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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. The largest factor that two or more numbers have in common.
Adding and Subtraction Polynomials
Characteristics of a Rectangle
Mixed Numbers and Improper Fractions
Greatest Common Factor
2. 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
Area of a Circle
Multiplying Fractions
Identifying the Parts and the Whole
Adding and Subtracting Roots
3. 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
Volume of a Rectangular Solid
Solving an Inequality
Volume of a Cylinder
The 3-4-5 Triangle
4. Change in y/ change in x rise/run
Multiples of 3 and 9
Using Two Points to Find the Slope
Setting up a Ratio
Simplifying Square Roots
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
Using an Equation to Find an Intercept
Solving a Quadratic Equation
Surface Area of a Rectangular Solid
Finding the Missing Number
6. 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
Characteristics of a Parallelogram
The 3-4-5 Triangle
Adding and Subtracting Roots
7. Combine equations in such a way that one of the variables cancel out
Multiples of 2 and 4
Solving a System of Equations
Even/Odd
Greatest Common Factor
8. 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
Counting Consecutive Integers
Counting the Possibilities
Average Rate
Relative Primes
9. 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
Area of a Circle
Adding and Subtracting monomials
Characteristics of a Rectangle
10. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Remainders
Parallel Lines and Transversals
Circumference of a Circle
Reducing Fractions
11. Surface Area = 2lw + 2wh + 2lh
Remainders
(Least) Common Multiple
Surface Area of a Rectangular Solid
Mixed Numbers and Improper Fractions
12. Subtract the smallest from the largest and add 1
Volume of a Rectangular Solid
The 3-4-5 Triangle
Greatest Common Factor
Counting Consecutive Integers
13. (average of the x coordinates - average of the y coordinates)
Average Rate
Using an Equation to Find the Slope
Area of a Triangle
Finding the midpoint
14. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
PEMDAS
Using an Equation to Find the Slope
Setting up a Ratio
Similar Triangles
15. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Intersection of sets
Percent Increase and Decrease
Average of Evenly Spaced Numbers
16. A square is a rectangle with four equal sides; Area of Square = side*side
PEMDAS
Characteristics of a Square
Setting up a Ratio
Repeating Decimal
17. 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
Area of a Sector
Intersecting Lines
Solving an Inequality
Multiplying and Dividing Powers
18. 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
Using the Average to Find the Sum
Rate
Percent Increase and Decrease
19. Multiply the exponents
Median and Mode
Raising Powers to Powers
Reducing Fractions
Characteristics of a Parallelogram
20. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Setting up a Ratio
Multiples of 2 and 4
Area of a Triangle
Adding and Subtracting Roots
21. 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
Adding/Subtracting Signed Numbers
Multiplying Monomials
Domain and Range of a Function
Exponential Growth
22. 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
Multiplying and Dividing Powers
Rate
Exponential Growth
Reciprocal
23. 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
The 3-4-5 Triangle
(Least) Common Multiple
Rate
Using an Equation to Find the Slope
24. 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
Adding and Subtracting Roots
Counting the Possibilities
Adding/Subtracting Signed Numbers
25. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying and Dividing Roots
Average Rate
Multiplying Monomials
Even/Odd
26. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Multiples of 3 and 9
Repeating Decimal
Average Rate
Finding the Distance Between Two Points
27. 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
Reciprocal
Length of an Arc
Isosceles and Equilateral triangles
Median and Mode
28. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Solving a System of Equations
Median and Mode
Identifying the Parts and the Whole
Using an Equation to Find an Intercept
29. To solve a proportion - cross multiply
Multiplying and Dividing Powers
Setting up a Ratio
Probability
Solving a Proportion
30. 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
Tangency
Multiplying/Dividing Signed Numbers
Mixed Numbers and Improper Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
31. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Adding and Subtraction Polynomials
Multiplying Fractions
Interior and Exterior Angles of a Triangle
32. Add the exponents and keep the same base
Factor/Multiple
Multiplying and Dividing Powers
Finding the Missing Number
Solving an Inequality
33. The smallest multiple (other than zero) that two or more numbers have in common.
Reciprocal
Greatest Common Factor
(Least) Common Multiple
Mixed Numbers and Improper Fractions
34. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Finding the Original Whole
Adding/Subtracting Signed Numbers
PEMDAS
35. 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
Triangle Inequality Theorem
Multiplying/Dividing Signed Numbers
Reciprocal
Tangency
36. 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
Interior Angles of a Polygon
Tangency
Combined Percent Increase and Decrease
Using an Equation to Find an Intercept
37. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Characteristics of a Rectangle
Average Formula -
Evaluating an Expression
Finding the Distance Between Two Points
38. 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
Finding the Missing Number
Union of Sets
The 5-12-13 Triangle
Percent Formula
39. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Interior and Exterior Angles of a Triangle
Prime Factorization
Adding and Subtraction Polynomials
40. 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
Reducing Fractions
Parallel Lines and Transversals
Characteristics of a Square
Interior and Exterior Angles of a Triangle
41. 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)
Area of a Sector
Parallel Lines and Transversals
Using Two Points to Find the Slope
Characteristics of a Square
42. 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
Multiplying and Dividing Roots
Using the Average to Find the Sum
Adding and Subtracting monomials
Percent Increase and Decrease
43. 2pr
Finding the Missing Number
Identifying the Parts and the Whole
Circumference of a Circle
Area of a Circle
44. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Multiples of 2 and 4
Simplifying Square Roots
Length of an Arc
Similar Triangles
45. Combine like terms
Adding and Subtraction Polynomials
Area of a Circle
Using the Average to Find the Sum
Volume of a Cylinder
46. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Reducing Fractions
Exponential Growth
Prime Factorization
Area of a Circle
47. 1. Re-express them with common denominators 2. Convert them to decimals
Surface Area of a Rectangular Solid
Using Two Points to Find the Slope
Percent Formula
Comparing Fractions
48. 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
The 3-4-5 Triangle
Finding the Original Whole
Exponential Growth
Interior and Exterior Angles of a Triangle
49. Area of Triangle = 1/2 (base)(height) - the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex
Greatest Common Factor
Area of a Triangle
Finding the Original Whole
Prime Factorization
50. 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
Combined Percent Increase and Decrease
Reciprocal
The 5-12-13 Triangle
Multiples of 3 and 9