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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 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
Finding the Missing Number
Negative Exponent and Rational Exponent
Solving a Quadratic Equation
Percent Increase and Decrease
2. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Using the Average to Find the Sum
Interior Angles of a Polygon
Multiplying and Dividing Powers
Identifying the Parts and the Whole
3. Part = Percent x Whole
Characteristics of a Rectangle
Adding and Subtraction Polynomials
Percent Formula
Even/Odd
4. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Using an Equation to Find the Slope
Multiplying and Dividing Powers
Setting up a Ratio
Using an Equation to Find an Intercept
5. 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.
Length of an Arc
Dividing Fractions
Number Categories
Rate
6. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Isosceles and Equilateral triangles
Characteristics of a Rectangle
Multiples of 3 and 9
Simplifying Square Roots
7. 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
Exponential Growth
Factor/Multiple
Multiplying and Dividing Powers
8. 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
Evaluating an Expression
Multiples of 2 and 4
Similar Triangles
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
Using an Equation to Find an Intercept
Adding and Subtraction Polynomials
Part-to-Part Ratios and Part-to-Whole Ratios
Union of Sets
10. 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
Triangle Inequality Theorem
Part-to-Part Ratios and Part-to-Whole Ratios
Pythagorean Theorem
11. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Part-to-Part Ratios and Part-to-Whole Ratios
(Least) Common Multiple
Tangency
Triangle Inequality Theorem
12. The whole # left over after division
Multiplying Monomials
Finding the Original Whole
Remainders
Raising Powers to Powers
13. 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
Triangle Inequality Theorem
Isosceles and Equilateral triangles
Area of a Sector
Counting the Possibilities
14. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Adding and Subtracting Roots
Circumference of a Circle
Finding the Distance Between Two Points
Intersecting Lines
15. To multiply fractions - multiply the numerators and multiply the denominators
Multiples of 3 and 9
Median and Mode
Multiplying Fractions
Finding the Original Whole
16. 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
Repeating Decimal
Dividing Fractions
Even/Odd
Average of Evenly Spaced Numbers
17. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Counting Consecutive Integers
Characteristics of a Rectangle
Finding the Original Whole
Multiplying/Dividing Signed Numbers
18. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Using an Equation to Find an Intercept
Similar Triangles
Multiplying and Dividing Roots
Determining Absolute Value
19. 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
Area of a Sector
Raising Powers to Powers
Negative Exponent and Rational Exponent
Percent Formula
20. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Prime Factorization
Finding the Original Whole
Surface Area of a Rectangular Solid
Circumference of a Circle
21. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Average of Evenly Spaced Numbers
Combined Percent Increase and Decrease
Using an Equation to Find the Slope
Reducing Fractions
22. To solve a proportion - cross multiply
Number Categories
Solving a Proportion
(Least) Common Multiple
Determining Absolute Value
23. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Average Formula -
Solving a Quadratic Equation
Mixed Numbers and Improper Fractions
24. 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
Average of Evenly Spaced Numbers
Interior and Exterior Angles of a Triangle
Parallel Lines and Transversals
Average Rate
25. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Intersecting Lines
The 5-12-13 Triangle
Adding and Subtracting monomials
26. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Solving a Quadratic Equation
Identifying the Parts and the Whole
Function - Notation - and Evaulation
Probability
27. 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
Area of a Triangle
The 3-4-5 Triangle
Average Rate
Relative Primes
28. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Finding the midpoint
Multiplying Monomials
Average Formula -
(Least) Common Multiple
29. 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)
Even/Odd
Average Rate
Area of a Sector
Dividing Fractions
30. 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
Relative Primes
Multiplying/Dividing Signed Numbers
Finding the Missing Number
Part-to-Part Ratios and Part-to-Whole Ratios
31. 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
Prime Factorization
Solving an Inequality
(Least) Common Multiple
Solving a Proportion
32. For all right triangles: a^2+b^2=c^2
Triangle Inequality Theorem
Pythagorean Theorem
Multiples of 2 and 4
The 5-12-13 Triangle
33. Subtract the smallest from the largest and add 1
Intersection of sets
Adding/Subtracting Signed Numbers
Interior Angles of a Polygon
Counting Consecutive Integers
34. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Isosceles and Equilateral triangles
Median and Mode
Intersecting Lines
Finding the Distance Between Two Points
35. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
PEMDAS
Solving a System of Equations
Adding and Subtracting monomials
Reducing Fractions
36. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Area of a Sector
Median and Mode
Multiplying and Dividing Roots
37. 1. Re-express them with common denominators 2. Convert them to decimals
Evaluating an Expression
Remainders
Comparing Fractions
Rate
38. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Greatest Common Factor
Part-to-Part Ratios and Part-to-Whole Ratios
Isosceles and Equilateral triangles
Evaluating an Expression
39. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Exponential Growth
Using an Equation to Find the Slope
Volume of a Cylinder
Parallel Lines and Transversals
40. 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
Comparing Fractions
The 5-12-13 Triangle
Using an Equation to Find an Intercept
The 3-4-5 Triangle
41. Surface Area = 2lw + 2wh + 2lh
Identifying the Parts and the Whole
Surface Area of a Rectangular Solid
Finding the Original Whole
Multiples of 2 and 4
42. 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
(Least) Common Multiple
Triangle Inequality Theorem
Using Two Points to Find the Slope
The 3-4-5 Triangle
43. Volume of a Cylinder = pr^2h
Median and Mode
Volume of a Cylinder
(Least) Common Multiple
Raising Powers to Powers
44. A square is a rectangle with four equal sides; Area of Square = side*side
Median and Mode
Characteristics of a Square
Negative Exponent and Rational Exponent
Adding/Subtracting Signed Numbers
45. 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
Interior and Exterior Angles of a Triangle
Multiplying/Dividing Signed Numbers
Using the Average to Find the Sum
Multiplying and Dividing Powers
46. pr^2
Parallel Lines and Transversals
Solving a Proportion
Area of a Circle
Tangency
47. Probability= Favorable Outcomes/Total Possible Outcomes
Solving a Proportion
Setting up a Ratio
Probability
Multiples of 3 and 9
48. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Factor/Multiple
Intersection of sets
Surface Area of a Rectangular Solid
Reducing Fractions
49. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Percent Increase and Decrease
Reducing Fractions
Counting Consecutive Integers
Union of Sets
50. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Area of a Circle
Parallel Lines and Transversals
Function - Notation - and Evaulation
The 3-4-5 Triangle