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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Study First
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. Combine like terms
Adding and Subtraction Polynomials
Multiples of 2 and 4
Volume of a Rectangular Solid
Mixed Numbers and Improper Fractions
2. Domain: all possible values of x for a function range: all possible outputs of a function
Volume of a Rectangular Solid
Part-to-Part Ratios and Part-to-Whole Ratios
PEMDAS
Domain and Range of a Function
3. 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
Adding and Subtracting monomials
Repeating Decimal
Evaluating an Expression
Characteristics of a Square
4. The median is the value that falls in the middle of the set - the mode is the value that appears most often
The 3-4-5 Triangle
Exponential Growth
Median and Mode
Percent Formula
5. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Average Rate
Volume of a Rectangular Solid
Area of a Sector
PEMDAS
6. 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
Adding/Subtracting Signed Numbers
Relative Primes
Characteristics of a Parallelogram
Characteristics of a Rectangle
7. Multiply the exponents
Exponential Growth
Raising Powers to Powers
Average Formula -
Solving a Quadratic Equation
8. 2pr
Greatest Common Factor
Volume of a Rectangular Solid
Circumference of a Circle
Isosceles and Equilateral triangles
9. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Percent Increase and Decrease
Domain and Range of a Function
Finding the Distance Between Two Points
Dividing Fractions
10. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Identifying the Parts and the Whole
Multiples of 3 and 9
Similar Triangles
Setting up a Ratio
11. 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
Prime Factorization
Finding the Original Whole
Volume of a Cylinder
Identifying the Parts and the Whole
12. pr^2
Area of a Circle
Mixed Numbers and Improper Fractions
Rate
Adding/Subtracting Signed Numbers
13. 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.
Factor/Multiple
Number Categories
Characteristics of a Rectangle
Interior and Exterior Angles of a Triangle
14. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Adding and Subtraction Polynomials
The 3-4-5 Triangle
Multiplying/Dividing Signed Numbers
Using an Equation to Find the Slope
15. 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
Prime Factorization
Function - Notation - and Evaulation
Percent Increase and Decrease
Negative Exponent and Rational Exponent
16. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Average of Evenly Spaced Numbers
Multiples of 3 and 9
Triangle Inequality Theorem
Adding and Subtraction Polynomials
17. 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)
Surface Area of a Rectangular Solid
Union of Sets
Area of a Sector
Multiplying/Dividing Signed Numbers
18. For all right triangles: a^2+b^2=c^2
Tangency
Using an Equation to Find the Slope
Pythagorean Theorem
The 5-12-13 Triangle
19. 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
Solving an Inequality
Simplifying Square Roots
Multiplying/Dividing Signed Numbers
20. The whole # left over after division
Characteristics of a Square
Area of a Triangle
Remainders
Using Two Points to Find the Slope
21. 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
Adding and Subtraction Polynomials
Relative Primes
Evaluating an Expression
Area of a Triangle
22. 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
Reducing Fractions
Multiples of 2 and 4
Rate
The 3-4-5 Triangle
23. you can add/subtract when the part under the radical is the same
Adding and Subtracting Roots
Volume of a Rectangular Solid
Determining Absolute Value
Average Rate
24. 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
Remainders
Multiplying Monomials
Adding and Subtracting monomials
Part-to-Part Ratios and Part-to-Whole Ratios
25. 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
Solving a System of Equations
Finding the Missing Number
Domain and Range of a Function
Part-to-Part Ratios and Part-to-Whole Ratios
26. The largest factor that two or more numbers have in common.
Adding/Subtracting Signed Numbers
Relative Primes
Greatest Common Factor
Using Two Points to Find the Slope
27. 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
Parallel Lines and Transversals
Similar Triangles
Mixed Numbers and Improper Fractions
Length of an Arc
28. To divide fractions - invert the second one and multiply
Surface Area of a Rectangular Solid
Probability
Dividing Fractions
Simplifying Square Roots
29. Change in y/ change in x rise/run
Setting up a Ratio
Intersection of sets
Solving an Inequality
Using Two Points to Find the Slope
30. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Characteristics of a Rectangle
Length of an Arc
Area of a Sector
31. 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
Pythagorean Theorem
Isosceles and Equilateral triangles
Union of Sets
Probability
32. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Percent Increase and Decrease
Multiples of 3 and 9
Negative Exponent and Rational Exponent
Median and Mode
33. Part = Percent x Whole
Similar Triangles
Percent Formula
Domain and Range of a Function
Average of Evenly Spaced Numbers
34. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Solving a System of Equations
Length of an Arc
Determining Absolute Value
35. 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
Greatest Common Factor
The 5-12-13 Triangle
Percent Increase and Decrease
Probability
36. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Isosceles and Equilateral triangles
Tangency
Multiplying and Dividing Powers
Evaluating an Expression
37. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Union of Sets
Solving a Quadratic Equation
Reducing Fractions
38. 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
Remainders
Direct and Inverse Variation
Finding the Original Whole
Percent Increase and Decrease
39. 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
Counting the Possibilities
Even/Odd
Union of Sets
Area of a Circle
40. Subtract the smallest from the largest and add 1
Percent Increase and Decrease
Counting Consecutive Integers
Factor/Multiple
Counting the Possibilities
41. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Raising Powers to Powers
Characteristics of a Parallelogram
Volume of a Cylinder
42. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Using an Equation to Find an Intercept
Multiples of 2 and 4
Raising Powers to Powers
43. 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)
(Least) Common Multiple
Length of an Arc
Percent Formula
Probability
44. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Simplifying Square Roots
Adding and Subtracting monomials
Multiples of 3 and 9
The 3-4-5 Triangle
45. To find the reciprocal of a fraction switch the numerator and the denominator
Adding/Subtracting Fractions
Reciprocal
Finding the Missing Number
Multiplying and Dividing Powers
46. 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
Determining Absolute Value
Multiplying and Dividing Roots
Solving an Inequality
47. 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
Union of Sets
Triangle Inequality Theorem
Interior Angles of a Polygon
48. 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 Proportion
Solving a Quadratic Equation
Multiplying/Dividing Signed Numbers
Dividing Fractions
49. Volume of a Cylinder = pr^2h
Exponential Growth
Finding the midpoint
Finding the Original Whole
Volume of a Cylinder
50. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Identifying the Parts and the Whole
Tangency
Using an Equation to Find the Slope
Multiples of 2 and 4