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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 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)
Volume of a Cylinder
Multiplying Fractions
Counting Consecutive Integers
Length of an Arc
2. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Intersection of sets
Tangency
Determining Absolute Value
Characteristics of a Square
3. Add the exponents and keep the same base
Multiplying and Dividing Powers
Area of a Triangle
Relative Primes
Adding and Subtraction Polynomials
4. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Similar Triangles
Multiples of 2 and 4
Identifying the Parts and the Whole
Factor/Multiple
5. To find the reciprocal of a fraction switch the numerator and the denominator
Union of Sets
Similar Triangles
Reciprocal
Using an Equation to Find an Intercept
6. 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
Median and Mode
Counting the Possibilities
Remainders
Finding the Original Whole
7. 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
Finding the Original Whole
Direct and Inverse Variation
Identifying the Parts and the Whole
Combined Percent Increase and Decrease
8. 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)
Simplifying Square Roots
Evaluating an Expression
Area of a Sector
Identifying the Parts and the Whole
9. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Triangle Inequality Theorem
Percent Formula
Area of a Sector
Characteristics of a Rectangle
10. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
(Least) Common Multiple
Isosceles and Equilateral triangles
Reducing Fractions
Solving a Quadratic Equation
11. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Characteristics of a Parallelogram
(Least) Common Multiple
Multiplying and Dividing Roots
Part-to-Part Ratios and Part-to-Whole Ratios
12. 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
Interior and Exterior Angles of a Triangle
Direct and Inverse Variation
Adding and Subtracting Roots
Relative Primes
13. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Setting up a Ratio
Reducing Fractions
Volume of a Rectangular Solid
14. 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
Finding the Original Whole
Finding the midpoint
(Least) Common Multiple
15. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Multiples of 2 and 4
Counting the Possibilities
Multiplying/Dividing Signed Numbers
16. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Solving a Quadratic Equation
Surface Area of a Rectangular Solid
Multiples of 3 and 9
Multiplying/Dividing Signed Numbers
17. Part = Percent x Whole
Volume of a Rectangular Solid
Finding the midpoint
Even/Odd
Percent Formula
18. pr^2
Length of an Arc
Area of a Triangle
Repeating Decimal
Area of a Circle
19. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Tangency
Volume of a Rectangular Solid
Parallel Lines and Transversals
Evaluating an Expression
20. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Solving an Inequality
Intersecting Lines
Multiplying and Dividing Powers
Intersection of sets
21. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Interior Angles of a Polygon
Average of Evenly Spaced Numbers
Prime Factorization
Using an Equation to Find the Slope
22. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Finding the Missing Number
Greatest Common Factor
Using Two Points to Find the Slope
Multiples of 2 and 4
23. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Solving a System of Equations
Average Rate
Reciprocal
24. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Remainders
Finding the midpoint
Solving a System of Equations
Average Formula -
25. 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
Median and Mode
Multiplying and Dividing Powers
The 5-12-13 Triangle
26. 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
Volume of a Rectangular Solid
Mixed Numbers and Improper Fractions
Solving a Quadratic Equation
Multiplying/Dividing Signed Numbers
27. 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
Multiples of 3 and 9
Adding and Subtracting monomials
Average Rate
Interior and Exterior Angles of a Triangle
28. 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
Length of an Arc
Mixed Numbers and Improper Fractions
Counting the Possibilities
29. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Determining Absolute Value
Multiplying/Dividing Signed Numbers
Reciprocal
Evaluating an Expression
30. 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
Pythagorean Theorem
Reciprocal
Combined Percent Increase and Decrease
Isosceles and Equilateral triangles
31. # 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
Multiples of 2 and 4
PEMDAS
Volume of a Cylinder
32. To multiply fractions - multiply the numerators and multiply the denominators
Adding and Subtracting monomials
Prime Factorization
Adding and Subtraction Polynomials
Multiplying Fractions
33. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Mixed Numbers and Improper Fractions
Multiplying/Dividing Signed Numbers
Even/Odd
Using an Equation to Find the Slope
34. The whole # left over after division
PEMDAS
Adding and Subtracting monomials
Remainders
Negative Exponent and Rational Exponent
35. (average of the x coordinates - average of the y coordinates)
Using an Equation to Find an Intercept
Finding the midpoint
Area of a Triangle
Average Formula -
36. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Setting up a Ratio
Characteristics of a Square
Adding and Subtracting monomials
Number Categories
37. Sum=(Average) x (Number of Terms)
Finding the Missing Number
Using the Average to Find the Sum
Adding and Subtracting monomials
Finding the Distance Between Two Points
38. 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
Circumference of a Circle
Reciprocal
Counting Consecutive Integers
39. you can add/subtract when the part under the radical is the same
Area of a Triangle
Adding and Subtracting Roots
Average Rate
Multiples of 3 and 9
40. Combine like terms
Greatest Common Factor
Adding and Subtraction Polynomials
Multiples of 2 and 4
Simplifying Square Roots
41. 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
Multiples of 2 and 4
Similar Triangles
Using an Equation to Find an Intercept
42. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Adding and Subtracting monomials
Average of Evenly Spaced Numbers
Median and Mode
Comparing Fractions
43. Probability= Favorable Outcomes/Total Possible Outcomes
Volume of a Cylinder
Probability
Average Formula -
Multiplying and Dividing Powers
44. 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
Finding the midpoint
Exponential Growth
Using the Average to Find the Sum
45. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Determining Absolute Value
The 5-12-13 Triangle
Prime Factorization
Probability
46. To divide fractions - invert the second one and multiply
Dividing Fractions
Interior and Exterior Angles of a Triangle
Triangle Inequality Theorem
Average Rate
47. To solve a proportion - cross multiply
Using an Equation to Find an Intercept
Relative Primes
Mixed Numbers and Improper Fractions
Solving a Proportion
48. 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.
Number Categories
Multiples of 3 and 9
Area of a Sector
Intersection of sets
49. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Prime Factorization
Finding the Distance Between Two Points
Adding and Subtraction Polynomials
Counting the Possibilities
50. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Adding/Subtracting Fractions
Volume of a Cylinder
Solving a Quadratic Equation
Domain and Range of a Function