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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. 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
Exponential Growth
Direct and Inverse Variation
Solving a System of Equations
2. The whole # left over after division
Remainders
Tangency
Using the Average to Find the Sum
(Least) Common Multiple
3. 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
Multiplying/Dividing Signed Numbers
Area of a Sector
Adding and Subtracting monomials
Finding the Missing Number
4. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Intersecting Lines
Reciprocal
Average Formula -
Volume of a Rectangular Solid
5. Factor out the perfect squares
Multiplying Fractions
Factor/Multiple
Interior and Exterior Angles of a Triangle
Simplifying Square Roots
6. To solve a proportion - cross multiply
Solving a Proportion
Median and Mode
Multiplying and Dividing Powers
Negative Exponent and Rational Exponent
7. Change in y/ change in x rise/run
Percent Formula
Function - Notation - and Evaulation
Using Two Points to Find the Slope
Raising Powers to Powers
8. pr^2
Area of a Circle
Mixed Numbers and Improper Fractions
Identifying the Parts and the Whole
Circumference of a Circle
9. 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
Multiplying and Dividing Powers
Remainders
Multiplying Monomials
10. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Finding the Distance Between Two Points
Average Rate
Volume of a Rectangular Solid
Similar Triangles
11. Sum=(Average) x (Number of Terms)
Using Two Points to Find the Slope
Percent Formula
Using the Average to Find the Sum
Triangle Inequality Theorem
12. 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
Greatest Common Factor
Negative Exponent and Rational Exponent
Area of a Sector
Solving a Quadratic Equation
13. 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
Multiples of 3 and 9
Finding the Distance Between Two Points
Adding/Subtracting Signed Numbers
Even/Odd
14. The largest factor that two or more numbers have in common.
Circumference of a Circle
Combined Percent Increase and Decrease
The 3-4-5 Triangle
Greatest Common Factor
15. you can add/subtract when the part under the radical is the same
Adding and Subtracting Roots
Solving an Inequality
Multiplying Monomials
Direct and Inverse Variation
16. 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
Area of a Circle
The 3-4-5 Triangle
Union of Sets
Simplifying Square Roots
17. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Direct and Inverse Variation
Adding/Subtracting Fractions
Number Categories
Using Two Points to Find the Slope
18. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Combined Percent Increase and Decrease
Solving a System of Equations
Counting Consecutive Integers
Multiples of 3 and 9
19. Probability= Favorable Outcomes/Total Possible Outcomes
Characteristics of a Square
Multiplying and Dividing Powers
Evaluating an Expression
Probability
20. 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
Adding and Subtraction Polynomials
Remainders
Interior Angles of a Polygon
Part-to-Part Ratios and Part-to-Whole Ratios
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
Adding and Subtracting Roots
Setting up a Ratio
Comparing Fractions
Relative Primes
22. 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
Relative Primes
Area of a Circle
Using Two Points to Find the Slope
23. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Setting up a Ratio
Adding and Subtracting monomials
Simplifying Square Roots
Solving a Quadratic Equation
24. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Finding the midpoint
Interior and Exterior Angles of a Triangle
Union of Sets
Using Two Points to Find the Slope
25. 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
Tangency
Combined Percent Increase and Decrease
Using the Average to Find the Sum
26. 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
Volume of a Rectangular Solid
Average Rate
Mixed Numbers and Improper Fractions
Average of Evenly Spaced Numbers
27. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Percent Formula
Multiplying Monomials
Remainders
Union of Sets
28. 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)
Function - Notation - and Evaulation
Surface Area of a Rectangular Solid
Adding/Subtracting Signed Numbers
Area of a Sector
29. 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
Average Formula -
Repeating Decimal
Characteristics of a Rectangle
Probability
30. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Pythagorean Theorem
Finding the midpoint
Solving a System of Equations
31. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Solving a Quadratic Equation
Similar Triangles
Combined Percent Increase and Decrease
Adding/Subtracting Fractions
32. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Rate
Prime Factorization
Multiplying Fractions
Multiples of 2 and 4
33. 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
Multiplying and Dividing Roots
Even/Odd
Solving a Proportion
Function - Notation - and Evaulation
34. Multiply the exponents
Adding and Subtracting monomials
Exponential Growth
Pythagorean Theorem
Raising Powers to Powers
35. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Prime Factorization
Solving an Inequality
Parallel Lines and Transversals
Median and Mode
36. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Average of Evenly Spaced Numbers
Using an Equation to Find the Slope
Finding the Original Whole
Median and Mode
37. (average of the x coordinates - average of the y coordinates)
Using the Average to Find the Sum
Adding/Subtracting Fractions
Even/Odd
Finding the midpoint
38. Combine like terms
Mixed Numbers and Improper Fractions
Relative Primes
Adding and Subtraction Polynomials
(Least) Common Multiple
39. 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 Parallelogram
Even/Odd
Relative Primes
Adding and Subtraction Polynomials
40. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Multiplying Fractions
Exponential Growth
Reducing Fractions
Finding the midpoint
41. 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
Adding/Subtracting Fractions
Reciprocal
Multiplying and Dividing Roots
42. 2pr
Remainders
Interior and Exterior Angles of a Triangle
Average of Evenly Spaced Numbers
Circumference of a Circle
43. 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
Circumference of a Circle
Triangle Inequality Theorem
Negative Exponent and Rational Exponent
Interior Angles of a Polygon
44. 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
Surface Area of a Rectangular Solid
Evaluating an Expression
Union of Sets
45. 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
Percent Increase and Decrease
Rate
Even/Odd
Using an Equation to Find the Slope
46. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Multiplying and Dividing Roots
Characteristics of a Rectangle
Negative Exponent and Rational Exponent
47. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Length of an Arc
Intersection of sets
Multiples of 2 and 4
Interior Angles of a Polygon
48. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Triangle Inequality Theorem
Multiplying and Dividing Roots
Prime Factorization
Pythagorean Theorem
49. 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
Domain and Range of a Function
(Least) Common Multiple
Using an Equation to Find an Intercept
Adding/Subtracting Signed Numbers
50. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Counting the Possibilities
Volume of a Rectangular Solid
Function - Notation - and Evaulation
Length of an Arc