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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. 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
Reciprocal
Dividing Fractions
2. 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
Function - Notation - and Evaulation
Similar Triangles
The 3-4-5 Triangle
Exponential Growth
3. 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
Adding and Subtracting monomials
Repeating Decimal
Multiples of 3 and 9
Median and Mode
4. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Multiples of 2 and 4
The 5-12-13 Triangle
Using an Equation to Find the Slope
Solving a Proportion
5. 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 Proportion
Multiplying/Dividing Signed Numbers
Area of a Sector
Raising Powers to Powers
6. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Relative Primes
Tangency
The 5-12-13 Triangle
Median and Mode
7. 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
Even/Odd
Area of a Sector
Adding/Subtracting Signed Numbers
Area of a Triangle
8. The smallest multiple (other than zero) that two or more numbers have in common.
Multiplying Monomials
Intersecting Lines
(Least) Common Multiple
The 3-4-5 Triangle
9. pr^2
Average of Evenly Spaced Numbers
Finding the midpoint
Multiplying Monomials
Area of a Circle
10. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Solving a Proportion
Repeating Decimal
Using the Average to Find the Sum
Average of Evenly Spaced Numbers
11. 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
The 5-12-13 Triangle
Rate
Direct and Inverse Variation
Length of an Arc
12. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Domain and Range of a Function
Union of Sets
Determining Absolute Value
13. Surface Area = 2lw + 2wh + 2lh
Using the Average to Find the Sum
Surface Area of a Rectangular Solid
Direct and Inverse Variation
Area of a Circle
14. Domain: all possible values of x for a function range: all possible outputs of a function
Factor/Multiple
Isosceles and Equilateral triangles
Using an Equation to Find the Slope
Domain and Range of a Function
15. The whole # left over after division
Remainders
Solving an Inequality
Pythagorean Theorem
Interior Angles of a Polygon
16. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Distance Between Two Points
Adding/Subtracting Signed Numbers
Area of a Sector
Counting the Possibilities
17. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Adding and Subtracting monomials
Simplifying Square Roots
Length of an Arc
18. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Part-to-Part Ratios and Part-to-Whole Ratios
Solving a Proportion
Volume of a Cylinder
Multiples of 2 and 4
19. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Solving a System of Equations
Tangency
Multiplying Monomials
Interior and Exterior Angles of a Triangle
20. The largest factor that two or more numbers have in common.
Raising Powers to Powers
Isosceles and Equilateral triangles
Average of Evenly Spaced Numbers
Greatest Common Factor
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
Remainders
Determining Absolute Value
Circumference of a Circle
Triangle Inequality Theorem
22. 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
Characteristics of a Parallelogram
Adding and Subtracting monomials
Remainders
Setting up a Ratio
23. 2pr
Intersecting Lines
PEMDAS
Using an Equation to Find an Intercept
Circumference of a Circle
24. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Adding and Subtracting Roots
Factor/Multiple
Function - Notation - and Evaulation
Surface Area of a Rectangular Solid
25. 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
Prime Factorization
Adding/Subtracting Signed Numbers
Using an Equation to Find an Intercept
Percent Increase and Decrease
26. Change in y/ change in x rise/run
Multiples of 2 and 4
Using Two Points to Find the Slope
Characteristics of a Parallelogram
Multiplying Monomials
27. A square is a rectangle with four equal sides; Area of Square = side*side
Raising Powers to Powers
Probability
Characteristics of a Square
Multiplying and Dividing Powers
28. 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
Percent Increase and Decrease
Adding and Subtraction Polynomials
Multiplying/Dividing Signed Numbers
Finding the midpoint
29. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Number Categories
Parallel Lines and Transversals
Combined Percent Increase and Decrease
30. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Percent Formula
Multiplying/Dividing Signed Numbers
Intersecting Lines
Exponential Growth
31. 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
Isosceles and Equilateral triangles
Intersection of sets
Part-to-Part Ratios and Part-to-Whole Ratios
Multiples of 3 and 9
32. 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
Counting the Possibilities
Combined Percent Increase and Decrease
Setting up a Ratio
Rate
33. 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
Reducing Fractions
Simplifying Square Roots
Function - Notation - and Evaulation
Remainders
34. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Repeating Decimal
Adding and Subtracting monomials
Characteristics of a Square
35. For all right triangles: a^2+b^2=c^2
Multiplying/Dividing Signed Numbers
Probability
Isosceles and Equilateral triangles
Pythagorean Theorem
36. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Repeating Decimal
Domain and Range of a Function
Multiplying Fractions
Volume of a Rectangular Solid
37. Add the exponents and keep the same base
Multiplying and Dividing Powers
Direct and Inverse Variation
Adding and Subtracting Roots
PEMDAS
38. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Raising Powers to Powers
Triangle Inequality Theorem
Median and Mode
Finding the midpoint
39. Subtract the smallest from the largest and add 1
The 3-4-5 Triangle
Factor/Multiple
Counting Consecutive Integers
Probability
40. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Median and Mode
Multiplying/Dividing Signed Numbers
Multiplying and Dividing Roots
The 3-4-5 Triangle
41. 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
Triangle Inequality Theorem
Finding the Missing Number
Circumference of a Circle
Identifying the Parts and the Whole
42. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Number Categories
Surface Area of a Rectangular Solid
Circumference of a Circle
Solving a Quadratic Equation
43. Probability= Favorable Outcomes/Total Possible Outcomes
Percent Increase and Decrease
Setting up a Ratio
Reducing Fractions
Probability
44. 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
Multiplying/Dividing Signed Numbers
Surface Area of a Rectangular Solid
Counting Consecutive Integers
Determining Absolute Value
45. 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
Area of a Circle
Dividing Fractions
Interior and Exterior Angles of a Triangle
Average Rate
46. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Prime Factorization
Characteristics of a Rectangle
Tangency
Area of a Circle
47. 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
Multiplying and Dividing Powers
Characteristics of a Parallelogram
Remainders
48. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Dividing Fractions
Adding/Subtracting Fractions
Reciprocal
Multiples of 3 and 9
49. 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
Interior and Exterior Angles of a Triangle
The 3-4-5 Triangle
The 5-12-13 Triangle
Characteristics of a Rectangle
50. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Adding and Subtraction Polynomials
Counting the Possibilities
Characteristics of a Rectangle