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