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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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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 reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Similar Triangles
Reciprocal
Reducing Fractions
Negative Exponent and Rational Exponent
2. 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
Multiplying/Dividing Signed Numbers
Average of Evenly Spaced Numbers
Intersection of sets
Volume of a Cylinder
3. The smallest multiple (other than zero) that two or more numbers have in common.
Average Rate
(Least) Common Multiple
Factor/Multiple
Number Categories
4. Subtract the smallest from the largest and add 1
Multiplying Fractions
Solving a Quadratic Equation
Counting Consecutive Integers
Percent Increase and Decrease
5. 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
Surface Area of a Rectangular Solid
Reducing Fractions
Identifying the Parts and the Whole
Dividing Fractions
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
Determining Absolute Value
The 5-12-13 Triangle
Solving a Quadratic Equation
Multiples of 3 and 9
7. Change in y/ change in x rise/run
Reciprocal
Solving a Quadratic Equation
Using Two Points to Find the Slope
Direct and Inverse Variation
8. you can add/subtract when the part under the radical is the same
Finding the Missing Number
Adding and Subtracting Roots
Volume of a Cylinder
Using the Average to Find the Sum
9. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Using an Equation to Find an Intercept
Adding/Subtracting Signed Numbers
Factor/Multiple
Solving an Inequality
10. Surface Area = 2lw + 2wh + 2lh
Adding and Subtraction Polynomials
Tangency
Rate
Surface Area of a Rectangular Solid
11. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Rate
Adding and Subtracting monomials
The 3-4-5 Triangle
Average of Evenly Spaced Numbers
12. 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
The 5-12-13 Triangle
Isosceles and Equilateral triangles
Intersecting Lines
Adding/Subtracting Fractions
13. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Dividing Fractions
Finding the Original Whole
PEMDAS
Parallel Lines and Transversals
14. 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
Interior and Exterior Angles of a Triangle
Part-to-Part Ratios and Part-to-Whole Ratios
Reducing Fractions
Counting the Possibilities
15. 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
Using an Equation to Find the Slope
Average Rate
Even/Odd
Using the Average to Find the Sum
16. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Determining Absolute Value
(Least) Common Multiple
Average Rate
Multiples of 2 and 4
17. 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
Evaluating an Expression
Adding/Subtracting Signed Numbers
Rate
Function - Notation - and Evaulation
18. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Intersecting Lines
Volume of a Rectangular Solid
Relative Primes
Characteristics of a Rectangle
19. Sum=(Average) x (Number of Terms)
Interior Angles of a Polygon
Using the Average to Find the Sum
Intersection of sets
Multiplying and Dividing Powers
20. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Median and Mode
Finding the midpoint
Multiples of 2 and 4
21. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Multiplying and Dividing Roots
Repeating Decimal
Using the Average to Find the Sum
Mixed Numbers and Improper Fractions
22. 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
Percent Increase and Decrease
Direct and Inverse Variation
Multiplying/Dividing Signed Numbers
23. 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
Solving a Quadratic Equation
Counting the Possibilities
Union of Sets
Part-to-Part Ratios and Part-to-Whole Ratios
24. For all right triangles: a^2+b^2=c^2
Counting the Possibilities
Area of a Sector
Pythagorean Theorem
Multiplying Fractions
25. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Using Two Points to Find the Slope
Solving an Inequality
Exponential Growth
26. 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
Factor/Multiple
Dividing Fractions
Repeating Decimal
27. The whole # left over after division
Adding and Subtracting monomials
Prime Factorization
Interior and Exterior Angles of a Triangle
Remainders
28. Combine equations in such a way that one of the variables cancel out
Multiplying Fractions
Adding/Subtracting Signed Numbers
Solving a System of Equations
Finding the Original Whole
29. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Raising Powers to Powers
Counting Consecutive Integers
Prime Factorization
Rate
30. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Function - Notation - and Evaulation
Finding the Missing Number
Multiplying Monomials
Repeating Decimal
31. 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
Probability
Combined Percent Increase and Decrease
Characteristics of a Square
Adding and Subtraction Polynomials
32. 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
Area of a Sector
Repeating Decimal
Average of Evenly Spaced Numbers
33. 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
Interior Angles of a Polygon
Prime Factorization
Mixed Numbers and Improper Fractions
The 5-12-13 Triangle
34. 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
Solving a System of Equations
Remainders
Adding/Subtracting Signed Numbers
Solving an Inequality
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
Identifying the Parts and the Whole
Similar Triangles
Setting up a Ratio
Adding and Subtracting monomials
36. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Tangency
Adding/Subtracting Fractions
Negative Exponent and Rational Exponent
PEMDAS
37. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Remainders
Pythagorean Theorem
Intersection of sets
Multiplying Monomials
38. Factor out the perfect squares
Interior Angles of a Polygon
Multiplying Fractions
Simplifying Square Roots
Multiplying Monomials
39. (average of the x coordinates - average of the y coordinates)
Using Two Points to Find the Slope
Average Rate
Counting Consecutive Integers
Finding the midpoint
40. 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
Characteristics of a Rectangle
Interior and Exterior Angles of a Triangle
Exponential Growth
Percent Increase and Decrease
41. 2pr
Prime Factorization
Circumference of a Circle
Counting Consecutive Integers
Raising Powers to Powers
42. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Intersecting Lines
Using the Average to Find the Sum
Surface Area of a Rectangular Solid
Exponential Growth
43. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Identifying the Parts and the Whole
Finding the Original Whole
Interior Angles of a Polygon
Dividing Fractions
44. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Counting Consecutive Integers
Multiplying/Dividing Signed Numbers
Reducing Fractions
Solving a Quadratic Equation
45. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Tangency
Surface Area of a Rectangular Solid
Multiplying/Dividing Signed Numbers
46. Domain: all possible values of x for a function range: all possible outputs of a function
Identifying the Parts and the Whole
Length of an Arc
Domain and Range of a Function
Median and Mode
47. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12
Characteristics of a Rectangle
Evaluating an Expression
Finding the Missing Number
Rate
48. 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
Mixed Numbers and Improper Fractions
Area of a Circle
Multiples of 2 and 4
Area of a Sector
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
Probability
Length of an Arc
Rate
Negative Exponent and Rational Exponent
50. 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.
Adding and Subtracting monomials
Number Categories
Adding/Subtracting Fractions
Pythagorean Theorem