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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. Domain: all possible values of x for a function range: all possible outputs of a function
Tangency
Triangle Inequality Theorem
Circumference of a Circle
Domain and Range of a Function
2. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Fractions
Counting Consecutive Integers
Multiplying Monomials
Intersection of sets
3. 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
Repeating Decimal
Domain and Range of a Function
Mixed Numbers and Improper Fractions
Simplifying Square Roots
4. Factor out the perfect squares
Negative Exponent and Rational Exponent
Part-to-Part Ratios and Part-to-Whole Ratios
Simplifying Square Roots
Determining Absolute Value
5. 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
Direct and Inverse Variation
The 3-4-5 Triangle
Intersection of sets
6. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Tangency
PEMDAS
Identifying the Parts and the Whole
Volume of a Cylinder
7. 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
Setting up a Ratio
Parallel Lines and Transversals
Mixed Numbers and Improper Fractions
8. 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
Mixed Numbers and Improper Fractions
Multiplying and Dividing Powers
Intersection of sets
Counting the Possibilities
9. 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
Volume of a Cylinder
Isosceles and Equilateral triangles
Remainders
Percent Increase and Decrease
10. 2pr
Circumference of a Circle
Characteristics of a Square
Greatest Common Factor
Direct and Inverse Variation
11. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Multiplying/Dividing Signed Numbers
Multiplying Fractions
Volume of a Rectangular Solid
Multiples of 2 and 4
12. 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
Adding and Subtracting monomials
Repeating Decimal
Using an Equation to Find the Slope
13. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Multiplying and Dividing Roots
(Least) Common Multiple
Combined Percent Increase and Decrease
14. 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.
Percent Increase and Decrease
Number Categories
Characteristics of a Rectangle
Mixed Numbers and Improper Fractions
15. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Number Categories
PEMDAS
Rate
Union of Sets
16. 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
Average Rate
Multiplying/Dividing Signed Numbers
Interior and Exterior Angles of a Triangle
Factor/Multiple
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
Factor/Multiple
Solving an Inequality
Relative Primes
Prime Factorization
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
Volume of a Cylinder
Area of a Circle
Using the Average to Find the Sum
19. Multiply the exponents
Raising Powers to Powers
Average Rate
Finding the Distance Between Two Points
Evaluating an Expression
20. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Circumference of a Circle
Average of Evenly Spaced Numbers
Solving a Quadratic Equation
Percent Formula
21. 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
Multiplying and Dividing Roots
Interior Angles of a Polygon
Using an Equation to Find an Intercept
Adding/Subtracting Fractions
22. The largest factor that two or more numbers have in common.
Greatest Common Factor
Direct and Inverse Variation
Dividing Fractions
Pythagorean Theorem
23. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Number Categories
Average of Evenly Spaced Numbers
Tangency
Determining Absolute Value
24. 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)
Finding the Missing Number
Circumference of a Circle
Area of a Sector
Pythagorean Theorem
25. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average Formula -
Comparing Fractions
Circumference of a Circle
Median and Mode
26. 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
Prime Factorization
Percent Formula
Using Two Points to Find the Slope
27. 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
Intersection of sets
Tangency
Volume of a Cylinder
28. Probability= Favorable Outcomes/Total Possible Outcomes
Solving a Proportion
Number Categories
Adding and Subtracting Roots
Probability
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
The 5-12-13 Triangle
Counting the Possibilities
Using an Equation to Find an Intercept
Pythagorean Theorem
30. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Combined Percent Increase and Decrease
Finding the Original Whole
Solving a Proportion
Setting up a Ratio
31. 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
Exponential Growth
Setting up a Ratio
Even/Odd
Combined Percent Increase and Decrease
32. 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
Union of Sets
Part-to-Part Ratios and Part-to-Whole Ratios
Finding the Missing Number
Direct and Inverse Variation
33. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Setting up a Ratio
Combined Percent Increase and Decrease
Part-to-Part Ratios and Part-to-Whole Ratios
Adding and Subtracting monomials
34. 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
Remainders
Simplifying Square Roots
Adding/Subtracting Signed Numbers
35. 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
Adding and Subtraction Polynomials
Combined Percent Increase and Decrease
Rate
Setting up a Ratio
36. 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
PEMDAS
Identifying the Parts and the Whole
Multiplying/Dividing Signed Numbers
Finding the Original Whole
37. Change in y/ change in x rise/run
Comparing Fractions
Repeating Decimal
Solving an Inequality
Using Two Points to Find the Slope
38. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Using Two Points to Find the Slope
Evaluating an Expression
Area of a Sector
Multiplying and Dividing Powers
39. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Probability
Multiples of 3 and 9
Adding/Subtracting Fractions
Finding the Missing Number
40. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Tangency
Finding the Distance Between Two Points
Using an Equation to Find the Slope
Volume of a Rectangular Solid
41. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Probability
Part-to-Part Ratios and Part-to-Whole Ratios
Reducing Fractions
Comparing Fractions
42. 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
Finding the Missing Number
Using the Average to Find the Sum
Interior and Exterior Angles of a Triangle
Comparing Fractions
43. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Finding the Missing Number
Average Rate
Comparing Fractions
44. you can add/subtract when the part under the radical is the same
Isosceles and Equilateral triangles
Adding and Subtracting Roots
Comparing Fractions
Number Categories
45. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Similar Triangles
Comparing Fractions
Volume of a Cylinder
Characteristics of a Square
46. 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
Relative Primes
Identifying the Parts and the Whole
Intersection of sets
The 3-4-5 Triangle
47. (average of the x coordinates - average of the y coordinates)
Function - Notation - and Evaulation
Finding the midpoint
Surface Area of a Rectangular Solid
Even/Odd
48. 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
Identifying the Parts and the Whole
Percent Formula
Intersection of sets
49. 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
Repeating Decimal
Adding/Subtracting Signed Numbers
Pythagorean Theorem
Remainders
50. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Prime Factorization
Evaluating an Expression
Parallel Lines and Transversals
Tangency