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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. 2pr
PEMDAS
Circumference of a Circle
Characteristics of a Parallelogram
Reciprocal
2. The largest factor that two or more numbers have in common.
Part-to-Part Ratios and Part-to-Whole Ratios
Greatest Common Factor
Multiplying and Dividing Roots
Solving a Quadratic Equation
3. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Intersecting Lines
Volume of a Cylinder
Multiplying Monomials
Pythagorean Theorem
4. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Interior Angles of a Polygon
Dividing Fractions
Solving a Quadratic Equation
Using an Equation to Find an Intercept
5. Surface Area = 2lw + 2wh + 2lh
Solving a Proportion
Area of a Sector
Rate
Surface Area of a Rectangular Solid
6. 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
Multiplying Fractions
Similar Triangles
Determining Absolute Value
7. 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)
Multiplying Fractions
Adding and Subtracting monomials
Percent Increase and Decrease
Length of an Arc
8. 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
Setting up a Ratio
Determining Absolute Value
Characteristics of a Parallelogram
(Least) Common Multiple
9. To divide fractions - invert the second one and multiply
Raising Powers to Powers
Evaluating an Expression
Dividing Fractions
Average Rate
10. 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
Multiplying and Dividing Roots
Tangency
Mixed Numbers and Improper Fractions
Counting the Possibilities
11. 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
Volume of a Cylinder
Part-to-Part Ratios and Part-to-Whole Ratios
Tangency
12. 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.
Intersection of sets
Area of a Circle
Number Categories
Multiples of 2 and 4
13. The smallest multiple (other than zero) that two or more numbers have in common.
(Least) Common Multiple
Average Rate
Characteristics of a Rectangle
Probability
14. Probability= Favorable Outcomes/Total Possible Outcomes
Union of Sets
Pythagorean Theorem
Combined Percent Increase and Decrease
Probability
15. 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
Multiples of 3 and 9
Union of Sets
Function - Notation - and Evaulation
Identifying the Parts and the Whole
16. 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
Dividing Fractions
Multiplying/Dividing Signed Numbers
Area of a Sector
Setting up a Ratio
17. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Reciprocal
Direct and Inverse Variation
Adding and Subtracting monomials
Prime Factorization
18. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
PEMDAS
Percent Increase and Decrease
Reducing Fractions
Surface Area of a Rectangular Solid
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
Probability
Volume of a Rectangular Solid
Factor/Multiple
Rate
20. Combine like terms
Relative Primes
Adding and Subtraction Polynomials
Function - Notation - and Evaulation
Prime Factorization
21. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Median and Mode
Average Formula -
Reducing Fractions
Remainders
22. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Exponential Growth
Tangency
Characteristics of a Rectangle
The 3-4-5 Triangle
23. Part = Percent x Whole
Area of a Triangle
Negative Exponent and Rational Exponent
Solving an Inequality
Percent Formula
24. 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
Reducing Fractions
Mixed Numbers and Improper Fractions
Multiplying and Dividing Powers
Direct and Inverse Variation
25. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Factor/Multiple
Interior and Exterior Angles of a Triangle
Tangency
Adding/Subtracting Signed Numbers
26. To find the reciprocal of a fraction switch the numerator and the denominator
Prime Factorization
Area of a Sector
Intersecting Lines
Reciprocal
27. 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
Area of a Triangle
Factor/Multiple
Greatest Common Factor
Finding the Original Whole
28. Factor out the perfect squares
Part-to-Part Ratios and Part-to-Whole Ratios
Simplifying Square Roots
(Least) Common Multiple
Number Categories
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
Multiplying Fractions
Mixed Numbers and Improper Fractions
Multiplying and Dividing Powers
Interior and Exterior Angles of a Triangle
30. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Parallel Lines and Transversals
Prime Factorization
Multiplying and Dividing Powers
Evaluating an Expression
31. pr^2
Part-to-Part Ratios and Part-to-Whole Ratios
Multiplying/Dividing Signed Numbers
Area of a Circle
Probability
32. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Multiplying and Dividing Powers
Characteristics of a Parallelogram
Mixed Numbers and Improper Fractions
Setting up a Ratio
33. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Relative Primes
Isosceles and Equilateral triangles
Characteristics of a Square
34. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Exponential Growth
Intersecting Lines
Mixed Numbers and Improper Fractions
35. To multiply fractions - multiply the numerators and multiply the denominators
Adding and Subtracting monomials
Multiplying Fractions
Characteristics of a Parallelogram
Multiplying/Dividing Signed Numbers
36. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Rate
Solving an Inequality
37. 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
Solving a Proportion
Relative Primes
Multiplying Monomials
38. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Prime Factorization
Simplifying Square Roots
Function - Notation - and Evaulation
Volume of a Rectangular Solid
39. 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)
Tangency
Solving an Inequality
Area of a Sector
Interior and Exterior Angles of a Triangle
40. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Multiples of 3 and 9
Median and Mode
Solving a System of Equations
Percent Formula
41. 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
Triangle Inequality Theorem
Combined Percent Increase and Decrease
Using Two Points to Find the Slope
Factor/Multiple
42. The whole # left over after division
Dividing Fractions
Remainders
Intersecting Lines
Average Formula -
43. 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
Pythagorean Theorem
Adding/Subtracting Signed Numbers
Percent Increase and Decrease
Even/Odd
44. Sum=(Average) x (Number of Terms)
Dividing Fractions
Using the Average to Find the Sum
Solving a Quadratic Equation
Adding and Subtracting Roots
45. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Rate
Dividing Fractions
Area of a Sector
46. 1. Re-express them with common denominators 2. Convert them to decimals
Average of Evenly Spaced Numbers
Average Rate
Comparing Fractions
Using Two Points to Find the Slope
47. 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
Median and Mode
Identifying the Parts and the Whole
Using an Equation to Find the Slope
Percent Formula
48. 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
Factor/Multiple
Negative Exponent and Rational Exponent
Repeating Decimal
Simplifying Square Roots
49. 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
Domain and Range of a Function
Percent Increase and Decrease
Multiplying Monomials
50. you can add/subtract when the part under the radical is the same
Setting up a Ratio
Raising Powers to Powers
Adding and Subtracting Roots
Relative Primes