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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. Volume of a Cylinder = pr^2h
Isosceles and Equilateral triangles
Average Formula -
Volume of a Cylinder
PEMDAS
2. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Similar Triangles
Intersection of sets
Characteristics of a Square
(Least) Common Multiple
3. Part = Percent x Whole
PEMDAS
Negative Exponent and Rational Exponent
Percent Formula
Prime Factorization
4. A square is a rectangle with four equal sides; Area of Square = side*side
Greatest Common Factor
Characteristics of a Square
Multiplying and Dividing Roots
Characteristics of a Parallelogram
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
Circumference of a Circle
Tangency
Average Rate
Area of a Circle
6. Domain: all possible values of x for a function range: all possible outputs of a function
Percent Increase and Decrease
Identifying the Parts and the Whole
Using the Average to Find the Sum
Domain and Range of a Function
7. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Tangency
Evaluating an Expression
Finding the Original Whole
Median and Mode
8. 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
Percent Increase and Decrease
Negative Exponent and Rational Exponent
Mixed Numbers and Improper Fractions
Exponential Growth
9. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Finding the Distance Between Two Points
Area of a Sector
Multiplying/Dividing Signed Numbers
10. 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
Using an Equation to Find an Intercept
Similar Triangles
Reciprocal
Part-to-Part Ratios and Part-to-Whole Ratios
11. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Volume of a Rectangular Solid
Adding/Subtracting Fractions
Probability
Reducing Fractions
12. To solve a proportion - cross multiply
Adding and Subtracting Roots
Characteristics of a Rectangle
Solving a Proportion
Circumference of a Circle
13. Probability= Favorable Outcomes/Total Possible Outcomes
Multiplying/Dividing Signed Numbers
Multiplying and Dividing Powers
Probability
Tangency
14. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Exponential Growth
Direct and Inverse Variation
Adding/Subtracting Signed Numbers
Finding the Distance Between Two Points
15. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Using an Equation to Find an Intercept
The 5-12-13 Triangle
PEMDAS
Solving a Quadratic Equation
16. you can add/subtract when the part under the radical is the same
Finding the midpoint
Interior Angles of a Polygon
Adding and Subtracting Roots
Adding and Subtracting monomials
17. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Determining Absolute Value
Multiplying and Dividing Roots
Interior and Exterior Angles of a Triangle
Relative Primes
18. Surface Area = 2lw + 2wh + 2lh
PEMDAS
The 3-4-5 Triangle
Union of Sets
Surface Area of a Rectangular Solid
19. 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
Multiplying/Dividing Signed Numbers
Parallel Lines and Transversals
Finding the midpoint
Pythagorean Theorem
20. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Evaluating an Expression
Mixed Numbers and Improper Fractions
Multiplying and Dividing Roots
Identifying the Parts and the Whole
21. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Circumference of a Circle
Determining Absolute Value
Using an Equation to Find the Slope
Volume of a Rectangular Solid
22. 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
Average of Evenly Spaced Numbers
Direct and Inverse Variation
Adding and Subtracting monomials
Triangle Inequality Theorem
23. Add the exponents and keep the same base
Exponential Growth
Surface Area of a Rectangular Solid
Multiplying and Dividing Powers
(Least) Common Multiple
24. 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 Original Whole
Counting Consecutive Integers
Reducing Fractions
Determining Absolute Value
25. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Remainders
Reducing Fractions
Multiples of 2 and 4
Multiples of 3 and 9
26. 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
Tangency
Factor/Multiple
The 3-4-5 Triangle
Characteristics of a Rectangle
27. 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
Rate
Identifying the Parts and the Whole
Counting Consecutive Integers
Counting the Possibilities
28. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Even/Odd
Adding and Subtracting monomials
Mixed Numbers and Improper Fractions
Finding the Original Whole
29. 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.
Average Rate
Setting up a Ratio
Factor/Multiple
Number Categories
30. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Area of a Circle
Volume of a Cylinder
Characteristics of a Parallelogram
31. 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
Negative Exponent and Rational Exponent
Remainders
Finding the Distance Between Two Points
Area of a Circle
32. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Circumference of a Circle
Adding and Subtraction Polynomials
Area of a Triangle
Prime Factorization
33. 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
Using an Equation to Find the Slope
The 5-12-13 Triangle
Identifying the Parts and the Whole
Remainders
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)
Function - Notation - and Evaulation
Comparing Fractions
Direct and Inverse Variation
Length of an Arc
35. Sum=(Average) x (Number of Terms)
Function - Notation - and Evaulation
Solving a Proportion
Finding the Distance Between Two Points
Using the Average to Find the Sum
36. 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
Dividing Fractions
Probability
Area of a Circle
Repeating Decimal
37. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Reciprocal
Finding the Distance Between Two Points
Multiples of 2 and 4
Evaluating an Expression
38. 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
Determining Absolute Value
Direct and Inverse Variation
Reducing Fractions
39. 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
Using an Equation to Find the Slope
Volume of a Cylinder
Median and Mode
40. 2pr
Evaluating an Expression
Prime Factorization
Circumference of a Circle
Rate
41. 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
Solving a System of Equations
Identifying the Parts and the Whole
Circumference of a Circle
Solving a Proportion
42. To multiply fractions - multiply the numerators and multiply the denominators
Intersection of sets
Percent Formula
Determining Absolute Value
Multiplying Fractions
43. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Determining Absolute Value
Prime Factorization
Characteristics of a Parallelogram
PEMDAS
44. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Direct and Inverse Variation
Adding and Subtracting Roots
Using an Equation to Find the Slope
45. 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
Parallel Lines and Transversals
Solving a System of Equations
Raising Powers to Powers
Counting the Possibilities
46. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Median and Mode
Setting up a Ratio
Adding and Subtracting Roots
Using an Equation to Find the Slope
47. 1. Re-express them with common denominators 2. Convert them to decimals
Adding and Subtraction Polynomials
Interior Angles of a Polygon
Comparing Fractions
Circumference of a Circle
48. 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
(Least) Common Multiple
Volume of a Rectangular Solid
The 5-12-13 Triangle
49. 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)
Setting up a Ratio
Area of a Sector
Reciprocal
Negative Exponent and Rational Exponent
50. 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
Using an Equation to Find an Intercept
Domain and Range of a Function
Reciprocal
Direct and Inverse Variation