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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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sat
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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. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Average of Evenly Spaced Numbers
Parallel Lines and Transversals
Multiplying/Dividing Signed Numbers
Counting the Possibilities
2. 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
Adding/Subtracting Fractions
Repeating Decimal
Dividing Fractions
Factor/Multiple
3. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Median and Mode
Volume of a Rectangular Solid
Direct and Inverse Variation
Interior and Exterior Angles of a Triangle
4. 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 Roots
Exponential Growth
Determining Absolute Value
Part-to-Part Ratios and Part-to-Whole Ratios
5. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Remainders
Reducing Fractions
PEMDAS
Area of a Sector
6. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Percent Formula
Multiplying/Dividing Signed Numbers
Intersection of sets
7. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Pythagorean Theorem
Multiplying and Dividing Roots
Characteristics of a Rectangle
Multiplying and Dividing Powers
8. 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
Length of an Arc
Isosceles and Equilateral triangles
Adding and Subtracting Roots
Rate
9. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average Formula -
Determining Absolute Value
Using an Equation to Find the Slope
Simplifying Square Roots
10. The whole # left over after division
Evaluating an Expression
Remainders
Percent Formula
Solving an Inequality
11. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Identifying the Parts and the Whole
The 3-4-5 Triangle
Volume of a Rectangular Solid
Determining Absolute Value
12. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Area of a Circle
Circumference of a Circle
Evaluating an Expression
Interior Angles of a Polygon
13. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Median and Mode
Evaluating an Expression
Using an Equation to Find the Slope
Number Categories
14. The smallest multiple (other than zero) that two or more numbers have in common.
Intersecting Lines
Using Two Points to Find the Slope
Adding and Subtracting Roots
(Least) Common Multiple
15. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Solving a Proportion
Area of a Circle
Tangency
Relative Primes
16. For all right triangles: a^2+b^2=c^2
Characteristics of a Parallelogram
Pythagorean Theorem
Probability
Average Formula -
17. Combine like terms
Number Categories
Interior and Exterior Angles of a Triangle
Average Formula -
Adding and Subtraction Polynomials
18. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Volume of a Rectangular Solid
Counting Consecutive Integers
Multiples of 2 and 4
Interior and Exterior Angles of a Triangle
19. 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
Negative Exponent and Rational Exponent
Isosceles and Equilateral triangles
Using an Equation to Find an Intercept
Finding the midpoint
20. If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 or 4:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side
Parallel Lines and Transversals
Evaluating an Expression
The 3-4-5 Triangle
Determining Absolute Value
21. Subtract the smallest from the largest and add 1
Using an Equation to Find the Slope
Domain and Range of a Function
Adding and Subtracting monomials
Counting Consecutive Integers
22. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Average Rate
(Least) Common Multiple
Finding the Missing Number
23. pr^2
Percent Increase and Decrease
Area of a Circle
Using Two Points to Find the Slope
Volume of a Rectangular Solid
24. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Comparing Fractions
Tangency
Exponential Growth
25. you can add/subtract when the part under the radical is the same
Multiples of 3 and 9
Finding the Distance Between Two Points
Adding and Subtracting Roots
Domain and Range of a Function
26. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Adding/Subtracting Signed Numbers
Multiples of 2 and 4
Union of Sets
Interior Angles of a Polygon
27. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Solving a Proportion
Area of a Circle
Solving a Quadratic Equation
Adding and Subtracting monomials
28. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Relative Primes
Multiplying/Dividing Signed Numbers
Identifying the Parts and the Whole
PEMDAS
29. 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
Counting Consecutive Integers
Adding/Subtracting Signed Numbers
Solving an Inequality
30. Factor out the perfect squares
Length of an Arc
Simplifying Square Roots
Dividing Fractions
Factor/Multiple
31. Change in y/ change in x rise/run
Part-to-Part Ratios and Part-to-Whole Ratios
Using Two Points to Find the Slope
Multiplying Fractions
Repeating Decimal
32. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Intersection of sets
Multiplying Fractions
Exponential Growth
Surface Area of a Rectangular Solid
33. 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
Area of a Triangle
Greatest Common Factor
Multiplying and Dividing Roots
Finding the Missing Number
34. Add the exponents and keep the same base
Counting Consecutive Integers
Factor/Multiple
Tangency
Multiplying and Dividing Powers
35. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Using the Average to Find the Sum
Characteristics of a Square
Finding the Distance Between Two Points
Intersecting Lines
36. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Multiplying and Dividing Powers
Domain and Range of a Function
Mixed Numbers and Improper Fractions
Multiples of 2 and 4
37. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of
Reciprocal
Exponential Growth
The 3-4-5 Triangle
Interior and Exterior Angles of a Triangle
38. (average of the x coordinates - average of the y coordinates)
Number Categories
Finding the midpoint
Surface Area of a Rectangular Solid
Reducing Fractions
39. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Interior and Exterior Angles of a Triangle
Prime Factorization
Part-to-Part Ratios and Part-to-Whole Ratios
Counting Consecutive Integers
40. 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.
Mixed Numbers and Improper Fractions
Number Categories
Simplifying Square Roots
The 3-4-5 Triangle
41. The largest factor that two or more numbers have in common.
Adding and Subtracting monomials
Prime Factorization
Greatest Common Factor
Even/Odd
42. 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
Area of a Triangle
Evaluating an Expression
Raising Powers to Powers
Reducing Fractions
43. 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
The 3-4-5 Triangle
Adding/Subtracting Signed Numbers
Characteristics of a Rectangle
44. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Multiplying and Dividing Roots
Greatest Common Factor
Mixed Numbers and Improper Fractions
The 5-12-13 Triangle
45. 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
Area of a Sector
Finding the Missing Number
Multiples of 2 and 4
Relative Primes
46. Multiply the exponents
Multiplying and Dividing Powers
Using the Average to Find the Sum
Raising Powers to Powers
Comparing Fractions
47. 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
Counting Consecutive Integers
Direct and Inverse Variation
Surface Area of a Rectangular Solid
Negative Exponent and Rational Exponent
48. To divide fractions - invert the second one and multiply
Determining Absolute Value
The 5-12-13 Triangle
Dividing Fractions
Even/Odd
49. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Distance Between Two Points
Multiples of 3 and 9
Multiplying and Dividing Powers
Circumference of a Circle
50. Surface Area = 2lw + 2wh + 2lh
Solving an Inequality
Exponential Growth
Average of Evenly Spaced Numbers
Surface Area of a Rectangular Solid