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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Study First
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. 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
Parallel Lines and Transversals
Identifying the Parts and the Whole
Using the Average to Find the Sum
Greatest Common Factor
2. 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
Counting the Possibilities
Interior Angles of a Polygon
Characteristics of a Square
Average Rate
3. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Length of an Arc
Multiples of 2 and 4
Finding the Missing Number
Multiplying Monomials
4. 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
Solving an Inequality
Negative Exponent and Rational Exponent
Length of an Arc
Characteristics of a Square
5. 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 Roots
Number Categories
Length of an Arc
Average Rate
6. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Domain and Range of a Function
Prime Factorization
Interior and Exterior Angles of a Triangle
Dividing Fractions
7. The smallest multiple (other than zero) that two or more numbers have in common.
(Least) Common Multiple
Greatest Common Factor
Using the Average to Find the Sum
Combined Percent Increase and Decrease
8. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Greatest Common Factor
Area of a Sector
Multiplying Fractions
Adding/Subtracting Fractions
9. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Factor/Multiple
Using the Average to Find the Sum
Negative Exponent and Rational Exponent
10. 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
Parallel Lines and Transversals
Mixed Numbers and Improper Fractions
Multiples of 3 and 9
Circumference of a Circle
11. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Even/Odd
Multiples of 3 and 9
Intersecting Lines
Finding the Missing Number
12. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Repeating Decimal
Counting the Possibilities
Average Formula -
13. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Mixed Numbers and Improper Fractions
Reducing Fractions
Evaluating an Expression
14. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Average of Evenly Spaced Numbers
Length of an Arc
Multiples of 2 and 4
Evaluating an Expression
15. (average of the x coordinates - average of the y coordinates)
Finding the midpoint
Interior and Exterior Angles of a Triangle
Mixed Numbers and Improper Fractions
Adding/Subtracting Signed Numbers
16. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Number Categories
Solving a Proportion
Adding and Subtracting monomials
Factor/Multiple
17. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Simplifying Square Roots
Isosceles and Equilateral triangles
Interior and Exterior Angles of a Triangle
18. 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
Solving a System of Equations
Pythagorean Theorem
Length of an Arc
Interior and Exterior Angles of a Triangle
19. 1. Re-express them with common denominators 2. Convert them to decimals
Average Rate
Adding/Subtracting Signed Numbers
Comparing Fractions
Dividing Fractions
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
Adding/Subtracting Fractions
Negative Exponent and Rational Exponent
Interior and Exterior Angles of a Triangle
Finding the Missing Number
21. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Multiplying and Dividing Roots
Remainders
Intersecting Lines
Surface Area of a Rectangular Solid
22. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Domain and Range of a Function
Counting the Possibilities
Adding and Subtracting Roots
Characteristics of a Rectangle
23. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Length of an Arc
Adding and Subtraction Polynomials
Average Rate
Setting up a Ratio
24. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiples of 2 and 4
Adding and Subtracting monomials
Greatest Common Factor
Multiplying Monomials
25. 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
Mixed Numbers and Improper Fractions
Adding/Subtracting Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
Percent Increase and Decrease
26. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Area of a Sector
Average Formula -
Characteristics of a Square
Using an Equation to Find an Intercept
27. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Area of a Circle
Negative Exponent and Rational Exponent
Tangency
Repeating Decimal
28. 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
Mixed Numbers and Improper Fractions
Similar Triangles
Average Formula -
Area of a Triangle
29. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Volume of a Rectangular Solid
Determining Absolute Value
Direct and Inverse Variation
Part-to-Part Ratios and Part-to-Whole Ratios
30. 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
Isosceles and Equilateral triangles
Solving an Inequality
Volume of a Cylinder
Using an Equation to Find an Intercept
31. 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
Simplifying Square Roots
Solving a System of Equations
Multiplying/Dividing Signed Numbers
Rate
32. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Multiplying Fractions
Average of Evenly Spaced Numbers
Adding/Subtracting Signed Numbers
Tangency
33. 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
Determining Absolute Value
Rate
The 3-4-5 Triangle
Solving an Inequality
34. 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
Multiplying and Dividing Powers
Using Two Points to Find the Slope
Solving a Quadratic Equation
35. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Interior Angles of a Polygon
Finding the Missing Number
Average Formula -
Circumference of a Circle
36. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Finding the midpoint
Volume of a Rectangular Solid
Intersection of sets
Multiplying and Dividing Roots
37. 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
Intersecting Lines
Characteristics of a Parallelogram
Volume of a Cylinder
Multiples of 2 and 4
38. you can add/subtract when the part under the radical is the same
Average of Evenly Spaced Numbers
The 5-12-13 Triangle
Percent Formula
Adding and Subtracting Roots
39. The whole # left over after division
Solving an Inequality
Finding the midpoint
Relative Primes
Remainders
40. 2pr
Even/Odd
Setting up a Ratio
Circumference of a Circle
The 3-4-5 Triangle
41. Multiply the exponents
Reciprocal
Raising Powers to Powers
Multiplying and Dividing Roots
Multiplying Fractions
42. 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
Length of an Arc
Solving a Quadratic Equation
Negative Exponent and Rational Exponent
Finding the Missing Number
43. To divide fractions - invert the second one and multiply
The 3-4-5 Triangle
Using the Average to Find the Sum
Triangle Inequality Theorem
Dividing Fractions
44. Volume of a Cylinder = pr^2h
Median and Mode
Direct and Inverse Variation
Volume of a Cylinder
Solving a Quadratic Equation
45. pr^2
Mixed Numbers and Improper Fractions
Using the Average to Find the Sum
Percent Formula
Area of a Circle
46. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Area of a Circle
Volume of a Rectangular Solid
Multiplying and Dividing Roots
Comparing Fractions
47. 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
Similar Triangles
Finding the Original Whole
Repeating Decimal
Direct and Inverse Variation
48. 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
Intersection of sets
Average of Evenly Spaced Numbers
Relative Primes
The 5-12-13 Triangle
49. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Solving a Quadratic Equation
Isosceles and Equilateral triangles
Number Categories
50. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Using an Equation to Find the Slope
Part-to-Part Ratios and Part-to-Whole Ratios
Multiplying/Dividing Signed Numbers
Characteristics of a Square