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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. 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
Adding/Subtracting Signed Numbers
Prime Factorization
Multiplying and Dividing Powers
2. Probability= Favorable Outcomes/Total Possible Outcomes
Intersection of sets
The 3-4-5 Triangle
Probability
Multiplying and Dividing Powers
3. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Setting up a Ratio
Evaluating an Expression
Circumference of a Circle
Area of a Sector
4. 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
Remainders
Relative Primes
Tangency
Interior and Exterior Angles of a Triangle
5. 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
Determining Absolute Value
PEMDAS
Parallel Lines and Transversals
Rate
6. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Volume of a Rectangular Solid
Average of Evenly Spaced Numbers
Characteristics of a Rectangle
Finding the Original Whole
7. 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
Intersection of sets
Mixed Numbers and Improper Fractions
Even/Odd
8. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Area of a Circle
Determining Absolute Value
Similar Triangles
Intersection of sets
9. Sum=(Average) x (Number of Terms)
Interior Angles of a Polygon
The 3-4-5 Triangle
Dividing Fractions
Using the Average to Find the Sum
10. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Finding the Distance Between Two Points
Combined Percent Increase and Decrease
Domain and Range of a Function
Prime Factorization
11. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Finding the Missing Number
Rate
Multiplying and Dividing Roots
Evaluating an Expression
12. 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 the Average to Find the Sum
Using Two Points to Find the Slope
Counting the Possibilities
Finding the midpoint
13. 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
Triangle Inequality Theorem
Percent Formula
Multiplying and Dividing Powers
Setting up a Ratio
14. 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
Percent Increase and Decrease
Direct and Inverse Variation
Intersection of sets
Negative Exponent and Rational Exponent
15. 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)
Length of an Arc
Isosceles and Equilateral triangles
Combined Percent Increase and Decrease
Area of a Sector
16. The largest factor that two or more numbers have in common.
Greatest Common Factor
Multiplying and Dividing Powers
Domain and Range of a Function
Dividing Fractions
17. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Evaluating an Expression
Domain and Range of a Function
Percent Formula
Median and Mode
18. 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
Combined Percent Increase and Decrease
Mixed Numbers and Improper Fractions
Adding and Subtracting Roots
Repeating Decimal
19. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Combined Percent Increase and Decrease
Part-to-Part Ratios and Part-to-Whole Ratios
Solving a Quadratic Equation
20. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Part-to-Part Ratios and Part-to-Whole Ratios
Using the Average to Find the Sum
Area of a Circle
Average Rate
21. 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
The 3-4-5 Triangle
Triangle Inequality Theorem
Remainders
Length of an Arc
22. The whole # left over after division
Volume of a Rectangular Solid
Remainders
(Least) Common Multiple
Finding the Original Whole
23. Surface Area = 2lw + 2wh + 2lh
Surface Area of a Rectangular Solid
Multiplying Monomials
Average Rate
Direct and Inverse Variation
24. 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
Dividing Fractions
Combined Percent Increase and Decrease
Percent Increase and Decrease
Setting up a Ratio
25. 1. Re-express them with common denominators 2. Convert them to decimals
Using Two Points to Find the Slope
Comparing Fractions
Isosceles and Equilateral triangles
Solving a Quadratic Equation
26. 2pr
Counting Consecutive Integers
Combined Percent Increase and Decrease
The 3-4-5 Triangle
Circumference of a Circle
27. 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
Pythagorean Theorem
Intersection of sets
Comparing Fractions
28. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Characteristics of a Square
Adding/Subtracting Fractions
Raising Powers to Powers
29. 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
Function - Notation - and Evaulation
Volume of a Cylinder
Repeating Decimal
Characteristics of a Square
30. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Finding the Missing Number
Solving a Quadratic Equation
Greatest Common Factor
31. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Intersecting Lines
Number Categories
The 3-4-5 Triangle
Function - Notation - and Evaulation
32. A square is a rectangle with four equal sides; Area of Square = side*side
Finding the Original Whole
Finding the Missing Number
Function - Notation - and Evaulation
Characteristics of a Square
33. 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
Relative Primes
Union of Sets
Even/Odd
Multiplying/Dividing Signed Numbers
34. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Comparing Fractions
Solving a Quadratic Equation
Area of a Sector
PEMDAS
35. Combine like terms
Adding/Subtracting Fractions
Tangency
Number Categories
Adding and Subtraction Polynomials
36. 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
Interior Angles of a Polygon
Solving an Inequality
Average Rate
Characteristics of a Rectangle
37. 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
Multiplying/Dividing Signed Numbers
Exponential Growth
Length of an Arc
38. 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
Rate
Finding the Original Whole
Triangle Inequality Theorem
Multiplying/Dividing Signed Numbers
39. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Greatest Common Factor
Using the Average to Find the Sum
Domain and Range of a Function
40. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Finding the Missing Number
Rate
Determining Absolute Value
Area of a Triangle
41. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Comparing Fractions
Interior Angles of a Polygon
Reducing Fractions
Characteristics of a Square
42. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Percent Increase and Decrease
Average Formula -
Repeating Decimal
Solving a System of Equations
43. 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
Finding the Distance Between Two Points
Exponential Growth
Circumference of a Circle
44. Add the exponents and keep the same base
Area of a Circle
Length of an Arc
Greatest Common Factor
Multiplying and Dividing Powers
45. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Simplifying Square Roots
Adding and Subtraction Polynomials
Setting up a Ratio
46. To find the reciprocal of a fraction switch the numerator and the denominator
Number Categories
Average Rate
Reciprocal
Volume of a Rectangular Solid
47. 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
Using an Equation to Find the Slope
Solving a Quadratic Equation
Counting the Possibilities
48. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Simplifying Square Roots
Part-to-Part Ratios and Part-to-Whole Ratios
Similar Triangles
Mixed Numbers and Improper Fractions
49. 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
Identifying the Parts and the Whole
Multiplying and Dividing Powers
Combined Percent Increase and Decrease
Intersecting Lines
50. The smallest multiple (other than zero) that two or more numbers have in common.
Greatest Common Factor
Function - Notation - and Evaulation
(Least) Common Multiple
Dividing Fractions