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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. Part = Percent x Whole
Area of a Triangle
Counting Consecutive Integers
Percent Formula
Relative Primes
2. 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)
Length of an Arc
Interior and Exterior Angles of a Triangle
Probability
Raising Powers to Powers
3. To divide fractions - invert the second one and multiply
Multiplying Monomials
Dividing Fractions
Characteristics of a Square
Adding and Subtracting Roots
4. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Raising Powers to Powers
Reducing Fractions
Median and Mode
Volume of a Rectangular Solid
5. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Area of a Circle
Average Formula -
Determining Absolute Value
Using an Equation to Find an Intercept
6. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Finding the Distance Between Two Points
Multiples of 2 and 4
Adding/Subtracting Signed Numbers
Area of a Triangle
7. 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
Greatest Common Factor
Percent Increase and Decrease
Area of a Triangle
Factor/Multiple
8. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Using an Equation to Find an Intercept
Similar Triangles
Volume of a Rectangular Solid
Percent Increase and Decrease
9. Surface Area = 2lw + 2wh + 2lh
Surface Area of a Rectangular Solid
Solving a System of Equations
Percent Formula
Adding/Subtracting Fractions
10. 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
Repeating Decimal
Multiples of 3 and 9
Identifying the Parts and the Whole
Multiplying Monomials
11. Volume of a Cylinder = pr^2h
Interior Angles of a Polygon
Number Categories
Volume of a Rectangular Solid
Volume of a Cylinder
12. 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
Evaluating an Expression
Characteristics of a Parallelogram
Reducing Fractions
Triangle Inequality Theorem
13. 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
Mixed Numbers and Improper Fractions
Function - Notation - and Evaulation
Identifying the Parts and the Whole
Repeating Decimal
14. 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
Reducing Fractions
Negative Exponent and Rational Exponent
Characteristics of a Square
15. 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
Adding and Subtracting monomials
Multiplying Monomials
Average Formula -
16. To solve a proportion - cross multiply
Reciprocal
Solving a Proportion
Tangency
Finding the Original Whole
17. If there are m ways one event can happen and n ways a second event can happen - then there are m × n ways for the 2 events to happen
Multiplying/Dividing Signed Numbers
Combined Percent Increase and Decrease
Counting the Possibilities
Characteristics of a Square
18. 2pr
Using the Average to Find the Sum
Evaluating an Expression
Direct and Inverse Variation
Circumference of a Circle
19. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Domain and Range of a Function
Comparing Fractions
Characteristics of a Rectangle
Raising Powers to Powers
20. Probability= Favorable Outcomes/Total Possible Outcomes
Probability
Adding and Subtracting Roots
Finding the Distance Between Two Points
Rate
21. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Multiplying Fractions
Combined Percent Increase and Decrease
Average of Evenly Spaced Numbers
22. 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
The 5-12-13 Triangle
Union of Sets
Intersection of sets
23. 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
Average Formula -
Solving a System of Equations
Adding/Subtracting Signed Numbers
Characteristics of a Square
24. 1. Re-express them with common denominators 2. Convert them to decimals
Number Categories
Probability
Comparing Fractions
Greatest Common Factor
25. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Intersecting Lines
Adding/Subtracting Fractions
Average Formula -
Comparing Fractions
26. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Function - Notation - and Evaulation
Volume of a Rectangular Solid
Average Rate
Solving a Quadratic Equation
27. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Mixed Numbers and Improper Fractions
Isosceles and Equilateral triangles
Volume of a Rectangular Solid
Determining Absolute Value
28. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Direct and Inverse Variation
Exponential Growth
Multiplying/Dividing Signed Numbers
Multiplying and Dividing Roots
29. Change in y/ change in x rise/run
Characteristics of a Square
Domain and Range of a Function
Using Two Points to Find the Slope
Function - Notation - and Evaulation
30. The smallest multiple (other than zero) that two or more numbers have in common.
Simplifying Square Roots
Volume of a Cylinder
Circumference of a Circle
(Least) Common Multiple
31. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Percent Formula
Area of a Circle
Volume of a Cylinder
32. Combine like terms
Adding and Subtraction Polynomials
Characteristics of a Parallelogram
Surface Area of a Rectangular Solid
Evaluating an Expression
33. 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
Comparing Fractions
PEMDAS
Interior Angles of a Polygon
34. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Function - Notation - and Evaulation
Tangency
Triangle Inequality Theorem
Circumference of a Circle
35. 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
Even/Odd
Part-to-Part Ratios and Part-to-Whole Ratios
Volume of a Rectangular Solid
Solving a Proportion
36. 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
Prime Factorization
Finding the Distance Between Two Points
Interior Angles of a Polygon
37. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Setting up a Ratio
Exponential Growth
Interior Angles of a Polygon
Prime Factorization
38. 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
Isosceles and Equilateral triangles
Solving a Proportion
Negative Exponent and Rational Exponent
Average of Evenly Spaced Numbers
39. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Relative Primes
Union of Sets
Using an Equation to Find an Intercept
Using the Average to Find the Sum
40. 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
Raising Powers to Powers
Length of an Arc
Mixed Numbers and Improper Fractions
PEMDAS
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
Counting Consecutive Integers
Characteristics of a Parallelogram
Determining Absolute Value
Function - Notation - and Evaulation
42. Add the exponents and keep the same base
Multiplying and Dividing Powers
Negative Exponent and Rational Exponent
Intersecting Lines
Characteristics of a Rectangle
43. 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
Number Categories
Volume of a Cylinder
44. pr^2
Area of a Triangle
Parallel Lines and Transversals
Number Categories
Area of a Circle
45. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Adding and Subtracting monomials
Prime Factorization
Reciprocal
Surface Area of a Rectangular Solid
46. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Reciprocal
Adding and Subtraction Polynomials
Using an Equation to Find the Slope
Multiplying and Dividing Roots
47. you can add/subtract when the part under the radical is the same
Area of a Circle
Adding and Subtracting Roots
Reciprocal
Using Two Points to Find the Slope
48. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Intersection of sets
Exponential Growth
Simplifying Square Roots
PEMDAS
49. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Multiplying Fractions
Relative Primes
Average Formula -
Average Rate
50. 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
Comparing Fractions
Finding the midpoint
Direct and Inverse Variation
Function - Notation - and Evaulation