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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. 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
Adding and Subtracting monomials
Finding the Original Whole
Solving an Inequality
Length of an Arc
2. Change in y/ change in x rise/run
Repeating Decimal
Using Two Points to Find the Slope
Characteristics of a Rectangle
Length of an Arc
3. 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
Length of an Arc
Finding the Original Whole
Median and Mode
4. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Mixed Numbers and Improper Fractions
Repeating Decimal
Similar Triangles
5. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Counting Consecutive Integers
Multiplying and Dividing Powers
Surface Area of a Rectangular Solid
Parallel Lines and Transversals
6. Multiply the exponents
Raising Powers to Powers
Solving an Inequality
The 3-4-5 Triangle
Multiplying Fractions
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
Counting the Possibilities
Characteristics of a Rectangle
Domain and Range of a Function
Isosceles and Equilateral triangles
8. 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
Tangency
Combined Percent Increase and Decrease
Relative Primes
Number Categories
9. Combine like terms
Adding and Subtraction Polynomials
Adding and Subtracting monomials
Probability
Finding the Distance Between Two Points
10. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Evaluating an Expression
Reducing Fractions
Area of a Circle
Greatest Common Factor
11. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Area of a Triangle
Counting the Possibilities
(Least) Common Multiple
Multiples of 3 and 9
12. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Average Rate
Characteristics of a Rectangle
Using Two Points to Find the Slope
Comparing Fractions
13. Factor out the perfect squares
Dividing Fractions
Multiplying/Dividing Signed Numbers
Simplifying Square Roots
Multiplying and Dividing Powers
14. To find the reciprocal of a fraction switch the numerator and the denominator
Part-to-Part Ratios and Part-to-Whole Ratios
Setting up a Ratio
Reciprocal
Counting Consecutive Integers
15. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average of Evenly Spaced Numbers
Multiplying/Dividing Signed Numbers
Characteristics of a Rectangle
Average Formula -
16. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Area of a Circle
Determining Absolute Value
Multiples of 2 and 4
Adding and Subtracting monomials
17. 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
Adding/Subtracting Fractions
Interior and Exterior Angles of a Triangle
Mixed Numbers and Improper Fractions
Interior Angles of a Polygon
18. 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)
Using Two Points to Find the Slope
Length of an Arc
Interior and Exterior Angles of a Triangle
Volume of a Rectangular Solid
19. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Reducing Fractions
Finding the Missing Number
Intersection of sets
Dividing Fractions
20. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Finding the midpoint
Characteristics of a Square
Remainders
21. 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
Using an Equation to Find an Intercept
Interior Angles of a Polygon
Finding the Original Whole
Average of Evenly Spaced Numbers
22. 1. Re-express them with common denominators 2. Convert them to decimals
Domain and Range of a Function
Raising Powers to Powers
Comparing Fractions
Exponential Growth
23. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Relative Primes
Area of a Circle
Finding the Distance Between Two Points
Median and Mode
24. To divide fractions - invert the second one and multiply
Prime Factorization
Dividing Fractions
Combined Percent Increase and Decrease
Union of Sets
25. 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
Volume of a Rectangular Solid
Counting Consecutive Integers
Identifying the Parts and the Whole
26. 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
Average of Evenly Spaced Numbers
Average Rate
Repeating Decimal
27. Surface Area = 2lw + 2wh + 2lh
Surface Area of a Rectangular Solid
Even/Odd
PEMDAS
Function - Notation - and Evaulation
28. The largest factor that two or more numbers have in common.
Domain and Range of a Function
Greatest Common Factor
Solving a Proportion
Raising Powers to Powers
29. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Identifying the Parts and the Whole
Similar Triangles
Tangency
Interior Angles of a Polygon
30. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Relative Primes
Multiples of 2 and 4
Union of Sets
Prime Factorization
31. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Reciprocal
Probability
Finding the midpoint
32. 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
Function - Notation - and Evaulation
Solving an Inequality
Raising Powers to Powers
Repeating Decimal
33. 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 the Possibilities
Similar Triangles
Triangle Inequality Theorem
Negative Exponent and Rational Exponent
34. 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
Adding and Subtracting monomials
Area of a Triangle
Even/Odd
35. you can add/subtract when the part under the radical is the same
Using the Average to Find the Sum
Comparing Fractions
Triangle Inequality Theorem
Adding and Subtracting Roots
36. pr^2
Reciprocal
Area of a Circle
Finding the midpoint
Dividing Fractions
37. 2pr
Remainders
Using an Equation to Find the Slope
Circumference of a Circle
(Least) Common Multiple
38. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Remainders
Adding/Subtracting Signed Numbers
Using an Equation to Find the Slope
Isosceles and Equilateral triangles
39. 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
Volume of a Rectangular Solid
Average Rate
Triangle Inequality Theorem
Adding and Subtracting Roots
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
Mixed Numbers and Improper Fractions
Using an Equation to Find the Slope
Adding/Subtracting Signed Numbers
Parallel Lines and Transversals
41. To solve a proportion - cross multiply
Area of a Triangle
Multiplying Fractions
Solving a Proportion
Using an Equation to Find the Slope
42. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Length of an Arc
Characteristics of a Rectangle
Volume of a Rectangular Solid
Combined Percent Increase and Decrease
43. 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
Finding the Missing Number
Adding and Subtraction Polynomials
Simplifying Square Roots
44. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Determining Absolute Value
Surface Area of a Rectangular Solid
Simplifying Square Roots
Dividing Fractions
45. 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
Area of a Sector
Exponential Growth
Median and Mode
Relative Primes
46. The smallest multiple (other than zero) that two or more numbers have in common.
Multiplying and Dividing Powers
Characteristics of a Rectangle
(Least) Common Multiple
Part-to-Part Ratios and Part-to-Whole Ratios
47. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Intersecting Lines
Union of Sets
Characteristics of a Parallelogram
Parallel Lines and Transversals
48. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle
Finding the Distance Between Two Points
Multiples of 2 and 4
The 5-12-13 Triangle
Characteristics of a Square
49. 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
Rate
Using an Equation to Find an Intercept
Volume of a Rectangular Solid
Setting up a Ratio
50. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Similar Triangles
Length of an Arc
Using the Average to Find the Sum
Tangency