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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. Probability= Favorable Outcomes/Total Possible Outcomes
Repeating Decimal
Characteristics of a Parallelogram
Probability
Multiplying/Dividing Signed Numbers
2. The largest factor that two or more numbers have in common.
Remainders
Greatest Common Factor
Interior and Exterior Angles of a Triangle
Adding and Subtracting Roots
3. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Percent Formula
Using an Equation to Find an Intercept
Parallel Lines and Transversals
Pythagorean Theorem
4. Combine equations in such a way that one of the variables cancel out
Solving a Proportion
Solving a System of Equations
The 5-12-13 Triangle
Area of a Sector
5. 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
Using an Equation to Find the Slope
Counting the Possibilities
PEMDAS
Using the Average to Find the Sum
6. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Rate
Average of Evenly Spaced Numbers
Direct and Inverse Variation
7. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Adding/Subtracting Fractions
Intersection of sets
Reducing Fractions
Average Rate
8. 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
Using Two Points to Find the Slope
Percent Formula
Raising Powers to Powers
9. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Combined Percent Increase and Decrease
Evaluating an Expression
Multiplying Fractions
Average Rate
10. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Intersecting Lines
Volume of a Rectangular Solid
Percent Formula
Using an Equation to Find an Intercept
11. 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)
Rate
Length of an Arc
Negative Exponent and Rational Exponent
Similar Triangles
12. 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
Interior Angles of a Polygon
Counting Consecutive Integers
Determining Absolute Value
13. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Finding the Missing Number
Average Rate
Counting the Possibilities
Determining Absolute Value
14. 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
Similar Triangles
Raising Powers to Powers
Multiplying Fractions
Relative Primes
15. 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
Reducing Fractions
Direct and Inverse Variation
The 3-4-5 Triangle
Pythagorean Theorem
16. 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
Multiples of 2 and 4
Probability
Average of Evenly Spaced Numbers
Area of a Triangle
17. 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
Median and Mode
Length of an Arc
Rate
Solving an Inequality
18. Surface Area = 2lw + 2wh + 2lh
Parallel Lines and Transversals
Characteristics of a Parallelogram
Surface Area of a Rectangular Solid
Part-to-Part Ratios and Part-to-Whole Ratios
19. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Using the Average to Find the Sum
Setting up a Ratio
Adding and Subtracting monomials
Multiplying Fractions
20. 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
Median and Mode
Finding the Missing Number
Volume of a Cylinder
Finding the Original Whole
21. 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
Adding/Subtracting Fractions
Multiplying and Dividing Roots
Exponential Growth
22. 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
Remainders
Factor/Multiple
Area of a Triangle
23. Part = Percent x Whole
Prime Factorization
Simplifying Square Roots
Percent Formula
Using an Equation to Find an Intercept
24. 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
Solving a System of Equations
Evaluating an Expression
Isosceles and Equilateral triangles
Pythagorean Theorem
25. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Average Rate
PEMDAS
Characteristics of a Square
Relative Primes
26. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Parallel Lines and Transversals
Solving a Quadratic Equation
Solving a Proportion
Using an Equation to Find the Slope
27. The whole # left over after division
Remainders
Raising Powers to Powers
Percent Formula
(Least) Common Multiple
28. 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
Counting Consecutive Integers
Combined Percent Increase and Decrease
Solving a Quadratic Equation
Using the Average to Find the Sum
29. Combine like terms
Characteristics of a Rectangle
Median and Mode
Adding and Subtraction Polynomials
Intersection of sets
30. Multiply the exponents
Function - Notation - and Evaulation
Raising Powers to Powers
Using an Equation to Find the Slope
Finding the midpoint
31. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Determining Absolute Value
Multiples of 2 and 4
Even/Odd
Identifying the Parts and the Whole
32. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Using the Average to Find the Sum
Percent Formula
Solving a Quadratic Equation
33. 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
Multiplying and Dividing Powers
Interior and Exterior Angles of a Triangle
Raising Powers to Powers
Finding the Original Whole
34. 1. Re-express them with common denominators 2. Convert them to decimals
Volume of a Cylinder
Similar Triangles
The 5-12-13 Triangle
Comparing 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
The 5-12-13 Triangle
Raising Powers to Powers
Average Formula -
Identifying the Parts and the Whole
36. 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
Greatest Common Factor
Adding/Subtracting Signed Numbers
Characteristics of a Parallelogram
Multiplying/Dividing Signed Numbers
37. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Percent Formula
Solving a Quadratic Equation
Surface Area of a Rectangular Solid
Domain and Range of a Function
38. Subtract the smallest from the largest and add 1
Multiplying and Dividing Roots
PEMDAS
Counting Consecutive Integers
Intersection of sets
39. A square is a rectangle with four equal sides; Area of Square = side*side
Intersecting Lines
Surface Area of a Rectangular Solid
Remainders
Characteristics of a Square
40. 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
Counting the Possibilities
Exponential Growth
Multiplying Fractions
Using the Average to Find the Sum
41. 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)
Finding the Missing Number
Relative Primes
Determining Absolute Value
Area of a Sector
42. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Using the Average to Find the Sum
Identifying the Parts and the Whole
Multiplying Monomials
43. 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
Repeating Decimal
Adding and Subtracting monomials
Average Formula -
Domain and Range of a Function
44. To find the reciprocal of a fraction switch the numerator and the denominator
Negative Exponent and Rational Exponent
Average of Evenly Spaced Numbers
Reciprocal
Raising Powers to Powers
45. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Finding the Original Whole
Factor/Multiple
Intersecting Lines
Adding and Subtracting monomials
46. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Characteristics of a Rectangle
The 5-12-13 Triangle
Using the Average to Find the Sum
Repeating Decimal
47. 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
Using the Average to Find the Sum
Percent Increase and Decrease
Prime Factorization
Simplifying Square Roots
48. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average Formula -
Function - Notation - and Evaulation
Finding the Missing Number
Volume of a Rectangular Solid
49. 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
Finding the Missing Number
Solving a Quadratic Equation
Even/Odd
Adding and Subtraction Polynomials
50. 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 Quadratic Equation
Finding the Missing Number
Prime Factorization
Comparing Fractions