying and Dividing Powers
Length of an Arc
20. To divide fractions  invert the second one and multiply
Using an Equation to Find an Intercept
Mixed Numbers and Improper Fractions
Dividing Fractions
Intersecting Lines
21. Use this example: Example: after a 5% increase  the population was 59 346. What was the population before the increase? Work: 1.05x=59 346 Answer: 56 520
Multiplying Fractions
Reciprocal
Finding the Original Whole
Parallel Lines and Transversals
22. A rectangle is a foursided figure with four right angles opposite sides are equal  diagonals are equal; Area of Rectangle = length x width
Intersecting Lines
Length of an Arc
Characteristics of a Rectangle
Multiples of 3 and 9
23. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Identifying the Parts and the Whole
Repeating Decimal
Union of Sets
24. To find the yintercept: put the equation into slopeintercept form (b is the yintercept): y=mx+b or plug x=0 and solve for y  To find the xintercept: plug y=0 and solve for x
Using an Equation to Find an Intercept
Exponential Growth
Counting the Possibilities
The 51213 Triangle
25. Probability= Favorable Outcomes/Total Possible Outcomes
Probability
Pythagorean Theorem
Adding/Subtracting Fractions
Intersecting Lines
26. To evaluate an algebraic expression  plug in the given values for the unknowns and calculate according to PEMDAS
Even/Odd
Evaluating an Expression
Multiplying Monomials
Interior and Exterior Angles of a Triangle
27. The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides
Intersecting Lines
Similar Triangles
Triangle Inequality Theorem
Adding/Subtracting Signed Numbers
28. For all right triangles: a^2+b^2=c^2
Finding the midpoint
Percent Formula
Counting Consecutive Integers
Pythagorean Theorem
29. Integers are whole numbers; they include negtavie whole numbers and zero  Rational numbers can be expressed as a ratio of two integers  irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.
Average of Evenly Spaced Numbers
Interior Angles of a Polygon
Probability
Number Categories
30. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds
Determining Absolute Value
Identifying the Parts and the Whole
Prime Factorization
Median and Mode
31. Start with 100 as a starting value  Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase?  Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110
Multiplying Monomials
Domain and Range of a Function
Combined Percent Increase and Decrease
Using the Average to Find the Sum
32. To solve an inequality do whatever is necessary to both sides to isolate the variable. When you multiply or divide both sides by a negative number you must reverse the sign
Solving an Inequality
Union of Sets
Adding/Subtracting Signed Numbers
Greatest Common Factor
33. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition  use the example: if there are 3 digits that repeat  every 3rd digit is the same. If you want the 31st digit  then the 30th digit is
Dividing Fractions
Volume of a Cylinder
Multiplying and Dividing Powers
Repeating Decimal
34. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
The 51213 Triangle
Relative Primes
Finding the Distance Between Two Points
35. Combine like terms
Circumference of a Circle
Adding and Subtraction Polynomials
Interior Angles of a Polygon
The 345 Triangle
36. Multiply the exponents
Raising Powers to Powers
Determining Absolute Value
Using Two Points to Find the Slope
Remainders
37. The whole # left over after division
Intersection of sets
Similar Triangles
The 345 Triangle
Remainders
38. Factor out the perfect squares
Median and Mode
The 51213 Triangle
Simplifying Square Roots
Isosceles and Equilateral triangles
39. Use special triangles  pythagorean theorem  or distance formula: v(x2x1)²+(y2y1)²
Adding/Subtracting Fractions
Finding the Distance Between Two Points
Adding/Subtracting Signed Numbers
Using the Average to Find the Sum
40. To combine like terms  keep the variable part unchanged while adding or subtracting the coefficients  Example: 2a+3a=? work: (2+3)a answer: 5a
Using an Equation to Find the Slope
(Least) Common Multiple
Characteristics of a Square
Adding and Subtracting monomials
41. A parallelogram has two pairs of parallel sides  opposite sides are equal  opposite angles are equal  consecutive angles add up to 180 degrees; Area of Parallelogram = base x height
Similar Triangles
Characteristics of a Parallelogram
Raising Powers to Powers
Area of a Circle
42. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the
Triangle Inequality Theorem
Intersecting Lines
Negative Exponent and Rational Exponent
Volume of a Rectangular Solid
43. The median is the value that falls in the middle of the set  the mode is the value that appears most often
Rate
Median and Mode
Setting up a Ratio
Mixed Numbers and Improper Fractions
44. To find the reciprocal of a fraction switch the numerator and the denominator
Multiplying/Dividing Signed Numbers
Mixed Numbers and Improper Fractions
Reciprocal
Multiplying Fractions
45. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Multiplying Monomials
Exponential Growth
Factor/Multiple
Counting the Possibilities
46. To find the slope of a line from an equation  put the equation into slopeintercept form (m is the slope): y=mx+b
Function  Notation  and Evaulation
Adding and Subtraction Polynomials
Multiplying Monomials
Using an Equation to Find the Slope
47. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Union of Sets
Domain and Range of a Function
Adding/Subtracting Signed Numbers
48. Use the sum  Example: if the average of 4 #s is 7  and the #s are 3  5  8  and ____  what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 2816=? Answer: 12
Evaluating an Expression
Characteristics of a Square
Finding the Missing Number
Remainders
49. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Adding and Subtracting Roots
Dividing Fractions
The 51213 Triangle
Average of Evenly Spaced Numbers
50. Area of Triangle = 1/2 (base)(height)  the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex
Intersection of sets
Using an Equation to Find the Slope
Finding the midpoint
Area of a Triangle