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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
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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. 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
Dividing Fractions
Pythagorean Theorem
Exponential Growth
Rate
2. 1. Re-express them with common denominators 2. Convert them to decimals
Adding/Subtracting Fractions
Comparing Fractions
PEMDAS
Mixed Numbers and Improper Fractions
3. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Solving a Proportion
Similar Triangles
Area of a Circle
4. 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
Prime Factorization
Adding and Subtracting monomials
Domain and Range of a Function
Solving an Inequality
5. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Solving an Inequality
Using Two Points to Find the Slope
Finding the Distance Between Two Points
6. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Average of Evenly Spaced Numbers
Median and Mode
Adding/Subtracting Fractions
Finding the Original Whole
7. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Mixed Numbers and Improper Fractions
Reducing Fractions
Intersection of sets
Solving a Proportion
8. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Area of a Sector
Multiplying and Dividing Roots
Relative Primes
Factor/Multiple
9. 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)
Characteristics of a Square
Percent Formula
Isosceles and Equilateral triangles
Area of a Sector
10. A square is a rectangle with four equal sides; Area of Square = side*side
Median and Mode
(Least) Common Multiple
Characteristics of a Square
Rate
11. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Counting the Possibilities
Determining Absolute Value
Reducing Fractions
Combined Percent Increase and Decrease
12. 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
Union of Sets
Area of a Sector
Adding/Subtracting Signed Numbers
13. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Reducing Fractions
Intersection of sets
Identifying the Parts and the Whole
14. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Intersection of sets
Direct and Inverse Variation
Probability
Adding/Subtracting Fractions
15. 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
Adding/Subtracting Signed Numbers
Similar Triangles
Direct and Inverse Variation
Combined Percent Increase and Decrease
16. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Using the Average to Find the Sum
Volume of a Cylinder
Multiplying and Dividing Powers
Using an Equation to Find the Slope
17. 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)
Percent Increase and Decrease
Finding the Distance Between Two Points
Length of an Arc
Interior Angles of a Polygon
18. 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
PEMDAS
Remainders
Similar Triangles
19. 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
Prime Factorization
Adding/Subtracting Signed Numbers
Finding the Missing Number
Average Formula -
20. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Circumference of a Circle
Function - Notation - and Evaulation
Finding the midpoint
Multiplying and Dividing Roots
21. 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 Original Whole
Counting the Possibilities
Average Rate
The 5-12-13 Triangle
22. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Intersecting Lines
Finding the Distance Between Two Points
Parallel Lines and Transversals
PEMDAS
23. Combine like terms
Adding and Subtraction Polynomials
Probability
Using the Average to Find the Sum
Similar Triangles
24. Volume of a Cylinder = pr^2h
Finding the midpoint
Volume of a Cylinder
Function - Notation - and Evaulation
Raising Powers to Powers
25. you can add/subtract when the part under the radical is the same
Probability
Multiplying and Dividing Roots
(Least) Common Multiple
Adding and Subtracting Roots
26. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Even/Odd
Characteristics of a Square
Similar Triangles
Interior Angles of a Polygon
27. Part = Percent x Whole
Multiples of 2 and 4
Percent Formula
Multiplying Monomials
Rate
28. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Evaluating an Expression
Similar Triangles
(Least) Common Multiple
Finding the Distance Between Two Points
29. 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
Using an Equation to Find an Intercept
Area of a Triangle
The 5-12-13 Triangle
Multiplying and Dividing Powers
30. 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
Probability
Finding the Missing Number
Multiplying and Dividing Powers
Exponential Growth
31. To find the reciprocal of a fraction switch the numerator and the denominator
Identifying the Parts and the Whole
Simplifying Square Roots
Reciprocal
Intersection of sets
32. 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
Length of an Arc
Rate
Isosceles and Equilateral triangles
Adding and Subtraction Polynomials
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
Finding the midpoint
Counting Consecutive Integers
Negative Exponent and Rational Exponent
Multiplying/Dividing Signed Numbers
34. 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
Using Two Points to Find the Slope
Multiplying/Dividing Signed Numbers
Probability
35. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Adding and Subtraction Polynomials
Tangency
Repeating Decimal
36. 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
Area of a Sector
Even/Odd
Average of Evenly Spaced Numbers
37. (average of the x coordinates - average of the y coordinates)
Similar Triangles
Finding the midpoint
Length of an Arc
Finding the Original Whole
38. 2pr
Intersecting Lines
Reducing Fractions
Circumference of a Circle
Characteristics of a Parallelogram
39. Multiply the exponents
Characteristics of a Square
Reducing Fractions
Raising Powers to Powers
Characteristics of a Parallelogram
40. Add the exponents and keep the same base
Multiplying and Dividing Powers
Union of Sets
Solving a Proportion
Simplifying Square Roots
41. 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
Tangency
Negative Exponent and Rational Exponent
Prime Factorization
Median and Mode
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
Finding the Missing Number
Triangle Inequality Theorem
Circumference of a Circle
Repeating Decimal
43. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Characteristics of a Rectangle
Union of Sets
Evaluating an Expression
Solving a Quadratic Equation
44. Change in y/ change in x rise/run
Number Categories
Adding/Subtracting Signed Numbers
Using Two Points to Find the Slope
Interior and Exterior Angles of a Triangle
45. 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
Number Categories
Similar Triangles
Negative Exponent and Rational Exponent
46. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Multiples of 2 and 4
Median and Mode
Prime Factorization
Rate
47. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Volume of a Cylinder
Characteristics of a Rectangle
Intersecting Lines
Multiples of 2 and 4
48. 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
Counting Consecutive Integers
Adding/Subtracting Signed Numbers
Finding the Original Whole
Area of a Triangle
49. Probability= Favorable Outcomes/Total Possible Outcomes
Probability
Finding the midpoint
Finding the Missing Number
Reducing Fractions
50. 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
Average of Evenly Spaced Numbers
Dividing Fractions
Domain and Range of a Function