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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
:
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. 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
Counting the Possibilities
Function - Notation - and Evaulation
Adding and Subtraction Polynomials
Characteristics of a Parallelogram
2. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Parallel Lines and Transversals
Counting Consecutive Integers
PEMDAS
Greatest Common Factor
3. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Tangency
Interior and Exterior Angles of a Triangle
Finding the Original Whole
4. 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
The 3-4-5 Triangle
Percent Increase and Decrease
Adding and Subtracting Roots
5. Sum=(Average) x (Number of Terms)
Mixed Numbers and Improper Fractions
Exponential Growth
Using the Average to Find the Sum
Parallel Lines and Transversals
6. 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
Area of a Sector
Characteristics of a Square
The 3-4-5 Triangle
Setting up a Ratio
7. 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 Missing Number
Counting the Possibilities
Finding the Original Whole
Exponential Growth
8. Multiply the exponents
Dividing Fractions
Parallel Lines and Transversals
Raising Powers to Powers
PEMDAS
9. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
The 3-4-5 Triangle
Interior Angles of a Polygon
Negative Exponent and Rational Exponent
Area of a Triangle
10. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Multiplying/Dividing Signed Numbers
Median and Mode
Adding/Subtracting Fractions
Raising Powers to Powers
11. 2pr
Multiplying and Dividing Powers
Circumference of a Circle
Setting up a Ratio
Length of an Arc
12. Factor out the perfect squares
Exponential Growth
Multiplying Monomials
Reciprocal
Simplifying Square Roots
13. A square is a rectangle with four equal sides; Area of Square = side*side
Adding and Subtraction Polynomials
Characteristics of a Square
Multiplying/Dividing Signed Numbers
Average of Evenly Spaced Numbers
14. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Multiplying Fractions
Volume of a Cylinder
Multiplying/Dividing Signed Numbers
15. 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
Length of an Arc
Circumference of a Circle
Repeating Decimal
16. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Prime Factorization
Median and Mode
Multiplying and Dividing Roots
Reducing Fractions
17. 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
Rate
Pythagorean Theorem
Solving a System of Equations
18. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Counting Consecutive Integers
Factor/Multiple
Comparing Fractions
19. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Solving a Quadratic Equation
Mixed Numbers and Improper Fractions
Identifying the Parts and the Whole
Multiplying/Dividing Signed Numbers
20. 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
Solving a System of Equations
Adding/Subtracting Signed Numbers
Length of an Arc
Rate
21. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Solving a Proportion
Combined Percent Increase and Decrease
Intersecting Lines
Finding the Distance Between Two Points
22. pr^2
Area of a Circle
Volume of a Rectangular Solid
Characteristics of a Rectangle
(Least) Common Multiple
23. Part = Percent x Whole
Finding the Missing Number
Percent Increase and Decrease
Percent Formula
Multiplying and Dividing Powers
24. The whole # left over after division
Remainders
Multiplying/Dividing Signed Numbers
Area of a Triangle
Dividing Fractions
25. To find the reciprocal of a fraction switch the numerator and the denominator
Volume of a Cylinder
The 5-12-13 Triangle
Percent Increase and Decrease
Reciprocal
26. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Number Categories
Solving a Quadratic Equation
Adding and Subtracting Roots
27. 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
Interior Angles of a Polygon
Finding the midpoint
Solving a Proportion
28. you can add/subtract when the part under the radical is the same
Repeating Decimal
Pythagorean Theorem
Adding and Subtracting Roots
Rate
29. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
(Least) Common Multiple
Factor/Multiple
Counting the Possibilities
Multiplying and Dividing Roots
30. 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
Average Rate
Adding and Subtraction Polynomials
Percent Increase and Decrease
Identifying the Parts and the Whole
31. 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
Finding the Missing Number
Exponential Growth
Evaluating an Expression
32. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Finding the Original Whole
Solving a Proportion
Length of an Arc
Tangency
33. 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
Percent Increase and Decrease
Factor/Multiple
Area of a Triangle
34. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Prime Factorization
Multiples of 3 and 9
Raising Powers to Powers
Pythagorean Theorem
35. 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
Adding/Subtracting Fractions
(Least) Common Multiple
Adding and Subtraction Polynomials
Percent Increase and Decrease
36. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Function - Notation - and Evaulation
Multiples of 3 and 9
Repeating Decimal
37. 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
Solving an Inequality
Rate
Volume of a Rectangular Solid
Identifying the Parts and the Whole
38. 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)
Number Categories
Length of an Arc
Area of a Sector
Multiplying and Dividing Powers
39. 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
Domain and Range of a Function
Multiples of 2 and 4
Similar Triangles
40. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Exponential Growth
Average Formula -
Adding/Subtracting Signed Numbers
Counting the Possibilities
41. Add the exponents and keep the same base
Function - Notation - and Evaulation
Solving a Quadratic Equation
Multiplying and Dividing Powers
Multiples of 3 and 9
42. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Area of a Circle
Using an Equation to Find an Intercept
Evaluating an Expression
Simplifying Square Roots
43. 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
Raising Powers to Powers
Using an Equation to Find an Intercept
Multiplying and Dividing Roots
Average Formula -
44. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Solving a Quadratic Equation
Characteristics of a Parallelogram
Multiplying and Dividing Powers
Characteristics of a Rectangle
45. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Determining Absolute Value
Volume of a Rectangular Solid
PEMDAS
Multiplying Monomials
46. 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
Percent Increase and Decrease
Setting up a Ratio
Parallel Lines and Transversals
Even/Odd
47. 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
Isosceles and Equilateral triangles
Characteristics of a Parallelogram
Prime Factorization
Reducing Fractions
48. 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
Number Categories
Using the Average to Find the Sum
Finding the Distance Between Two Points
Triangle Inequality Theorem
49. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Relative Primes
Multiplying and Dividing Roots
Solving a Quadratic Equation
50. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Tangency
Adding and Subtraction Polynomials
Circumference of a Circle
Average Rate