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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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sat
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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. 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
Tangency
Combined Percent Increase and Decrease
Area of a Triangle
2. pr^2
Area of a Circle
Interior and Exterior Angles of a Triangle
Identifying the Parts and the Whole
Area of a Triangle
3. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Factor/Multiple
Domain and Range of a Function
Solving a Quadratic Equation
Using Two Points to Find the Slope
4. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
(Least) Common Multiple
Intersecting Lines
Volume of a Rectangular Solid
5. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Simplifying Square Roots
Number Categories
Volume of a Rectangular Solid
Solving a Proportion
6. 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
Raising Powers to Powers
Adding and Subtraction Polynomials
Adding/Subtracting Signed Numbers
Finding the Original Whole
7. The largest factor that two or more numbers have in common.
Greatest Common Factor
Characteristics of a Square
(Least) Common Multiple
Using Two Points to Find the Slope
8. 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
Using the Average to Find the Sum
Isosceles and Equilateral triangles
Area of a Sector
Multiplying Fractions
9. 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
Isosceles and Equilateral triangles
Negative Exponent and Rational Exponent
(Least) Common Multiple
The 3-4-5 Triangle
10. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Factor/Multiple
Finding the Distance Between Two Points
Adding/Subtracting Signed Numbers
Counting Consecutive Integers
11. Surface Area = 2lw + 2wh + 2lh
Surface Area of a Rectangular Solid
Finding the midpoint
Pythagorean Theorem
Solving a Proportion
12. To solve a proportion - cross multiply
Probability
Number Categories
Dividing Fractions
Solving a Proportion
13. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Triangle Inequality Theorem
PEMDAS
Isosceles and Equilateral triangles
Function - Notation - and Evaulation
14. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Adding/Subtracting Signed Numbers
Interior and Exterior Angles of a Triangle
Adding and Subtracting monomials
Direct and Inverse Variation
15. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Median and Mode
Volume of a Rectangular Solid
Multiplying Monomials
Adding and Subtraction Polynomials
16. Combine like terms
Adding and Subtraction Polynomials
Counting Consecutive Integers
Interior and Exterior Angles of a Triangle
Tangency
17. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Multiples of 3 and 9
Tangency
Characteristics of a Rectangle
Factor/Multiple
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
Prime Factorization
Parallel Lines and Transversals
Pythagorean Theorem
19. 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
Parallel Lines and Transversals
Even/Odd
Solving a Quadratic Equation
Characteristics of a Parallelogram
20. Subtract the smallest from the largest and add 1
Characteristics of a Square
Even/Odd
Adding/Subtracting Fractions
Counting Consecutive Integers
21. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Multiples of 2 and 4
Adding and Subtraction Polynomials
Adding and Subtracting Roots
Solving a System of Equations
22. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Using Two Points to Find the Slope
Part-to-Part Ratios and Part-to-Whole Ratios
Tangency
Raising Powers to Powers
23. 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
Tangency
Multiplying Fractions
Determining Absolute Value
24. 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
Using an Equation to Find an Intercept
Using the Average to Find the Sum
Adding and Subtraction Polynomials
Repeating Decimal
25. Domain: all possible values of x for a function range: all possible outputs of a function
Probability
Adding/Subtracting Signed Numbers
Multiplying and Dividing Roots
Domain and Range of a Function
26. 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 midpoint
Length of an Arc
Determining Absolute Value
Area of a Sector
27. The smallest multiple (other than zero) that two or more numbers have in common.
Finding the midpoint
Part-to-Part Ratios and Part-to-Whole Ratios
(Least) Common Multiple
Multiplying/Dividing Signed Numbers
28. 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
Triangle Inequality Theorem
Percent Increase and Decrease
Tangency
The 5-12-13 Triangle
29. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Length of an Arc
Using the Average to Find the Sum
Interior Angles of a Polygon
Prime Factorization
30. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Intersection of sets
Reciprocal
Prime Factorization
Adding and Subtracting monomials
31. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Factor/Multiple
Average Rate
Similar Triangles
Combined Percent Increase and Decrease
32. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Prime Factorization
Remainders
Adding/Subtracting Fractions
Similar Triangles
33. 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
Dividing Fractions
Raising Powers to Powers
Solving a System of Equations
34. Multiply the exponents
Counting Consecutive Integers
Raising Powers to Powers
Adding and Subtraction Polynomials
Using Two Points to Find the Slope
35. 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
Percent Increase and Decrease
Reciprocal
Dividing Fractions
36. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Number Categories
Probability
Average Formula -
Evaluating an Expression
37. 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
Function - Notation - and Evaulation
Prime Factorization
Solving an Inequality
Adding and Subtraction Polynomials
38. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Intersecting Lines
Adding and Subtracting monomials
Isosceles and Equilateral triangles
Average of Evenly Spaced Numbers
39. 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
Counting the Possibilities
Finding the Original Whole
PEMDAS
Solving a Quadratic Equation
40. 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)
Solving a Quadratic Equation
Multiplying Monomials
Area of a Sector
Adding and Subtraction Polynomials
41. 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
Surface Area of a Rectangular Solid
Counting the Possibilities
Comparing Fractions
Using an Equation to Find an Intercept
42. (average of the x coordinates - average of the y coordinates)
Triangle Inequality Theorem
Raising Powers to Powers
Finding the midpoint
Multiplying and Dividing Powers
43. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Characteristics of a Rectangle
Parallel Lines and Transversals
Setting up a Ratio
Multiplying and Dividing Roots
44. Combine equations in such a way that one of the variables cancel out
Intersection of sets
Solving a System of Equations
Finding the Distance Between Two Points
Mixed Numbers and Improper Fractions
45. 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
Direct and Inverse Variation
Solving a Quadratic Equation
Identifying the Parts and the Whole
Multiplying and Dividing Roots
46. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Volume of a Rectangular Solid
Similar Triangles
Counting the Possibilities
47. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Parallel Lines and Transversals
Solving an Inequality
Multiplying Monomials
Adding and Subtracting Roots
48. 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)
Solving an Inequality
Length of an Arc
Average Rate
Remainders
49. 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
Finding the Missing Number
PEMDAS
Average Rate
50. 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
Finding the Original Whole
Rate
Area of a Triangle
Adding and Subtraction Polynomials