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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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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. Surface Area = 2lw + 2wh + 2lh
Identifying the Parts and the Whole
Finding the Original Whole
Surface Area of a Rectangular Solid
Length of an Arc
2. 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
Multiplying Monomials
Rate
Relative Primes
Intersecting Lines
3. 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)
Reciprocal
Length of an Arc
Percent Formula
Finding the Distance Between Two Points
4. 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
(Least) Common Multiple
Identifying the Parts and the Whole
Characteristics of a Rectangle
Solving an Inequality
5. 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
Using the Average to Find the Sum
Average Rate
Factor/Multiple
6. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Multiplying/Dividing Signed Numbers
Finding the Distance Between Two Points
Parallel Lines and Transversals
The 3-4-5 Triangle
7. 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.
Multiples of 2 and 4
Number Categories
Solving a Proportion
Counting Consecutive Integers
8. 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
Simplifying Square Roots
Length of an Arc
(Least) Common Multiple
Function - Notation - and Evaulation
9. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Volume of a Rectangular Solid
Simplifying Square Roots
Finding the Original Whole
Function - Notation - and Evaulation
10. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Remainders
Identifying the Parts and the Whole
Solving a Proportion
11. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Remainders
Adding and Subtracting monomials
Area of a Circle
Characteristics of a Parallelogram
12. 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
Evaluating an Expression
The 3-4-5 Triangle
Multiplying Fractions
The 5-12-13 Triangle
13. 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
Function - Notation - and Evaulation
Characteristics of a Rectangle
Part-to-Part Ratios and Part-to-Whole Ratios
Finding the Original Whole
14. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Multiplying and Dividing Roots
Counting the Possibilities
Intersection of sets
Prime Factorization
15. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Relative Primes
Intersection of sets
Similar Triangles
Average Rate
16. pr^2
Intersection of sets
Reciprocal
Relative Primes
Area of a Circle
17. The smallest multiple (other than zero) that two or more numbers have in common.
Relative Primes
Using an Equation to Find the Slope
(Least) Common Multiple
Factor/Multiple
18. The largest factor that two or more numbers have in common.
Greatest Common Factor
Function - Notation - and Evaulation
Adding/Subtracting Fractions
Repeating Decimal
19. Subtract the smallest from the largest and add 1
Using Two Points to Find the Slope
Prime Factorization
Counting Consecutive Integers
Rate
20. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Finding the Missing Number
Determining Absolute Value
Surface Area of a Rectangular Solid
Isosceles and Equilateral triangles
21. 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
Exponential Growth
Even/Odd
Counting the Possibilities
Adding and Subtracting Roots
22. 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
Characteristics of a Square
Percent Formula
Union of Sets
23. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Finding the Original Whole
Multiplying Monomials
Combined Percent Increase and Decrease
Average Formula -
24. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
(Least) Common Multiple
Comparing Fractions
Prime Factorization
Average Formula -
25. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Determining Absolute Value
Raising Powers to Powers
Reciprocal
Multiples of 3 and 9
26. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Reciprocal
Solving an Inequality
Multiples of 3 and 9
Multiples of 2 and 4
27. Probability= Favorable Outcomes/Total Possible Outcomes
Probability
Multiples of 2 and 4
Raising Powers to Powers
Exponential Growth
28. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Surface Area of a Rectangular Solid
Adding/Subtracting Fractions
Median and Mode
Solving a System of Equations
29. 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
Evaluating an Expression
Intersection of sets
Mixed Numbers and Improper Fractions
Characteristics of a Rectangle
30. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
(Least) Common Multiple
Intersection of sets
Comparing Fractions
Using an Equation to Find the Slope
31. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Volume of a Rectangular Solid
Adding and Subtracting monomials
Tangency
Prime Factorization
32. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height
Domain and Range of a Function
Simplifying Square Roots
Characteristics of a Parallelogram
Combined Percent Increase and Decrease
33. 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
Even/Odd
Characteristics of a Square
Setting up a Ratio
Using an Equation to Find the Slope
34. Volume of a Cylinder = pr^2h
Simplifying Square Roots
Volume of a Cylinder
Solving a Quadratic Equation
Characteristics of a Square
35. # 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
Rate
Counting Consecutive Integers
Using the Average to Find the Sum
36. Combine equations in such a way that one of the variables cancel out
Percent Increase and Decrease
Solving a System of Equations
Remainders
Union of Sets
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
Length of an Arc
Surface Area of a Rectangular Solid
Interior and Exterior Angles of a Triangle
Using Two Points to Find the Slope
38. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Determining Absolute Value
Using an Equation to Find the Slope
Average Formula -
39. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Multiplying and Dividing Roots
Solving a Quadratic Equation
Solving a System of Equations
Solving a Proportion
40. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Circumference of a Circle
Adding and Subtracting Roots
Reducing Fractions
Using Two Points to Find the Slope
41. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Even/Odd
Percent Increase and Decrease
Average of Evenly Spaced Numbers
Mixed Numbers and Improper Fractions
42. 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
Characteristics of a Square
Finding the Distance Between Two Points
Raising Powers to Powers
43. The whole # left over after division
Length of an Arc
Remainders
Prime Factorization
Using an Equation to Find the Slope
44. 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
Negative Exponent and Rational Exponent
Raising Powers to Powers
Area of a Triangle
Solving an Inequality
45. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Using an Equation to Find an Intercept
Probability
Comparing Fractions
46. 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
Interior Angles of a Polygon
Domain and Range of a Function
Direct and Inverse Variation
Reducing Fractions
47. 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
Length of an Arc
Remainders
Counting the Possibilities
Setting up a Ratio
48. A square is a rectangle with four equal sides; Area of Square = side*side
Intersecting Lines
Adding and Subtracting Roots
The 5-12-13 Triangle
Characteristics of a Square
49. 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
Using an Equation to Find an Intercept
Relative Primes
Average Formula -
Solving an Inequality
50. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Pythagorean Theorem
Raising Powers to Powers
Evaluating an Expression
Adding and Subtracting Roots