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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Study First
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 re-enforces your understanding as you take the test each time.
1. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Area of a Sector
Multiples of 2 and 4
Domain and Range of a Function
2. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Setting up a Ratio
Determining Absolute Value
Greatest Common Factor
3. The smallest multiple (other than zero) that two or more numbers have in common.
Raising Powers to Powers
Combined Percent Increase and Decrease
Average of Evenly Spaced Numbers
(Least) Common Multiple
4. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Characteristics of a Rectangle
Pythagorean Theorem
Combined Percent Increase and Decrease
The 5-12-13 Triangle
5. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Solving a System of Equations
Multiples of 3 and 9
The 5-12-13 Triangle
Remainders
6. 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
Solving a Quadratic Equation
Combined Percent Increase and Decrease
Solving an Inequality
Triangle Inequality Theorem
7. 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
Finding the Original Whole
Average Rate
Isosceles and Equilateral triangles
Finding the midpoint
8. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Percent Increase and Decrease
Volume of a Rectangular Solid
Parallel Lines and Transversals
Direct and Inverse Variation
9. Combine like terms
PEMDAS
Volume of a Cylinder
Adding and Subtraction Polynomials
Characteristics of a Parallelogram
10. 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
Reducing Fractions
Volume of a Rectangular Solid
Triangle Inequality Theorem
Greatest Common Factor
11. you can add/subtract when the part under the radical is the same
Adding and Subtracting Roots
Multiples of 2 and 4
Finding the Distance Between Two Points
Multiplying and Dividing Roots
12. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Average of Evenly Spaced Numbers
Interior Angles of a Polygon
Multiplying and Dividing Roots
Adding/Subtracting Fractions
13. 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
Isosceles and Equilateral triangles
Average Formula -
Simplifying Square Roots
Relative Primes
14. 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
Triangle Inequality Theorem
Area of a Triangle
Percent Formula
Evaluating an Expression
15. 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
Multiplying/Dividing Signed Numbers
Isosceles and Equilateral triangles
Median and Mode
Domain and Range of a Function
16. Volume of a Cylinder = pr^2h
Exponential Growth
Interior and Exterior Angles of a Triangle
Volume of a Cylinder
Union of Sets
17. Part = Percent x Whole
Finding the Original Whole
Counting Consecutive Integers
Factor/Multiple
Percent Formula
18. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Characteristics of a Square
Identifying the Parts and the Whole
Volume of a Cylinder
Average Formula -
19. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Median and Mode
Prime Factorization
Isosceles and Equilateral triangles
Parallel Lines and Transversals
20. 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
Negative Exponent and Rational Exponent
Circumference of a Circle
Similar Triangles
Reciprocal
21. 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.
Number Categories
Setting up a Ratio
Multiples of 2 and 4
Prime Factorization
22. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Area of a Triangle
Length of an Arc
Adding/Subtracting Fractions
Intersecting Lines
23. Combine equations in such a way that one of the variables cancel out
Percent Formula
Solving a System of Equations
Solving a Proportion
Adding and Subtracting Roots
24. To solve a proportion - cross multiply
Percent Formula
Adding/Subtracting Fractions
Solving a Proportion
Multiples of 2 and 4
25. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)
Repeating Decimal
Direct and Inverse Variation
Length of an Arc
Function - Notation - and Evaulation
26. 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
Percent Increase and Decrease
Repeating Decimal
Relative Primes
Even/Odd
27. 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
Greatest Common Factor
Solving an Inequality
Finding the Distance Between Two Points
Multiplying/Dividing Signed Numbers
28. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Comparing Fractions
Using an Equation to Find an Intercept
Solving a Quadratic Equation
Adding and Subtracting monomials
29. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet
Multiples of 3 and 9
Prime Factorization
Rate
Adding/Subtracting Fractions
30. To convert a mixed number to an improper fraction - multiply the whole number by the denominator - then add the numerator over the same denominator - to convert an improper fraction to a mixed number - divide the denominator into the numerator to get
Mixed Numbers and Improper Fractions
Factor/Multiple
Counting Consecutive Integers
Dividing Fractions
31. Add the exponents and keep the same base
Multiplying and Dividing Powers
Tangency
Triangle Inequality Theorem
The 3-4-5 Triangle
32. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Circumference of a Circle
Median and Mode
Simplifying Square Roots
Counting Consecutive Integers
33. To find the reciprocal of a fraction switch the numerator and the denominator
Multiples of 2 and 4
Reciprocal
Multiples of 3 and 9
Simplifying Square Roots
34. Surface Area = 2lw + 2wh + 2lh
Surface Area of a Rectangular Solid
Multiplying and Dividing Powers
Intersecting Lines
Identifying the Parts and the Whole
35. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Prime Factorization
Area of a Sector
Evaluating an Expression
Median and Mode
36. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x
Length of an Arc
Area of a Circle
Circumference of a Circle
Using an Equation to Find an Intercept
37. (average of the x coordinates - average of the y coordinates)
Dividing Fractions
Repeating Decimal
Finding the midpoint
Probability
38. Sum=(Average) x (Number of Terms)
Even/Odd
Using the Average to Find the Sum
Negative Exponent and Rational Exponent
Raising Powers to Powers
39. Probability= Favorable Outcomes/Total Possible Outcomes
Probability
Average of Evenly Spaced Numbers
Surface Area of a Rectangular Solid
Negative Exponent and Rational Exponent
40. Subtract the smallest from the largest and add 1
Using the Average to Find the Sum
Counting Consecutive Integers
Adding and Subtracting Roots
PEMDAS
41. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Percent Increase and Decrease
Adding and Subtraction Polynomials
Intersection of sets
Mixed Numbers and Improper Fractions
42. To add a positive and negative integer first ignore the signs and find the positive difference between the two integers - attatch the sign of the original with higher absolute value - to subtract negative integers simply change it into an addition pr
Function - Notation - and Evaulation
Similar Triangles
Volume of a Rectangular Solid
Adding/Subtracting Signed Numbers
43. 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 28-16=? Answer: 12
Finding the Missing Number
Volume of a Rectangular Solid
Finding the Original Whole
Remainders
44. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Tangency
(Least) Common Multiple
Percent Formula
45. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Intersection of sets
Multiples of 2 and 4
Multiplying Fractions
Tangency
46. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Prime Factorization
Length of an Arc
Reciprocal
Multiplying Monomials
47. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Parallel Lines and Transversals
Multiplying and Dividing Powers
Negative Exponent and Rational Exponent
Interior Angles of a Polygon
48. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Union of Sets
Using an Equation to Find an Intercept
Average Rate
Solving a Quadratic Equation
49. The whole # left over after division
Using Two Points to Find the Slope
Circumference of a Circle
Remainders
Multiples of 2 and 4
50. To multiply fractions - multiply the numerators and multiply the denominators
Finding the Original Whole
Pythagorean Theorem
Rate
Multiplying Fractions