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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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sat
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math
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
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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. Domain: all possible values of x for a function range: all possible outputs of a function
Volume of a Cylinder
Percent Formula
Counting Consecutive Integers
Domain and Range of a Function
2. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Repeating Decimal
Solving a System of Equations
Number Categories
Determining Absolute Value
3. Use this example: Example: after a 5% increase - the population was 59 -346. What was the population before the increase? Work: 1.05x=59 -346 Answer: 56 -520
Domain and Range of a Function
Multiples of 2 and 4
Pythagorean Theorem
Finding the Original Whole
4. 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
Circumference of a Circle
Counting the Possibilities
Pythagorean Theorem
Adding and Subtracting monomials
5. 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
Interior Angles of a Polygon
Interior and Exterior Angles of a Triangle
Remainders
Solving a System of Equations
6. 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
Characteristics of a Rectangle
Percent Increase and Decrease
Adding/Subtracting Fractions
Volume of a Cylinder
7. 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
Combined Percent Increase and Decrease
Counting Consecutive Integers
Repeating Decimal
Adding and Subtracting Roots
8. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Median and Mode
Using Two Points to Find the Slope
Adding/Subtracting Fractions
Area of a Triangle
9. 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
PEMDAS
Area of a Triangle
Domain and Range of a Function
Negative Exponent and Rational Exponent
10. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Reducing Fractions
Adding and Subtraction Polynomials
Remainders
Finding the Distance Between Two Points
11. 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
Triangle Inequality Theorem
PEMDAS
Multiplying and Dividing Roots
Solving an Inequality
12. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Average of Evenly Spaced Numbers
Parallel Lines and Transversals
Adding and Subtracting monomials
Surface Area of a Rectangular Solid
13. 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
Function - Notation - and Evaulation
Adding and Subtracting monomials
Multiples of 2 and 4
Exponential Growth
14. you can add/subtract when the part under the radical is the same
Determining Absolute Value
Solving a Quadratic Equation
Tangency
Adding and Subtracting Roots
15. 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
Length of an Arc
Factor/Multiple
Reciprocal
16. To solve a proportion - cross multiply
Multiplying/Dividing Signed Numbers
Volume of a Rectangular Solid
Repeating Decimal
Solving a Proportion
17. 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
Using the Average to Find the Sum
Negative Exponent and Rational Exponent
PEMDAS
18. 1. Re-express them with common denominators 2. Convert them to decimals
Identifying the Parts and the Whole
Average of Evenly Spaced Numbers
Comparing Fractions
Counting the Possibilities
19. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Characteristics of a Parallelogram
Solving a Quadratic Equation
Part-to-Part Ratios and Part-to-Whole Ratios
20. Subtract the smallest from the largest and add 1
PEMDAS
Finding the Original Whole
Counting Consecutive Integers
Multiplying Fractions
21. Combine like terms
Adding and Subtraction Polynomials
Interior Angles of a Polygon
Area of a Sector
Even/Odd
22. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Tangency
Solving an Inequality
Dividing Fractions
23. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Parallel Lines and Transversals
Exponential Growth
Similar Triangles
Prime Factorization
24. 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.
Isosceles and Equilateral triangles
Number Categories
Interior Angles of a Polygon
Relative Primes
25. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Percent Formula
Interior Angles of a Polygon
Number Categories
Comparing Fractions
26. The smallest multiple (other than zero) that two or more numbers have in common.
(Least) Common Multiple
Counting Consecutive Integers
Function - Notation - and Evaulation
Setting up a Ratio
27. 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
Finding the Original Whole
Comparing Fractions
Direct and Inverse Variation
28. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Area of a Sector
Rate
Function - Notation - and Evaulation
Average Formula -
29. 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
Tangency
Combined Percent Increase and Decrease
Surface Area of a Rectangular Solid
Identifying the Parts and the Whole
30. 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
Interior Angles of a Polygon
Reducing Fractions
Multiplying Monomials
31. The whole # left over after division
Remainders
Adding and Subtracting monomials
Relative Primes
Median and Mode
32. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Prime Factorization
Multiples of 3 and 9
Mixed Numbers and Improper Fractions
Solving an Inequality
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
The 5-12-13 Triangle
Triangle Inequality Theorem
Average Rate
Multiplying and Dividing Powers
34. To divide fractions - invert the second one and multiply
The 3-4-5 Triangle
Characteristics of a Rectangle
Circumference of a Circle
Dividing Fractions
35. 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
Multiplying/Dividing Signed Numbers
Negative Exponent and Rational Exponent
Finding the Missing Number
Remainders
36. 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
Using an Equation to Find an Intercept
Isosceles and Equilateral triangles
Multiplying Fractions
The 3-4-5 Triangle
37. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Solving a Quadratic Equation
Identifying the Parts and the Whole
Parallel Lines and Transversals
Triangle Inequality Theorem
38. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Multiples of 2 and 4
Characteristics of a Square
Adding and Subtracting monomials
Characteristics of a Rectangle
39. Volume of a Cylinder = pr^2h
Interior Angles of a Polygon
Negative Exponent and Rational Exponent
Reciprocal
Volume of a Cylinder
40. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Volume of a Rectangular Solid
Finding the Missing Number
Percent Formula
41. 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
(Least) Common Multiple
Multiplying Monomials
Multiplying/Dividing Signed Numbers
Area of a Triangle
42. pr^2
Multiplying Monomials
Multiples of 2 and 4
Average of Evenly Spaced Numbers
Area of a Circle
43. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
(Least) Common Multiple
Exponential Growth
Setting up a Ratio
Isosceles and Equilateral triangles
44. 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
Multiplying and Dividing Powers
Average of Evenly Spaced Numbers
Interior Angles of a Polygon
45. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Exponential Growth
Remainders
Volume of a Cylinder
Prime Factorization
46. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Adding/Subtracting Signed Numbers
Identifying the Parts and the Whole
Tangency
Repeating Decimal
47. Add the exponents and keep the same base
Characteristics of a Rectangle
Multiplying and Dividing Powers
Adding and Subtracting monomials
The 3-4-5 Triangle
48. 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
Factor/Multiple
Finding the Original Whole
Repeating Decimal
Setting up a Ratio
49. 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
Multiples of 3 and 9
Interior Angles of a Polygon
Mixed Numbers and Improper Fractions
Raising Powers to Powers
50. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Raising Powers to Powers
Multiplying/Dividing Signed Numbers
Exponential Growth
Multiplying Monomials