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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. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Negative Exponent and Rational Exponent
Exponential Growth
Finding the Original Whole
Prime Factorization
2. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Exponential Growth
The 3-4-5 Triangle
Percent Increase and Decrease
Reducing Fractions
3. 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
Rate
Solving a System of Equations
Using the Average to Find the Sum
Interior and Exterior Angles of a Triangle
4. 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
Characteristics of a Square
Area of a Circle
Rate
Average Rate
5. 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)
Length of an Arc
Area of a Sector
Reducing Fractions
Median and Mode
6. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Domain and Range of a Function
Multiplying Monomials
Finding the Original Whole
(Least) Common Multiple
7. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Function - Notation - and Evaulation
Identifying the Parts and the Whole
Volume of a Rectangular Solid
Area of a Triangle
8. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Direct and Inverse Variation
Counting the Possibilities
Median and Mode
Union of Sets
9. 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
Similar Triangles
Adding/Subtracting Fractions
Triangle Inequality Theorem
10. The smallest multiple (other than zero) that two or more numbers have in common.
(Least) Common Multiple
Characteristics of a Rectangle
Finding the Original Whole
Volume of a Rectangular Solid
11. Add the exponents and keep the same base
Multiplying and Dividing Powers
Finding the midpoint
Using an Equation to Find the Slope
Percent Formula
12. Combine like terms
Prime Factorization
Adding and Subtraction Polynomials
Solving a System of Equations
Factor/Multiple
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.
Interior Angles of a Polygon
PEMDAS
Number Categories
Percent Increase and Decrease
14. 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
Rate
Repeating Decimal
Triangle Inequality Theorem
Characteristics of a Rectangle
15. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Intersection of sets
Adding and Subtracting Roots
Intersecting Lines
Interior and Exterior Angles of a Triangle
16. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Distance Between Two Points
Area of a Sector
Comparing Fractions
Adding and Subtracting monomials
17. 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
The 5-12-13 Triangle
Evaluating an Expression
Multiplying and Dividing Roots
Direct and Inverse Variation
18. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Parallel Lines and Transversals
Average of Evenly Spaced Numbers
Setting up a Ratio
Part-to-Part Ratios and Part-to-Whole Ratios
19. For all right triangles: a^2+b^2=c^2
Characteristics of a Parallelogram
Multiplying Monomials
Pythagorean Theorem
Intersection of sets
20. 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
Rate
Factor/Multiple
Combined Percent Increase and Decrease
21. Subtract the smallest from the largest and add 1
Exponential Growth
Counting Consecutive Integers
Number Categories
Using an Equation to Find an Intercept
22. To find the reciprocal of a fraction switch the numerator and the denominator
Using an Equation to Find an Intercept
Reciprocal
Reducing Fractions
Direct and Inverse Variation
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
Intersection of sets
Multiples of 3 and 9
Mixed Numbers and Improper Fractions
Counting Consecutive Integers
24. 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
Adding/Subtracting Signed Numbers
Finding the Distance Between Two Points
Average Rate
Comparing Fractions
25. 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
Percent Formula
Counting the Possibilities
Number Categories
Prime Factorization
26. To divide fractions - invert the second one and multiply
Mixed Numbers and Improper Fractions
Direct and Inverse Variation
Dividing Fractions
Median and Mode
27. Domain: all possible values of x for a function range: all possible outputs of a function
Characteristics of a Parallelogram
Function - Notation - and Evaulation
Median and Mode
Domain and Range of a Function
28. 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
Simplifying Square Roots
Combined Percent Increase and Decrease
Using an Equation to Find an Intercept
Function - Notation - and Evaulation
29. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Similar Triangles
Adding and Subtraction Polynomials
Interior Angles of a Polygon
Finding the Missing Number
30. pr^2
Area of a Circle
Characteristics of a Parallelogram
Rate
Triangle Inequality Theorem
31. 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
Using the Average to Find the Sum
Percent Increase and Decrease
Negative Exponent and Rational Exponent
Multiplying Fractions
32. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Identifying the Parts and the Whole
Domain and Range of a Function
Setting up a Ratio
Interior Angles of a Polygon
33. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Multiples of 2 and 4
Identifying the Parts and the Whole
PEMDAS
The 3-4-5 Triangle
34. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Reducing Fractions
Characteristics of a Rectangle
Raising Powers to Powers
35. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Prime Factorization
Solving a Quadratic Equation
Evaluating an Expression
Identifying the Parts and the Whole
36. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Area of a Circle
Area of a Sector
Tangency
Dividing Fractions
37. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Negative Exponent and Rational Exponent
Multiples of 3 and 9
Using an Equation to Find the Slope
Volume of a Rectangular Solid
38. To multiply fractions - multiply the numerators and multiply the denominators
PEMDAS
Multiplying Fractions
(Least) Common Multiple
Interior Angles of a Polygon
39. 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
Average Formula -
Counting the Possibilities
Adding/Subtracting Fractions
Characteristics of a Parallelogram
40. Sum=(Average) x (Number of Terms)
Adding/Subtracting Signed Numbers
Using the Average to Find the Sum
Intersecting Lines
Evaluating an Expression
41. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Part-to-Part Ratios and Part-to-Whole Ratios
Multiplying Fractions
Pythagorean Theorem
42. The whole # left over after division
Area of a Sector
Multiplying Fractions
Remainders
Finding the midpoint
43. 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
Interior Angles of a Polygon
Dividing Fractions
Direct and Inverse Variation
Using the Average to Find the Sum
44. To solve a proportion - cross multiply
Solving a Proportion
Intersecting Lines
Adding and Subtracting Roots
Adding and Subtracting monomials
45. A square is a rectangle with four equal sides; Area of Square = side*side
PEMDAS
Characteristics of a Square
Adding and Subtraction Polynomials
Part-to-Part Ratios and Part-to-Whole Ratios
46. 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
Rate
Volume of a Rectangular Solid
The 3-4-5 Triangle
Multiplying and Dividing Roots
47. 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
Adding/Subtracting Fractions
Triangle Inequality Theorem
Finding the Missing Number
Finding the Original Whole
48. 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
Exponential Growth
Even/Odd
Adding/Subtracting Signed Numbers
Intersecting Lines
49. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Percent Formula
Using an Equation to Find the Slope
Intersection of sets
Similar Triangles
50. Probability= Favorable Outcomes/Total Possible Outcomes
Characteristics of a Square
Volume of a Rectangular Solid
Multiplying and Dividing Roots
Probability