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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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sat
,
math
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
study here
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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. 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
Repeating Decimal
Adding/Subtracting Fractions
Multiplying Fractions
2. 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
Combined Percent Increase and Decrease
Characteristics of a Square
The 3-4-5 Triangle
Volume of a Cylinder
3. 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
Even/Odd
Multiplying and Dividing Roots
4. 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 and Dividing Powers
Finding the Missing Number
Identifying the Parts and the Whole
Area of a Sector
5. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Percent Formula
Identifying the Parts and the Whole
Parallel Lines and Transversals
Using an Equation to Find the Slope
6. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Intersecting Lines
Multiplying and Dividing Powers
Median and Mode
Finding the Missing Number
7. The whole # left over after division
Percent Increase and Decrease
Raising Powers to Powers
Using an Equation to Find the Slope
Remainders
8. 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
Raising Powers to Powers
Mixed Numbers and Improper Fractions
Evaluating an Expression
The 5-12-13 Triangle
9. you can add/subtract when the part under the radical is the same
Volume of a Rectangular Solid
Length of an Arc
Using an Equation to Find the Slope
Adding and Subtracting Roots
10. 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
Interior and Exterior Angles of a Triangle
Greatest Common Factor
Negative Exponent and Rational Exponent
Solving an Inequality
11. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Adding and Subtracting monomials
Isosceles and Equilateral triangles
Solving a Quadratic Equation
Average Rate
12. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Adding and Subtracting Roots
Average Formula -
Multiplying Fractions
Combined Percent Increase and Decrease
13. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Repeating Decimal
Multiplying Monomials
Finding the Distance Between Two Points
Negative Exponent and Rational Exponent
14. 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
Direct and Inverse Variation
Domain and Range of a Function
Setting up a Ratio
15. pr^2
Volume of a Cylinder
Adding/Subtracting Fractions
Area of a Circle
Rate
16. Subtract the smallest from the largest and add 1
The 5-12-13 Triangle
Counting Consecutive Integers
Characteristics of a Parallelogram
Combined Percent Increase and Decrease
17. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Using an Equation to Find the Slope
Greatest Common Factor
Characteristics of a Rectangle
18. Part = Percent x Whole
Factor/Multiple
Volume of a Cylinder
Percent Formula
Rate
19. To multiply fractions - multiply the numerators and multiply the denominators
Greatest Common Factor
Tangency
Repeating Decimal
Multiplying Fractions
20. 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
Adding and Subtracting monomials
Identifying the Parts and the Whole
Setting up a Ratio
Multiples of 3 and 9
21. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Domain and Range of a Function
Intersection of sets
Multiplying Monomials
Solving a Proportion
22. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Triangle Inequality Theorem
The 3-4-5 Triangle
Multiplying and Dividing Powers
23. Add the exponents and keep the same base
Relative Primes
Using an Equation to Find the Slope
Multiplying and Dividing Powers
Remainders
24. 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
Probability
Using Two Points to Find the Slope
Adding/Subtracting Fractions
25. The smallest multiple (other than zero) that two or more numbers have in common.
Interior and Exterior Angles of a Triangle
Counting the Possibilities
Circumference of a Circle
(Least) Common Multiple
26. 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)
Area of a Sector
Percent Formula
Length of an Arc
Counting the Possibilities
27. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Volume of a Rectangular Solid
Negative Exponent and Rational Exponent
Intersection of sets
Similar Triangles
28. 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
Finding the Distance Between Two Points
Solving a System of Equations
Repeating Decimal
Solving an Inequality
29. To find the reciprocal of a fraction switch the numerator and the denominator
Solving an Inequality
Reciprocal
Function - Notation - and Evaulation
Remainders
30. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Adding/Subtracting Fractions
Multiplying and Dividing Roots
Circumference of a Circle
Area of a Triangle
31. 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
Intersecting Lines
Solving an Inequality
Using an Equation to Find an Intercept
Reducing Fractions
32. Change in y/ change in x rise/run
Average Rate
Rate
Percent Increase and Decrease
Using Two Points to Find the Slope
33. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Intersecting Lines
Parallel Lines and Transversals
Greatest Common Factor
Average Formula -
34. 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
Adding and Subtraction Polynomials
Repeating Decimal
Characteristics of a Parallelogram
35. 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
The 3-4-5 Triangle
Determining Absolute Value
Finding the Missing Number
Median and Mode
36. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Average Rate
Using the Average to Find the Sum
Interior and Exterior Angles of a Triangle
Setting up a Ratio
37. 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
Similar Triangles
Using an Equation to Find an Intercept
The 5-12-13 Triangle
Negative Exponent and Rational Exponent
38. 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
Mixed Numbers and Improper Fractions
Counting Consecutive Integers
Average Formula -
Probability
39. 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
Interior and Exterior Angles of a Triangle
Identifying the Parts and the Whole
Counting Consecutive Integers
Solving a System of Equations
40. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Greatest Common Factor
Multiplying/Dividing Signed Numbers
Union of Sets
The 3-4-5 Triangle
41. The largest factor that two or more numbers have in common.
Combined Percent Increase and Decrease
Finding the Original Whole
Similar Triangles
Greatest Common Factor
42. Multiply the exponents
Median and Mode
Multiplying/Dividing Signed Numbers
Raising Powers to Powers
Negative Exponent and Rational Exponent
43. Combine like terms
Number Categories
Adding and Subtraction Polynomials
Even/Odd
Mixed Numbers and Improper Fractions
44. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Finding the Distance Between Two Points
Intersection of sets
Pythagorean Theorem
Multiples of 2 and 4
45. 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
Median and Mode
Direct and Inverse Variation
Dividing Fractions
46. 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
Average Formula -
The 3-4-5 Triangle
Solving a Quadratic Equation
Area of a Triangle
47. 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
Isosceles and Equilateral triangles
Using Two Points to Find the Slope
Domain and Range of a Function
Negative Exponent and Rational Exponent
48. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Finding the Missing Number
Characteristics of a Parallelogram
Solving a Quadratic Equation
Adding and Subtracting monomials
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
Using an Equation to Find an Intercept
Even/Odd
Interior Angles of a Polygon
Prime Factorization
50. To divide fractions - invert the second one and multiply
Dividing Fractions
Raising Powers to Powers
Even/Odd
Intersecting Lines
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