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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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sat
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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. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Interior Angles of a Polygon
Using an Equation to Find the Slope
Solving a Proportion
Function - Notation - and Evaulation
2. 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
Characteristics of a Rectangle
Relative Primes
Characteristics of a Square
Solving a Proportion
3. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Finding the Distance Between Two Points
Remainders
Interior and Exterior Angles of a Triangle
4. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Solving a System of Equations
Counting Consecutive Integers
Average Rate
Circumference of a Circle
5. 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
Average of Evenly Spaced Numbers
Solving an Inequality
Evaluating an Expression
Setting up a Ratio
6. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Using an Equation to Find the Slope
Intersection of sets
Adding and Subtracting monomials
Counting the Possibilities
7. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Characteristics of a Rectangle
Union of Sets
Adding/Subtracting Fractions
Raising Powers to Powers
8. 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
Finding the Missing Number
Finding the Original Whole
Characteristics of a Square
Union of Sets
9. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
(Least) Common Multiple
Multiples of 3 and 9
Average Rate
Adding/Subtracting Fractions
10. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Volume of a Rectangular Solid
Similar Triangles
Multiples of 3 and 9
Identifying the Parts and the Whole
11. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Solving an Inequality
Volume of a Rectangular Solid
Direct and Inverse Variation
Repeating Decimal
12. Volume of a Cylinder = pr^2h
Intersecting Lines
The 5-12-13 Triangle
Probability
Volume of a Cylinder
13. Combine equations in such a way that one of the variables cancel out
Relative Primes
Solving a System of Equations
Triangle Inequality Theorem
Average Rate
14. The smallest multiple (other than zero) that two or more numbers have in common.
(Least) Common Multiple
Comparing Fractions
Setting up a Ratio
Solving an Inequality
15. A square is a rectangle with four equal sides; Area of Square = side*side
Adding and Subtraction Polynomials
Determining Absolute Value
Average Rate
Characteristics of a Square
16. Part = Percent x Whole
Percent Formula
Pythagorean Theorem
Area of a Triangle
Rate
17. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Multiples of 3 and 9
Simplifying Square Roots
Function - Notation - and Evaulation
18. Combine like terms
Comparing Fractions
Adding and Subtraction Polynomials
Multiples of 3 and 9
Multiplying and Dividing Roots
19. 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)
Isosceles and Equilateral triangles
Relative Primes
Using Two Points to Find the Slope
Area of a Sector
20. you can add/subtract when the part under the radical is the same
Multiples of 3 and 9
Characteristics of a Square
Adding and Subtracting Roots
Solving an Inequality
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
Using an Equation to Find the Slope
Multiples of 2 and 4
Factor/Multiple
22. (average of the x coordinates - average of the y coordinates)
Multiples of 3 and 9
Finding the midpoint
Combined Percent Increase and Decrease
Intersecting Lines
23. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Percent Increase and Decrease
Area of a Sector
Greatest Common Factor
Intersecting Lines
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
Exponential Growth
Multiples of 2 and 4
Adding/Subtracting Signed Numbers
Percent Increase and Decrease
25. The whole # left over after division
Adding and Subtracting Roots
Pythagorean Theorem
Similar Triangles
Remainders
26. 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
Finding the midpoint
Union of Sets
Counting the Possibilities
The 5-12-13 Triangle
27. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
The 3-4-5 Triangle
Dividing Fractions
Finding the Distance Between Two Points
(Least) Common Multiple
28. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Similar Triangles
Adding and Subtracting monomials
Multiplying and Dividing Powers
Prime Factorization
29. 2pr
Circumference of a Circle
Multiplying and Dividing Roots
Raising Powers to Powers
The 5-12-13 Triangle
30. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Evaluating an Expression
Interior and Exterior Angles of a Triangle
Solving a Quadratic Equation
(Least) Common Multiple
31. Subtract the smallest from the largest and add 1
Triangle Inequality Theorem
Counting Consecutive Integers
Intersection of sets
Isosceles and Equilateral triangles
32. Change in y/ change in x rise/run
Number Categories
Area of a Sector
Using Two Points to Find the Slope
Exponential Growth
33. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Identifying the Parts and the Whole
Multiples of 3 and 9
Adding/Subtracting Signed Numbers
Multiplying and Dividing Roots
34. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Isosceles and Equilateral triangles
Exponential Growth
Probability
Reducing Fractions
35. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Average of Evenly Spaced Numbers
Simplifying Square Roots
Domain and Range of a Function
Tangency
36. 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
Negative Exponent and Rational Exponent
Adding and Subtracting Roots
Circumference of a Circle
Multiplying Fractions
37. 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
Average Formula -
Domain and Range of a Function
Simplifying Square Roots
Combined Percent Increase and Decrease
38. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Tangency
Setting up a Ratio
PEMDAS
Multiples of 3 and 9
39. Surface Area = 2lw + 2wh + 2lh
Surface Area of a Rectangular Solid
Length of an Arc
Number Categories
(Least) Common Multiple
40. 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
Solving an Inequality
Even/Odd
Using an Equation to Find the Slope
Direct and Inverse Variation
41. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Adding and Subtracting monomials
Comparing Fractions
Solving a System of Equations
Solving a Quadratic Equation
42. 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
Triangle Inequality Theorem
Characteristics of a Rectangle
Direct and Inverse Variation
Probability
43. 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
(Least) Common Multiple
Area of a Sector
Solving a Quadratic Equation
44. 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)
PEMDAS
Even/Odd
Length of an Arc
Greatest Common Factor
45. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Area of a Circle
Prime Factorization
Median and Mode
Average of Evenly Spaced Numbers
46. pr^2
Multiples of 2 and 4
Area of a Circle
Multiplying and Dividing Roots
Intersection of sets
47. Factor out the perfect squares
Interior Angles of a Polygon
Reducing Fractions
Simplifying Square Roots
PEMDAS
48. The largest factor that two or more numbers have in common.
Characteristics of a Rectangle
Greatest Common Factor
(Least) Common Multiple
Multiples of 2 and 4
49. Probability= Favorable Outcomes/Total Possible Outcomes
Area of a Sector
Probability
Characteristics of a Parallelogram
The 3-4-5 Triangle
50. 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
Setting up a Ratio
Exponential Growth
Direct and Inverse Variation
Adding/Subtracting Fractions