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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. 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
Negative Exponent and Rational Exponent
Multiples of 2 and 4
Union of Sets
2. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Dividing Fractions
Remainders
Multiples of 2 and 4
3. pr^2
Counting the Possibilities
Area of a Circle
Finding the midpoint
The 3-4-5 Triangle
4. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Reducing Fractions
Evaluating an Expression
Solving an Inequality
Circumference of a Circle
5. 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
Area of a Circle
Area of a Triangle
Surface Area of a Rectangular Solid
6. Add the exponents and keep the same base
Factor/Multiple
Multiplying and Dividing Powers
Dividing Fractions
Characteristics of a Square
7. 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
Adding and Subtracting monomials
Part-to-Part Ratios and Part-to-Whole Ratios
Interior and Exterior Angles of a Triangle
Mixed Numbers and Improper Fractions
8. 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
Median and Mode
Rate
Length of an Arc
Adding/Subtracting Signed Numbers
9. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Simplifying Square Roots
Similar Triangles
Intersecting Lines
Factor/Multiple
10. 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
Combined Percent Increase and Decrease
The 3-4-5 Triangle
Multiplying/Dividing Signed Numbers
11. 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
Exponential Growth
Intersection of sets
Multiples of 3 and 9
Remainders
12. 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
Adding and Subtracting monomials
Using an Equation to Find the Slope
Area of a Triangle
Dividing Fractions
13. For all right triangles: a^2+b^2=c^2
Average Rate
Evaluating an Expression
Pythagorean Theorem
Using the Average to Find the Sum
14. Change in y/ change in x rise/run
Finding the Original Whole
Intersection of sets
Multiplying and Dividing Powers
Using Two Points to Find the Slope
15. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Multiples of 2 and 4
Interior Angles of a Polygon
Using an Equation to Find the Slope
Similar Triangles
16. 2pr
Triangle Inequality Theorem
Adding and Subtracting Roots
Part-to-Part Ratios and Part-to-Whole Ratios
Circumference of a Circle
17. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Identifying the Parts and the Whole
Prime Factorization
Length of an Arc
Using an Equation to Find the Slope
18. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Adding and Subtracting monomials
Average Rate
Remainders
Evaluating an Expression
19. Subtract the smallest from the largest and add 1
PEMDAS
Counting Consecutive Integers
Finding the Distance Between Two Points
Characteristics of a Parallelogram
20. 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
Interior and Exterior Angles of a Triangle
Negative Exponent and Rational Exponent
Parallel Lines and Transversals
Number Categories
21. 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)
The 3-4-5 Triangle
Area of a Sector
(Least) Common Multiple
Average Formula -
22. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Finding the Missing Number
Tangency
Average Formula -
Using an Equation to Find the Slope
23. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Median and Mode
Interior Angles of a Polygon
Number Categories
Interior and Exterior Angles of a Triangle
24. Surface Area = 2lw + 2wh + 2lh
Combined Percent Increase and Decrease
Adding and Subtracting monomials
Surface Area of a Rectangular Solid
Relative Primes
25. 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
Setting up a Ratio
Identifying the Parts and the Whole
Multiplying Monomials
The 3-4-5 Triangle
26. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
The 5-12-13 Triangle
Solving a Quadratic Equation
Exponential Growth
Length of an Arc
27. 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
Median and Mode
Volume of a Cylinder
Raising Powers to Powers
28. 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)
Part-to-Part Ratios and Part-to-Whole Ratios
Length of an Arc
Similar Triangles
Domain and Range of a Function
29. 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
Multiples of 3 and 9
Rate
(Least) Common Multiple
Adding/Subtracting Fractions
30. 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
Finding the Missing Number
Percent Increase and Decrease
Characteristics of a Rectangle
Repeating Decimal
31. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Counting Consecutive Integers
Combined Percent Increase and Decrease
Characteristics of a Square
Characteristics of a Rectangle
32. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Area of a Circle
Characteristics of a Square
Finding the Distance Between Two Points
Solving a Proportion
33. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Multiples of 3 and 9
Determining Absolute Value
Volume of a Rectangular Solid
Area of a Sector
34. Sum=(Average) x (Number of Terms)
Factor/Multiple
Using the Average to Find the Sum
Similar Triangles
Using Two Points to Find the Slope
35. The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides
Parallel Lines and Transversals
Triangle Inequality Theorem
Multiplying Fractions
Factor/Multiple
36. Part = Percent x Whole
Median and Mode
Percent Formula
Volume of a Cylinder
Even/Odd
37. Probability= Favorable Outcomes/Total Possible Outcomes
Multiplying and Dividing Roots
Reciprocal
Probability
Area of a Sector
38. you can add/subtract when the part under the radical is the same
Average Rate
Adding and Subtracting Roots
Multiplying Fractions
Determining Absolute Value
39. 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
PEMDAS
Function - Notation - and Evaulation
The 5-12-13 Triangle
Domain and Range of a Function
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
Percent Formula
Counting Consecutive Integers
Adding and Subtracting monomials
Interior and Exterior Angles of a Triangle
41. The largest factor that two or more numbers have in common.
Greatest Common Factor
Solving a System of Equations
Probability
Surface Area of a Rectangular Solid
42. 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
Raising Powers to Powers
Multiplying and Dividing Roots
Isosceles and Equilateral triangles
Part-to-Part Ratios and Part-to-Whole Ratios
43. 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
Adding and Subtracting monomials
Counting Consecutive Integers
Surface Area of a Rectangular Solid
44. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Determining Absolute Value
Multiples of 3 and 9
Factor/Multiple
Exponential Growth
45. 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
Surface Area of a Rectangular Solid
Pythagorean Theorem
The 3-4-5 Triangle
Finding the Original Whole
46. 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
Repeating Decimal
Solving an Inequality
The 3-4-5 Triangle
Parallel Lines and Transversals
47. 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
Percent Increase and Decrease
Characteristics of a Parallelogram
Parallel Lines and Transversals
Median and Mode
48. (average of the x coordinates - average of the y coordinates)
Probability
Finding the Original Whole
Finding the midpoint
Reciprocal
49. 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
Tangency
Combined Percent Increase and Decrease
Characteristics of a Square
Multiplying and Dividing Powers
50. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Counting Consecutive Integers
Circumference of a Circle
Average Rate