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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
Using the Average to Find the Sum
Exponential Growth
Negative Exponent and Rational Exponent
Solving an Inequality
2. Surface Area = 2lw + 2wh + 2lh
Reducing Fractions
Direct and Inverse Variation
Surface Area of a Rectangular Solid
Adding/Subtracting Signed Numbers
3. For all right triangles: a^2+b^2=c^2
Counting Consecutive Integers
Greatest Common Factor
Pythagorean Theorem
Finding the midpoint
4. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Adding/Subtracting Fractions
Isosceles and Equilateral triangles
Function - Notation - and Evaulation
PEMDAS
5. 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
Solving a System of Equations
Length of an Arc
Volume of a Cylinder
The 3-4-5 Triangle
6. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Using an Equation to Find the Slope
Characteristics of a Rectangle
Finding the Distance Between Two Points
Adding and Subtraction Polynomials
7. To divide fractions - invert the second one and multiply
Dividing Fractions
(Least) Common Multiple
Intersecting Lines
Mixed Numbers and Improper Fractions
8. Integers are whole numbers; they include negtavie whole numbers and zero - Rational numbers can be expressed as a ratio of two integers - irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.
Number Categories
Intersecting Lines
Tangency
Average Rate
9. To multiply fractions - multiply the numerators and multiply the denominators
Adding/Subtracting Fractions
Multiplying Fractions
Finding the Missing Number
Domain and Range of a Function
10. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Similar Triangles
Adding/Subtracting Fractions
Mixed Numbers and Improper Fractions
Relative Primes
11. 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
Characteristics of a Parallelogram
Dividing Fractions
Negative Exponent and Rational Exponent
Counting Consecutive Integers
12. pr^2
The 3-4-5 Triangle
Using Two Points to Find the Slope
Area of a Circle
Direct and Inverse Variation
13. To solve a proportion - cross multiply
Solving a Proportion
Intersecting Lines
Average of Evenly Spaced Numbers
Combined Percent Increase and Decrease
14. 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
Finding the Distance Between Two Points
Simplifying Square Roots
Exponential Growth
15. 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
Determining Absolute Value
Characteristics of a Square
Direct and Inverse Variation
16. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Using an Equation to Find the Slope
Area of a Circle
Probability
Union of Sets
17. 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
Multiplying and Dividing Powers
Area of a Sector
Rate
18. 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
Factor/Multiple
Function - Notation - and Evaulation
Length of an Arc
Number Categories
19. 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
Probability
Factor/Multiple
Surface Area of a Rectangular Solid
Identifying the Parts and the Whole
20. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Pythagorean Theorem
Multiplying Monomials
Comparing Fractions
The 5-12-13 Triangle
21. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
PEMDAS
Probability
Direct and Inverse Variation
Tangency
22. 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 an Equation to Find the Slope
Using an Equation to Find an Intercept
Evaluating an Expression
Multiplying Monomials
23. 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
Adding and Subtracting monomials
Setting up a Ratio
Triangle Inequality Theorem
Area of a Circle
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)
Multiples of 2 and 4
Adding and Subtracting monomials
Length of an Arc
Interior Angles of a Polygon
25. Probability= Favorable Outcomes/Total Possible Outcomes
Average Rate
Evaluating an Expression
Identifying the Parts and the Whole
Probability
26. Sum=(Average) x (Number of Terms)
Intersecting Lines
Using the Average to Find the Sum
Reducing Fractions
Characteristics of a Square
27. Change in y/ change in x rise/run
Combined Percent Increase and Decrease
Using Two Points to Find the Slope
Factor/Multiple
Multiplying and Dividing Roots
28. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Direct and Inverse Variation
Function - Notation - and Evaulation
Volume of a Rectangular Solid
Average Formula -
29. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Repeating Decimal
Evaluating an Expression
Interior Angles of a Polygon
Comparing Fractions
30. 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
Area of a Triangle
Interior and Exterior Angles of a Triangle
The 5-12-13 Triangle
Simplifying Square Roots
31. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Similar Triangles
Solving a Quadratic Equation
Prime Factorization
Adding and Subtraction Polynomials
32. 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
Finding the midpoint
Percent Formula
Using an Equation to Find an Intercept
Adding and Subtracting Roots
33. 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
Greatest Common Factor
Surface Area of a Rectangular Solid
Isosceles and Equilateral triangles
Using the Average to Find the Sum
34. Domain: all possible values of x for a function range: all possible outputs of a function
Number Categories
Multiplying and Dividing Roots
Finding the midpoint
Domain and Range of a Function
35. 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
Characteristics of a Square
Tangency
Similar Triangles
36. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Multiplying Fractions
Number Categories
Multiples of 3 and 9
Negative Exponent and Rational Exponent
37. 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
Combined Percent Increase and Decrease
Interior and Exterior Angles of a Triangle
Multiplying/Dividing Signed Numbers
Pythagorean Theorem
38. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Remainders
Reducing Fractions
Finding the Distance Between Two Points
PEMDAS
39. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Domain and Range of a Function
Volume of a Rectangular Solid
Multiples of 2 and 4
Relative Primes
40. 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 and Subtracting Roots
Average of Evenly Spaced Numbers
Union of Sets
Adding/Subtracting Signed Numbers
41. 2pr
Percent Increase and Decrease
Characteristics of a Parallelogram
Circumference of a Circle
Characteristics of a Rectangle
42. 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 an Inequality
Average Rate
Surface Area of a Rectangular Solid
Reducing Fractions
43. 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 a Quadratic Equation
Even/Odd
Multiplying and Dividing Roots
Volume of a Rectangular Solid
44. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Using Two Points to Find the Slope
Using an Equation to Find the Slope
Comparing Fractions
Adding/Subtracting Fractions
45. 1. Re-express them with common denominators 2. Convert them to decimals
Using an Equation to Find the Slope
Number Categories
Median and Mode
Comparing Fractions
46. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
PEMDAS
Identifying the Parts and the Whole
Area of a Triangle
Adding and Subtracting monomials
47. The whole # left over after division
Remainders
Number Categories
Percent Formula
Using an Equation to Find the Slope
48. 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
Relative Primes
Triangle Inequality Theorem
Length of an Arc
Repeating Decimal
49. Part = Percent x Whole
Percent Formula
Simplifying Square Roots
Length of an Arc
Domain and Range of a Function
50. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Using an Equation to Find an Intercept
Area of a Triangle
Pythagorean Theorem
Factor/Multiple
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