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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. The largest factor that two or more numbers have in common.
Greatest Common Factor
Area of a Sector
Part-to-Part Ratios and Part-to-Whole Ratios
Solving a System of Equations
2. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Volume of a Rectangular Solid
Triangle Inequality Theorem
Using an Equation to Find the Slope
Median and Mode
3. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Multiplying and Dividing Roots
Surface Area of a Rectangular Solid
Pythagorean Theorem
Tangency
4. 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
Finding the midpoint
Negative Exponent and Rational Exponent
Raising Powers to Powers
Characteristics of a Square
5. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Prime Factorization
Intersecting Lines
Average of Evenly Spaced Numbers
Similar Triangles
6. Combine like terms
Domain and Range of a Function
Even/Odd
Adding and Subtraction Polynomials
Similar Triangles
7. you can add/subtract when the part under the radical is the same
Union of Sets
Adding and Subtracting Roots
Solving a Quadratic Equation
Multiples of 3 and 9
8. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Average Rate
Median and Mode
Finding the Original Whole
Reducing Fractions
9. To solve a proportion - cross multiply
Determining Absolute Value
Finding the Original Whole
Intersecting Lines
Solving a Proportion
10. 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
Adding and Subtracting monomials
Direct and Inverse Variation
Comparing Fractions
Percent Formula
11. 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
Solving a Proportion
Volume of a Rectangular Solid
Multiples of 3 and 9
Finding the Missing Number
12. pr^2
Volume of a Rectangular Solid
Multiplying and Dividing Roots
Area of a Circle
Domain and Range of a Function
13. To divide fractions - invert the second one and multiply
Prime Factorization
Identifying the Parts and the Whole
Dividing Fractions
Characteristics of a Rectangle
14. Subtract the smallest from the largest and add 1
Intersecting Lines
Greatest Common Factor
Counting Consecutive Integers
Adding and Subtracting Roots
15. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Relative Primes
Intersecting Lines
Intersection of sets
Even/Odd
16. The smallest multiple (other than zero) that two or more numbers have in common.
Relative Primes
(Least) Common Multiple
Interior and Exterior Angles of a Triangle
Similar Triangles
17. 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
Identifying the Parts and the Whole
Area of a Triangle
Triangle Inequality Theorem
Raising Powers to Powers
18. 1. Re-express them with common denominators 2. Convert them to decimals
Even/Odd
Domain and Range of a Function
Dividing Fractions
Comparing Fractions
19. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Evaluating an Expression
Percent Formula
Multiplying Fractions
Characteristics of a Rectangle
20. 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
Probability
Intersecting Lines
Prime Factorization
The 5-12-13 Triangle
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
Solving a System of Equations
Intersecting Lines
Counting the Possibilities
Multiplying and Dividing Roots
22. For all right triangles: a^2+b^2=c^2
Solving a System of Equations
Adding and Subtracting Roots
Even/Odd
Pythagorean Theorem
23. 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)
Solving a Quadratic Equation
Adding and Subtracting Roots
The 5-12-13 Triangle
Area of a Sector
24. 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
Finding the Missing Number
Volume of a Rectangular Solid
Interior Angles of a Polygon
25. Part = Percent x Whole
Percent Formula
Percent Increase and Decrease
Finding the Original Whole
Finding the Missing Number
26. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Tangency
Prime Factorization
Solving an Inequality
Probability
27. Surface Area = 2lw + 2wh + 2lh
Counting Consecutive Integers
Setting up a Ratio
Prime Factorization
Surface Area of a Rectangular Solid
28. Multiply the exponents
Part-to-Part Ratios and Part-to-Whole Ratios
Even/Odd
Raising Powers to Powers
Multiples of 2 and 4
29. To multiply fractions - multiply the numerators and multiply the denominators
Average Rate
Simplifying Square Roots
Multiplying Fractions
Reducing Fractions
30. 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
Characteristics of a Rectangle
Multiplying/Dividing Signed Numbers
Median and Mode
Function - Notation - and Evaulation
31. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Intersecting Lines
Combined Percent Increase and Decrease
Area of a Triangle
Negative Exponent and Rational Exponent
32. 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
Dividing Fractions
Multiplying Fractions
The 3-4-5 Triangle
Finding the Distance Between Two Points
33. 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)
Repeating Decimal
Even/Odd
PEMDAS
Length of an Arc
34. 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
Finding the Original Whole
Rate
Characteristics of a Parallelogram
Even/Odd
35. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
PEMDAS
Exponential Growth
Determining Absolute Value
Remainders
36. Volume of a Cylinder = pr^2h
Area of a Sector
Interior Angles of a Polygon
Volume of a Cylinder
Repeating Decimal
37. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Volume of a Rectangular Solid
Average of Evenly Spaced Numbers
Raising Powers to Powers
The 3-4-5 Triangle
38. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Exponential Growth
Adding/Subtracting Fractions
Union of Sets
Raising Powers to Powers
39. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Average of Evenly Spaced Numbers
Solving an Inequality
Average Rate
40. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Original Whole
Finding the Distance Between Two Points
Repeating Decimal
Adding/Subtracting Fractions
41. 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
Adding/Subtracting Signed Numbers
Repeating Decimal
Mixed Numbers and Improper Fractions
Raising Powers to Powers
42. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Surface Area of a Rectangular Solid
Dividing Fractions
The 5-12-13 Triangle
43. 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
Adding/Subtracting Signed Numbers
Using an Equation to Find an Intercept
Average of Evenly Spaced Numbers
Probability
44. 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.
Number Categories
Probability
Repeating Decimal
The 5-12-13 Triangle
45. 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
Relative Primes
Parallel Lines and Transversals
Even/Odd
Finding the Distance Between Two Points
46. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Using Two Points to Find the Slope
Comparing Fractions
Multiplying/Dividing Signed Numbers
47. The whole # left over after division
Solving a Quadratic Equation
Adding/Subtracting Fractions
Interior and Exterior Angles of a Triangle
Remainders
48. 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
Using an Equation to Find an Intercept
Adding/Subtracting Signed Numbers
Adding and Subtracting Roots
Rate
49. 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
Using the Average to Find the Sum
Solving a System of Equations
Multiplying and Dividing Powers
Relative Primes
50. 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
Function - Notation - and Evaulation
Multiplying and Dividing Powers
Combined Percent Increase and Decrease
Multiplying Fractions