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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. 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.
Domain and Range of a Function
Number Categories
Triangle Inequality Theorem
Probability
2. Combine like terms
Adding and Subtraction Polynomials
Finding the Missing Number
Simplifying Square Roots
Determining Absolute Value
3. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiples of 2 and 4
Solving a System of Equations
Multiplying Monomials
Volume of a Cylinder
4. 1. Re-express them with common denominators 2. Convert them to decimals
Percent Increase and Decrease
Comparing Fractions
Raising Powers to Powers
Characteristics of a Rectangle
5. 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
Finding the midpoint
Adding and Subtracting Roots
Multiplying Monomials
6. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Length of an Arc
Finding the Distance Between Two Points
Adding and Subtracting monomials
Setting up a Ratio
7. Change in y/ change in x rise/run
Area of a Sector
Using Two Points to Find the Slope
Characteristics of a Square
Comparing Fractions
8. you can add/subtract when the part under the radical is the same
Reducing Fractions
Counting the Possibilities
Adding and Subtracting Roots
Length of an Arc
9. 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
Probability
Comparing Fractions
Union of Sets
10. # 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
Interior Angles of a Polygon
Finding the Original Whole
Surface Area of a Rectangular Solid
11. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Finding the midpoint
Using an Equation to Find the Slope
Combined Percent Increase and Decrease
Multiplying/Dividing Signed Numbers
12. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Solving a System of Equations
Part-to-Part Ratios and Part-to-Whole Ratios
Union of Sets
Volume of a Rectangular Solid
13. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Prime Factorization
Solving a Quadratic Equation
Adding/Subtracting Fractions
Counting Consecutive Integers
14. Part = Percent x Whole
Adding/Subtracting Signed Numbers
Multiplying/Dividing Signed Numbers
Relative Primes
Percent Formula
15. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Even/Odd
Rate
Prime Factorization
Reciprocal
16. pr^2
Finding the midpoint
Finding the Distance Between Two Points
Area of a Circle
Multiples of 2 and 4
17. For all right triangles: a^2+b^2=c^2
Area of a Triangle
Solving a System of Equations
Counting the Possibilities
Pythagorean Theorem
18. The largest factor that two or more numbers have in common.
Using an Equation to Find an Intercept
Dividing Fractions
Average Rate
Greatest Common Factor
19. 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
Interior and Exterior Angles of a Triangle
Raising Powers to Powers
Union of Sets
20. 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
Using Two Points to Find the Slope
Adding and Subtracting monomials
Identifying the Parts and the Whole
Average Rate
21. 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
Multiplying/Dividing Signed Numbers
The 3-4-5 Triangle
Multiplying Fractions
22. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Similar Triangles
Length of an Arc
Multiples of 3 and 9
Factor/Multiple
23. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Surface Area of a Rectangular Solid
Characteristics of a Rectangle
Triangle Inequality Theorem
Using an Equation to Find an Intercept
24. 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
Domain and Range of a Function
Adding and Subtracting Roots
Intersection of sets
25. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Pythagorean Theorem
Multiples of 2 and 4
Relative Primes
Simplifying Square Roots
26. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Volume of a Rectangular Solid
Interior Angles of a Polygon
Multiplying Monomials
Multiplying and Dividing Powers
27. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Intersection of sets
Average Formula -
Intersecting Lines
Mixed Numbers and Improper Fractions
28. Multiply the exponents
Multiples of 2 and 4
Raising Powers to Powers
Area of a Circle
Volume of a Rectangular Solid
29. 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
Triangle Inequality Theorem
Adding/Subtracting Signed Numbers
Area of a Sector
30. 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
Tangency
Evaluating an Expression
Adding/Subtracting Fractions
Direct and Inverse Variation
31. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Adding and Subtraction Polynomials
Intersection of sets
Tangency
Multiples of 3 and 9
32. To multiply fractions - multiply the numerators and multiply the denominators
Adding and Subtracting Roots
Setting up a Ratio
Multiplying Fractions
Finding the Distance Between Two Points
33. 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
Raising Powers to Powers
Finding the Distance Between Two Points
Median and Mode
34. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Mixed Numbers and Improper Fractions
Relative Primes
Triangle Inequality Theorem
PEMDAS
35. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Using an Equation to Find the Slope
Percent Increase and Decrease
Average Formula -
Similar Triangles
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
Remainders
Using an Equation to Find an Intercept
Reciprocal
37. 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
Volume of a Rectangular Solid
Average of Evenly Spaced Numbers
Remainders
Function - Notation - and Evaulation
38. 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)
Surface Area of a Rectangular Solid
Adding and Subtracting Roots
Length of an Arc
Multiplying/Dividing Signed Numbers
39. 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
The 3-4-5 Triangle
Isosceles and Equilateral triangles
Area of a Sector
Repeating Decimal
40. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Area of a Triangle
Counting Consecutive Integers
Similar Triangles
Number Categories
41. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Multiplying and Dividing Roots
Greatest Common Factor
Union of Sets
Multiplying Fractions
42. 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
Characteristics of a Square
Multiplying/Dividing Signed Numbers
Number Categories
Characteristics of a Parallelogram
43. (average of the x coordinates - average of the y coordinates)
Finding the midpoint
Multiples of 3 and 9
The 5-12-13 Triangle
Using Two Points to Find the Slope
44. Sum=(Average) x (Number of Terms)
Similar Triangles
Intersection of sets
Using the Average to Find the Sum
Tangency
45. 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
Area of a Circle
Multiplying Monomials
Part-to-Part Ratios and Part-to-Whole Ratios
Pythagorean Theorem
46. To divide fractions - invert the second one and multiply
Multiplying and Dividing Powers
Dividing Fractions
Adding/Subtracting Fractions
Adding and Subtracting monomials
47. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110
Combined Percent Increase and Decrease
Area of a Sector
(Least) Common Multiple
Characteristics of a Rectangle
48. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Triangle Inequality Theorem
Remainders
Circumference of a Circle
Average of Evenly Spaced Numbers
49. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Multiples of 2 and 4
Average of Evenly Spaced Numbers
Multiplying/Dividing Signed Numbers
50. Surface Area = 2lw + 2wh + 2lh
Counting Consecutive Integers
Multiplying and Dividing Powers
Adding and Subtracting Roots
Surface Area of a Rectangular Solid