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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. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Multiples of 3 and 9
Percent Formula
Solving an Inequality
Triangle Inequality Theorem
2. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Dividing Fractions
Reducing Fractions
The 3-4-5 Triangle
Circumference of a Circle
3. The largest factor that two or more numbers have in common.
Greatest Common Factor
PEMDAS
Multiplying and Dividing Roots
Number Categories
4. 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
Area of a Triangle
Domain and Range of a Function
Percent Formula
Adding and Subtracting monomials
5. 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)
Using Two Points to Find the Slope
Average Rate
Length of an Arc
Factor/Multiple
6. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Exponential Growth
Relative Primes
Using the Average to Find the Sum
7. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Circumference of a Circle
Rate
Average Rate
Multiplying and Dividing Powers
8. 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
Union of Sets
Characteristics of a Rectangle
Reciprocal
9. For all right triangles: a^2+b^2=c^2
Reciprocal
Finding the midpoint
Pythagorean Theorem
Area of a Circle
10. Multiply the exponents
Multiplying and Dividing Powers
Raising Powers to Powers
Area of a Sector
Average of Evenly Spaced Numbers
11. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Multiplying/Dividing Signed Numbers
Reciprocal
Area of a Triangle
Average Formula -
12. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Multiples of 3 and 9
Using an Equation to Find the Slope
Probability
Intersecting Lines
13. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Using the Average to Find the Sum
Multiplying and Dividing Roots
Solving a Quadratic Equation
Comparing Fractions
14. To multiply fractions - multiply the numerators and multiply the denominators
Identifying the Parts and the Whole
(Least) Common Multiple
Multiplying Fractions
Multiples of 2 and 4
15. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Greatest Common Factor
Volume of a Rectangular Solid
Solving a Quadratic Equation
Area of a Sector
16. 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
Multiplying/Dividing Signed Numbers
Rate
Intersection of sets
Counting Consecutive Integers
17. 2pr
Simplifying Square Roots
Counting Consecutive Integers
Circumference of a Circle
Interior and Exterior Angles of a Triangle
18. The whole # left over after division
Remainders
Area of a Circle
Combined Percent Increase and Decrease
Solving a System of Equations
19. 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
Percent Formula
Solving a Quadratic Equation
Solving a Proportion
20. 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
Average of Evenly Spaced Numbers
Identifying the Parts and the Whole
Direct and Inverse Variation
Part-to-Part Ratios and Part-to-Whole Ratios
21. Sum=(Average) x (Number of Terms)
Multiples of 2 and 4
Part-to-Part Ratios and Part-to-Whole Ratios
Solving a Quadratic Equation
Using the Average to Find the Sum
22. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Simplifying Square Roots
Average Formula -
Parallel Lines and Transversals
Prime Factorization
23. 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
Domain and Range of a Function
Rate
Finding the Missing Number
Length of an Arc
24. 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
Average Rate
Interior and Exterior Angles of a Triangle
Volume of a Rectangular Solid
25. Probability= Favorable Outcomes/Total Possible Outcomes
(Least) Common Multiple
Solving a Proportion
Solving a System of Equations
Probability
26. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Remainders
Using the Average to Find the Sum
Average of Evenly Spaced Numbers
Direct and Inverse Variation
27. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Length of an Arc
Percent Formula
Prime Factorization
Mixed Numbers and Improper Fractions
28. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Circumference of a Circle
Area of a Circle
Length of an Arc
PEMDAS
29. Factor out the perfect squares
Reciprocal
Multiples of 3 and 9
Simplifying Square Roots
Finding the midpoint
30. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
The 5-12-13 Triangle
Solving an Inequality
Exponential Growth
31. Add the exponents and keep the same base
Interior and Exterior Angles of a Triangle
Probability
Using Two Points to Find the Slope
Multiplying and Dividing Powers
32. Subtract the smallest from the largest and add 1
Solving an Inequality
Raising Powers to Powers
Area of a Sector
Counting Consecutive Integers
33. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height
Characteristics of a Square
Simplifying Square Roots
Rate
Characteristics of a Parallelogram
34. Change in y/ change in x rise/run
Median and Mode
The 5-12-13 Triangle
Using Two Points to Find the Slope
Reducing Fractions
35. 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
Multiples of 3 and 9
Multiplying and Dividing Roots
Similar Triangles
The 5-12-13 Triangle
36. you can add/subtract when the part under the radical is the same
Adding and Subtracting Roots
The 5-12-13 Triangle
Mixed Numbers and Improper Fractions
Average of Evenly Spaced Numbers
37. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Intersecting Lines
Multiples of 2 and 4
Adding/Subtracting Signed Numbers
Adding/Subtracting Fractions
38. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Length of an Arc
Reducing Fractions
Combined Percent Increase and Decrease
Union of Sets
39. 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
Using Two Points to Find the Slope
Negative Exponent and Rational Exponent
Rate
Using the Average to Find the Sum
40. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Interior Angles of a Polygon
Intersection of sets
Determining Absolute Value
Tangency
41. 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 an Intercept
Even/Odd
Percent Formula
Simplifying Square Roots
42. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Using an Equation to Find the Slope
Repeating Decimal
Intersecting Lines
Finding the Distance Between Two Points
43. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Interior Angles of a Polygon
Factor/Multiple
Using the Average to Find the Sum
44. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Using Two Points to Find the Slope
Intersection of sets
Adding and Subtracting monomials
Exponential Growth
45. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Similar Triangles
The 5-12-13 Triangle
Counting the Possibilities
Identifying the Parts and the Whole
46. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Setting up a Ratio
Multiplying/Dividing Signed Numbers
PEMDAS
Domain and Range of a Function
47. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Interior and Exterior Angles of a Triangle
Median and Mode
Characteristics of a Rectangle
Multiples of 2 and 4
48. 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
The 3-4-5 Triangle
Using the Average to Find the Sum
Similar Triangles
49. To divide fractions - invert the second one and multiply
Domain and Range of a Function
Even/Odd
Raising Powers to Powers
Dividing Fractions
50. 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
Parallel Lines and Transversals
Raising Powers to Powers
Function - Notation - and Evaulation
Volume of a Rectangular Solid