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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. 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
Greatest Common Factor
Isosceles and Equilateral triangles
Reducing Fractions
Factor/Multiple
2. 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
Setting up a Ratio
Pythagorean Theorem
Solving a System of Equations
3. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Characteristics of a Square
Solving a System of Equations
Similar Triangles
Multiples of 2 and 4
4. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of
Exponential Growth
Area of a Sector
Finding the Missing Number
Parallel Lines and Transversals
5. 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
Relative Primes
Multiples of 3 and 9
Percent Increase and Decrease
Characteristics of a Rectangle
6. A square is a rectangle with four equal sides; Area of Square = side*side
Percent Increase and Decrease
Characteristics of a Square
Multiplying and Dividing Powers
Multiplying and Dividing Roots
7. Multiply the exponents
Raising Powers to Powers
Reducing Fractions
Finding the Distance Between Two Points
Average of Evenly Spaced Numbers
8. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Multiples of 2 and 4
PEMDAS
Combined Percent Increase and Decrease
Tangency
9. To find the reciprocal of a fraction switch the numerator and the denominator
Median and Mode
Even/Odd
Multiples of 2 and 4
Reciprocal
10. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Function - Notation - and Evaulation
Average Rate
Remainders
Intersecting Lines
11. Sum=(Average) x (Number of Terms)
Average of Evenly Spaced Numbers
Solving a System of Equations
Using the Average to Find the Sum
Setting up a Ratio
12. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Volume of a Rectangular Solid
Adding and Subtracting Roots
Average Formula -
13. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Solving a Quadratic Equation
Adding and Subtraction Polynomials
Median and Mode
Length of an Arc
14. 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
Multiplying/Dividing Signed Numbers
Using an Equation to Find an Intercept
The 3-4-5 Triangle
Factor/Multiple
15. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Triangle Inequality Theorem
Interior Angles of a Polygon
Reciprocal
Negative Exponent and Rational Exponent
16. 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.
Union of Sets
Remainders
Tangency
Number Categories
17. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Exponential Growth
Parallel Lines and Transversals
Factor/Multiple
Finding the Missing Number
18. 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
Multiplying/Dividing Signed Numbers
Comparing Fractions
Solving a Proportion
19. To divide fractions - invert the second one and multiply
Adding and Subtraction Polynomials
Dividing Fractions
Tangency
Counting Consecutive Integers
20. The smallest multiple (other than zero) that two or more numbers have in common.
Solving a System of Equations
(Least) Common Multiple
Characteristics of a Square
Intersecting Lines
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
Multiplying and Dividing Roots
Function - Notation - and Evaulation
Relative Primes
Percent Increase and Decrease
22. To multiply fractions - multiply the numerators and multiply the denominators
Adding/Subtracting Fractions
Using an Equation to Find the Slope
PEMDAS
Multiplying Fractions
23. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Counting the Possibilities
Multiples of 2 and 4
Similar Triangles
Union of Sets
24. Combine like terms
Intersection of sets
Adding and Subtraction Polynomials
Finding the midpoint
Reducing Fractions
25. Change in y/ change in x rise/run
Factor/Multiple
Remainders
Using Two Points to Find the Slope
Function - Notation - and Evaulation
26. 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
Average Rate
Solving a Proportion
PEMDAS
27. Part = Percent x Whole
Combined Percent Increase and Decrease
Percent Formula
(Least) Common Multiple
Adding and Subtraction Polynomials
28. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Multiplying Fractions
Domain and Range of a Function
Identifying the Parts and the Whole
29. 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
Function - Notation - and Evaulation
Combined Percent Increase and Decrease
Part-to-Part Ratios and Part-to-Whole Ratios
Percent Increase and Decrease
30. The 3 angles of any triangle add up to 180 degrees - an exterior angles of a triangle is equal to the sum of the remote interior angles - the 3 exterior angles add up to 360 degrees
Interior and Exterior Angles of a Triangle
Domain and Range of a Function
Median and Mode
Length of an Arc
31. 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
Adding/Subtracting Signed Numbers
Finding the Original Whole
Negative Exponent and Rational Exponent
Area of a Triangle
32. Probability= Favorable Outcomes/Total Possible Outcomes
Probability
Reducing Fractions
Mixed Numbers and Improper Fractions
Intersecting Lines
33. 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
Even/Odd
Triangle Inequality Theorem
Evaluating an Expression
Characteristics of a Parallelogram
34. 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
Mixed Numbers and Improper Fractions
Similar Triangles
Reducing Fractions
Characteristics of a Square
35. 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
Counting Consecutive Integers
Finding the Original Whole
Tangency
Triangle Inequality Theorem
36. The largest factor that two or more numbers have in common.
Adding and Subtraction Polynomials
Greatest Common Factor
Multiplying and Dividing Roots
Raising Powers to Powers
37. 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
Direct and Inverse Variation
Union of Sets
Using an Equation to Find an Intercept
38. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Adding and Subtracting monomials
Multiples of 3 and 9
Counting the Possibilities
Multiplying and Dividing Roots
39. 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
Volume of a Cylinder
Probability
Mixed Numbers and Improper Fractions
Characteristics of a Parallelogram
40. 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
Identifying the Parts and the Whole
Solving an Inequality
Length of an Arc
41. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Using the Average to Find the Sum
Solving an Inequality
Solving a Proportion
Determining Absolute Value
42. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Domain and Range of a Function
Union of Sets
Surface Area of a Rectangular Solid
43. 2pr
Circumference of a Circle
Length of an Arc
Probability
Interior Angles of a Polygon
44. 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
The 5-12-13 Triangle
The 3-4-5 Triangle
Area of a Triangle
Combined Percent Increase and Decrease
45. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Evaluating an Expression
Solving a Quadratic Equation
Prime Factorization
Multiples of 2 and 4
46. 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
Probability
Part-to-Part Ratios and Part-to-Whole Ratios
Intersection of sets
Function - Notation - and Evaulation
47. Volume of a Cylinder = pr^2h
Average of Evenly Spaced Numbers
Solving a System of Equations
Relative Primes
Volume of a Cylinder
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
Simplifying Square Roots
Setting up a Ratio
Determining Absolute Value
49. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
The 5-12-13 Triangle
Pythagorean Theorem
Characteristics of a Square
50. The whole # left over after division
Using the Average to Find the Sum
Finding the midpoint
Pythagorean Theorem
Remainders