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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 re-enforces your understanding as you take the test each time.
1. 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
PEMDAS
Negative Exponent and Rational Exponent
Even/Odd
Exponential Growth
2. To divide fractions - invert the second one and multiply
Rate
Multiples of 2 and 4
PEMDAS
Dividing Fractions
3. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Using an Equation to Find the Slope
Reciprocal
Similar Triangles
4. 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
Surface Area of a Rectangular Solid
Multiplying Monomials
Area of a Triangle
Mixed Numbers and Improper Fractions
5. Surface Area = 2lw + 2wh + 2lh
Finding the Original Whole
Reciprocal
Surface Area of a Rectangular Solid
Area of a Triangle
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
Relative Primes
Combined Percent Increase and Decrease
Volume of a Cylinder
Similar Triangles
7. (average of the x coordinates - average of the y coordinates)
Finding the midpoint
(Least) Common Multiple
Solving a Proportion
Median and Mode
8. A square is a rectangle with four equal sides; Area of Square = side*side
Interior and Exterior Angles of a Triangle
Multiplying Monomials
Pythagorean Theorem
Characteristics of a Square
9. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50
Mixed Numbers and Improper Fractions
Multiplying/Dividing Signed Numbers
Percent Increase and Decrease
Adding and Subtracting Roots
10. pr^2
Multiplying and Dividing Roots
Average Formula -
Function - Notation - and Evaulation
Area of a Circle
11. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Adding and Subtracting Roots
Finding the Original Whole
Solving a Quadratic Equation
Characteristics of a Rectangle
12. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Dividing Fractions
Intersecting Lines
Adding/Subtracting Fractions
Multiples of 3 and 9
13. 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.
Comparing Fractions
The 3-4-5 Triangle
Isosceles and Equilateral triangles
Number Categories
14. 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
Finding the Original Whole
Adding and Subtracting monomials
Finding the midpoint
Identifying the Parts and the Whole
15. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Negative Exponent and Rational Exponent
Factor/Multiple
Multiples of 2 and 4
Evaluating an Expression
16. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Similar Triangles
Volume of a Cylinder
Determining Absolute Value
Parallel Lines and Transversals
17. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Adding/Subtracting Signed Numbers
Parallel Lines and Transversals
Intersection of sets
Multiplying and Dividing Roots
18. To solve a proportion - cross multiply
Multiplying/Dividing Signed Numbers
Solving a Proportion
Characteristics of a Parallelogram
Percent Increase and Decrease
19. Sum=(Average) x (Number of Terms)
Reciprocal
Pythagorean Theorem
Solving a Proportion
Using the Average to Find the Sum
20. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Characteristics of a Parallelogram
Rate
Prime Factorization
Triangle Inequality Theorem
21. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Raising Powers to Powers
Relative Primes
Finding the midpoint
Union of Sets
22. To find the reciprocal of a fraction switch the numerator and the denominator
Length of an Arc
Solving a Proportion
Even/Odd
Reciprocal
23. 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
The 5-12-13 Triangle
Volume of a Rectangular Solid
Percent Formula
Mixed Numbers and Improper Fractions
24. To multiply fractions - multiply the numerators and multiply the denominators
Dividing Fractions
Multiplying Fractions
Reciprocal
Circumference of a Circle
25. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Function - Notation - and Evaulation
Solving a Proportion
Multiples of 2 and 4
26. Multiply the exponents
Raising Powers to Powers
Mixed Numbers and Improper Fractions
Median and Mode
Percent Formula
27. 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
Determining Absolute Value
Surface Area of a Rectangular Solid
Solving a System of Equations
Isosceles and Equilateral triangles
28. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
The 5-12-13 Triangle
Solving a Quadratic Equation
Repeating Decimal
Adding and Subtracting Roots
29. 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)
Area of a Circle
Characteristics of a Parallelogram
Multiplying and Dividing Powers
Length of an Arc
30. The 3 angles of any triangle add up to 180 degrees - an exterior angles of a triangle is equal to the sum of the remote interior angles - the 3 exterior angles add up to 360 degrees
Similar Triangles
Interior and Exterior Angles of a Triangle
Area of a Circle
Determining Absolute Value
31. Domain: all possible values of x for a function range: all possible outputs of a function
Part-to-Part Ratios and Part-to-Whole Ratios
Prime Factorization
Domain and Range of a Function
Factor/Multiple
32. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Intersecting Lines
Intersection of sets
Average Formula -
Volume of a Rectangular Solid
33. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Volume of a Cylinder
Tangency
Adding and Subtracting monomials
Circumference of a Circle
34. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa
Domain and Range of a Function
Using an Equation to Find the Slope
Direct and Inverse Variation
Multiplying Monomials
35. 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
Reducing Fractions
Negative Exponent and Rational Exponent
Probability
Solving a Quadratic Equation
36. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Counting the Possibilities
Interior Angles of a Polygon
Finding the Original Whole
Identifying the Parts and the Whole
37. The largest factor that two or more numbers have in common.
Finding the Missing Number
Identifying the Parts and the Whole
Greatest Common Factor
The 5-12-13 Triangle
38. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Multiplying Fractions
Average Rate
Union of Sets
39. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Intersection of sets
Tangency
Adding/Subtracting Fractions
Adding and Subtracting monomials
40. 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
Combined Percent Increase and Decrease
Rate
Counting Consecutive Integers
Adding/Subtracting Signed Numbers
41. Volume of a Cylinder = pr^2h
(Least) Common Multiple
Volume of a Cylinder
Multiples of 3 and 9
Setting up a Ratio
42. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Adding and Subtracting Roots
Area of a Sector
Multiples of 2 and 4
Repeating Decimal
43. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Part-to-Part Ratios and Part-to-Whole Ratios
Number Categories
Reducing Fractions
Using the Average to Find the Sum
44. 2pr
Circumference of a Circle
Finding the midpoint
Average Formula -
Tangency
45. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Percent Increase and Decrease
Relative Primes
Adding/Subtracting Fractions
Average of Evenly Spaced Numbers
46. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Exponential Growth
(Least) Common Multiple
Counting the Possibilities
Median and Mode
47. Part = Percent x Whole
Finding the Original Whole
Percent Formula
Adding and Subtracting monomials
Similar Triangles
48. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Intersecting Lines
Characteristics of a Rectangle
Using Two Points to Find the Slope
Volume of a Rectangular Solid
49. 1. Re-express them with common denominators 2. Convert them to decimals
Using the Average to Find the Sum
Median and Mode
Comparing Fractions
Finding the Original Whole
50. A sector is a piece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (pr^2)
Prime Factorization
Adding and Subtraction Polynomials
Area of a Sector
PEMDAS