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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. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Domain and Range of a Function
Isosceles and Equilateral triangles
Setting up a Ratio
2. 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
Raising Powers to Powers
Parallel Lines and Transversals
Mixed Numbers and Improper Fractions
Rate
3. 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
Relative Primes
Pythagorean Theorem
Counting the Possibilities
Finding the Original Whole
4. 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
Intersection of sets
Multiplying and Dividing Roots
The 3-4-5 Triangle
Reducing Fractions
5. Factor out the perfect squares
Solving a Quadratic Equation
Characteristics of a Square
Pythagorean Theorem
Simplifying Square Roots
6. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Union of Sets
Multiplying and Dividing Roots
Area of a Triangle
Reciprocal
7. The whole # left over after division
Parallel Lines and Transversals
Remainders
Factor/Multiple
Average Formula -
8. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Pythagorean Theorem
Characteristics of a Rectangle
Multiples of 3 and 9
Using Two Points to Find the Slope
9. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Evaluating an Expression
Multiples of 3 and 9
Reducing Fractions
Intersection of sets
10. 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
Function - Notation - and Evaulation
Relative Primes
Isosceles and Equilateral triangles
11. 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
Exponential Growth
Using Two Points to Find the Slope
Raising Powers to Powers
12. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
The 5-12-13 Triangle
Dividing Fractions
Domain and Range of a Function
13. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Number Categories
Using Two Points to Find the Slope
Percent Increase and Decrease
PEMDAS
14. Part = Percent x Whole
Domain and Range of a Function
Percent Formula
Part-to-Part Ratios and Part-to-Whole Ratios
Length of an Arc
15. Domain: all possible values of x for a function range: all possible outputs of a function
Adding/Subtracting Signed Numbers
Raising Powers to Powers
Function - Notation - and Evaulation
Domain and Range of a Function
16. 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
Evaluating an Expression
Finding the Distance Between Two Points
Parallel Lines and Transversals
Isosceles and Equilateral triangles
17. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Probability
Adding/Subtracting Fractions
Using Two Points to Find the Slope
Adding and Subtracting monomials
18. Add the exponents and keep the same base
Using the Average to Find the Sum
Multiplying and Dividing Powers
Area of a Triangle
Multiplying Fractions
19. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Area of a Triangle
Prime Factorization
Interior and Exterior Angles of a Triangle
Similar Triangles
20. Combine like terms
Triangle Inequality Theorem
Multiplying Fractions
Adding and Subtraction Polynomials
Volume of a Rectangular Solid
21. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Rate
Average Formula -
Triangle Inequality Theorem
Evaluating an Expression
22. 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
Solving an Inequality
Combined Percent Increase and Decrease
Tangency
Multiplying/Dividing Signed Numbers
23. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Direct and Inverse Variation
Exponential Growth
Repeating Decimal
Multiples of 2 and 4
24. 1. Re-express them with common denominators 2. Convert them to decimals
Multiples of 3 and 9
Interior Angles of a Polygon
Comparing Fractions
Intersecting Lines
25. 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
Adding and Subtracting monomials
Isosceles and Equilateral triangles
Exponential Growth
Percent Increase and Decrease
26. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Dividing Fractions
Median and Mode
Area of a Triangle
The 5-12-13 Triangle
27. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Counting Consecutive Integers
Raising Powers to Powers
Using an Equation to Find the Slope
Multiplying and Dividing Powers
28. 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
Similar Triangles
Function - Notation - and Evaulation
Intersection of sets
Triangle Inequality Theorem
29. 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
Factor/Multiple
Volume of a Rectangular Solid
Intersecting Lines
30. 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
Isosceles and Equilateral triangles
Combined Percent Increase and Decrease
31. pr^2
Length of an Arc
Finding the Distance Between Two Points
Greatest Common Factor
Area of a Circle
32. 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
Pythagorean Theorem
Factor/Multiple
Using an Equation to Find an Intercept
Raising Powers to Powers
33. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Multiplying and Dividing Powers
Evaluating an Expression
Interior Angles of a Polygon
Average of Evenly Spaced Numbers
34. A square is a rectangle with four equal sides; Area of Square = side*side
(Least) Common Multiple
Adding/Subtracting Fractions
Characteristics of a Square
Exponential Growth
35. The largest factor that two or more numbers have in common.
Adding and Subtracting Roots
Evaluating an Expression
Length of an Arc
Greatest Common Factor
36. Subtract the smallest from the largest and add 1
Triangle Inequality Theorem
Finding the Original Whole
Counting Consecutive Integers
Characteristics of a Parallelogram
37. 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)
Volume of a Rectangular Solid
Determining Absolute Value
Length of an Arc
Characteristics of a Parallelogram
38. Change in y/ change in x rise/run
The 5-12-13 Triangle
Using Two Points to Find the Slope
Multiplying and Dividing Roots
Reciprocal
39. you can add/subtract when the part under the radical is the same
Adding and Subtracting Roots
Triangle Inequality Theorem
Characteristics of a Parallelogram
Part-to-Part Ratios and Part-to-Whole Ratios
40. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Length of an Arc
Multiplying Fractions
PEMDAS
Average Rate
41. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Counting Consecutive Integers
The 5-12-13 Triangle
Union of Sets
Negative Exponent and Rational Exponent
42. 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
Finding the Original Whole
Adding and Subtracting Roots
Adding/Subtracting Signed Numbers
43. To divide fractions - invert the second one and multiply
Dividing Fractions
Percent Formula
Pythagorean Theorem
Using Two Points to Find the Slope
44. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Using the Average to Find the Sum
Mixed Numbers and Improper Fractions
PEMDAS
Factor/Multiple
45. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Percent Increase and Decrease
Function - Notation - and Evaulation
Adding/Subtracting Fractions
Average of Evenly Spaced Numbers
46. 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
Isosceles and Equilateral triangles
Solving a Quadratic Equation
Prime Factorization
Identifying the Parts and the Whole
47. 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
Reducing Fractions
Exponential Growth
Finding the Original Whole
Circumference of a Circle
48. 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
Using an Equation to Find an Intercept
Characteristics of a Square
Finding the Missing Number
Characteristics of a Parallelogram
49. 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)
Multiplying Fractions
Area of a Sector
Reciprocal
Remainders
50. To solve a proportion - cross multiply
Solving a Proportion
Even/Odd
Solving an Inequality
Adding and Subtracting monomials