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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. Factor out the perfect squares
Average Formula -
Average of Evenly Spaced Numbers
Simplifying Square Roots
Characteristics of a Rectangle
2. 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
Pythagorean Theorem
Direct and Inverse Variation
Part-to-Part Ratios and Part-to-Whole Ratios
Characteristics of a Parallelogram
3. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Prime Factorization
Remainders
Raising Powers to Powers
Counting the Possibilities
4. 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
Interior and Exterior Angles of a Triangle
Function - Notation - and Evaulation
Adding/Subtracting Signed Numbers
Average Rate
5. 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
Adding/Subtracting Signed Numbers
Solving a Quadratic Equation
Even/Odd
6. The largest factor that two or more numbers have in common.
Number Categories
Greatest Common Factor
Negative Exponent and Rational Exponent
Finding the Distance Between Two Points
7. 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
Isosceles and Equilateral triangles
Greatest Common Factor
Evaluating an Expression
8. The whole # left over after division
Simplifying Square Roots
Remainders
Negative Exponent and Rational Exponent
Interior and Exterior Angles of a Triangle
9. A square is a rectangle with four equal sides; Area of Square = side*side
Finding the midpoint
Characteristics of a Square
Factor/Multiple
Multiplying Monomials
10. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Average Rate
Volume of a Rectangular Solid
Characteristics of a Square
Probability
11. 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
Finding the Distance Between Two Points
Surface Area of a Rectangular Solid
Intersection of sets
12. pr^2
Relative Primes
Characteristics of a Rectangle
Rate
Area of a Circle
13. Part = Percent x Whole
Using the Average to Find the Sum
Counting Consecutive Integers
Percent Formula
Adding/Subtracting Signed Numbers
14. Domain: all possible values of x for a function range: all possible outputs of a function
Volume of a Cylinder
Domain and Range of a Function
Determining Absolute Value
Repeating Decimal
15. Probability= Favorable Outcomes/Total Possible Outcomes
Solving a Quadratic Equation
Probability
Isosceles and Equilateral triangles
Combined Percent Increase and Decrease
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
Rate
(Least) Common Multiple
Multiples of 3 and 9
Adding and Subtraction Polynomials
17. Combine like terms
Intersection of sets
Adding and Subtraction Polynomials
Combined Percent Increase and Decrease
Remainders
18. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Adding and Subtracting Roots
Average Formula -
Multiplying Fractions
Rate
19. To solve a proportion - cross multiply
Solving a Proportion
Average Formula -
Raising Powers to Powers
Interior and Exterior Angles of a Triangle
20. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Function - Notation - and Evaulation
Solving a System of Equations
Intersecting Lines
Percent Formula
21. 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
Solving a Quadratic Equation
Intersection of sets
Characteristics of a Rectangle
22. 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)
Adding/Subtracting Signed Numbers
Triangle Inequality Theorem
Length of an Arc
Median and Mode
23. 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
Direct and Inverse Variation
(Least) Common Multiple
Parallel Lines and Transversals
Repeating Decimal
24. 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
Characteristics of a Rectangle
Parallel Lines and Transversals
Counting Consecutive Integers
25. 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 a Quadratic Equation
Percent Formula
Solving an Inequality
Isosceles and Equilateral triangles
26. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Solving an Inequality
Setting up a Ratio
Factor/Multiple
Using the Average to Find the Sum
27. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Characteristics of a Rectangle
Relative Primes
Finding the Original Whole
Reducing Fractions
28. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Using an Equation to Find the Slope
Area of a Sector
Adding/Subtracting Fractions
Mixed Numbers and Improper Fractions
29. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Evaluating an Expression
Finding the midpoint
Even/Odd
Setting up a Ratio
30. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Characteristics of a Square
Median and Mode
Determining Absolute Value
Simplifying Square Roots
31. 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
(Least) Common Multiple
Mixed Numbers and Improper Fractions
Combined Percent Increase and Decrease
Finding the midpoint
32. To divide fractions - invert the second one and multiply
Domain and Range of a Function
Dividing Fractions
Reducing Fractions
Multiples of 2 and 4
33. Add the exponents and keep the same base
Parallel Lines and Transversals
Multiplying and Dividing Powers
Setting up a Ratio
Multiplying Monomials
34. 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
Characteristics of a Square
Comparing Fractions
Surface Area of a Rectangular Solid
35. Sum=(Average) x (Number of Terms)
Counting Consecutive Integers
Multiplying Fractions
Counting the Possibilities
Using the Average to Find the Sum
36. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Adding/Subtracting Signed Numbers
Parallel Lines and Transversals
Characteristics of a Parallelogram
Multiples of 3 and 9
37. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Multiplying and Dividing Powers
Adding/Subtracting Signed Numbers
Interior Angles of a Polygon
Function - Notation - and Evaulation
38. 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
Identifying the Parts and the Whole
Multiplying and Dividing Powers
Even/Odd
Solving a Proportion
39. Multiply the exponents
Raising Powers to Powers
Multiplying and Dividing Powers
Percent Formula
Number Categories
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
Rate
Exponential Growth
Percent Formula
Parallel Lines and Transversals
41. 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
The 3-4-5 Triangle
Area of a Circle
Finding the Original Whole
42. 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
Finding the Missing Number
Prime Factorization
Negative Exponent and Rational Exponent
43. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Characteristics of a Rectangle
Counting the Possibilities
Solving a Quadratic Equation
Median and Mode
44. Combine equations in such a way that one of the variables cancel out
Tangency
Using Two Points to Find the Slope
Solving a System of Equations
Characteristics of a Rectangle
45. 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
Intersecting Lines
Even/Odd
Finding the Missing Number
46. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Average Rate
PEMDAS
Direct and Inverse Variation
Multiplying Fractions
47. 1. Re-express them with common denominators 2. Convert them to decimals
Evaluating an Expression
Relative Primes
Interior Angles of a Polygon
Comparing Fractions
48. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Using an Equation to Find the Slope
Combined Percent Increase and Decrease
Dividing Fractions
49. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Multiplying Monomials
The 3-4-5 Triangle
Multiplying/Dividing Signed Numbers
Adding and Subtracting monomials
50. 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
Negative Exponent and Rational Exponent
The 3-4-5 Triangle
Probability
Percent Increase and Decrease