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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. you can add/subtract when the part under the radical is the same
Intersecting Lines
Adding/Subtracting Signed Numbers
Area of a Circle
Adding and Subtracting Roots
2. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Relative Primes
Multiples of 2 and 4
Finding the Distance Between Two Points
Finding the Original Whole
3. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Prime Factorization
Identifying the Parts and the Whole
Area of a Triangle
Median and Mode
4. 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
Union of Sets
Remainders
Exponential Growth
Negative Exponent and Rational Exponent
5. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Repeating Decimal
Multiplying Fractions
Reducing Fractions
Function - Notation - and Evaulation
6. To find the reciprocal of a fraction switch the numerator and the denominator
Multiples of 3 and 9
Reciprocal
Intersection of sets
Probability
7. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Determining Absolute Value
Multiples of 2 and 4
Interior Angles of a Polygon
Prime Factorization
8. 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
Solving a Quadratic Equation
Counting Consecutive Integers
Using an Equation to Find an Intercept
Finding the Original Whole
9. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Similar Triangles
Length of an Arc
Characteristics of a Rectangle
Evaluating an Expression
10. Part = Percent x Whole
Using Two Points to Find the Slope
Adding/Subtracting Signed Numbers
Multiplying Monomials
Percent Formula
11. 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
Length of an Arc
Comparing Fractions
Surface Area of a Rectangular Solid
Exponential Growth
12. 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
Interior Angles of a Polygon
Tangency
Area of a Triangle
Adding and Subtracting monomials
13. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Simplifying Square Roots
Comparing Fractions
Greatest Common Factor
14. 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
Interior and Exterior Angles of a Triangle
Solving a Quadratic Equation
Counting the Possibilities
15. 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
Relative Primes
Parallel Lines and Transversals
The 5-12-13 Triangle
16. Add the exponents and keep the same base
Number Categories
Reducing Fractions
Direct and Inverse Variation
Multiplying and Dividing Powers
17. Factor out the perfect squares
Multiplying and Dividing Powers
Multiples of 2 and 4
Repeating Decimal
Simplifying Square Roots
18. 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)
(Least) Common Multiple
Area of a Sector
Characteristics of a Square
Multiplying Monomials
19. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Exponential Growth
Interior Angles of a Polygon
Reciprocal
Adding and Subtracting Roots
20. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Characteristics of a Parallelogram
Average Rate
Setting up a Ratio
Average Formula -
21. 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
Using an Equation to Find an Intercept
Determining Absolute Value
Percent Increase and Decrease
Even/Odd
22. 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 3-4-5 Triangle
Multiplying and Dividing Roots
Direct and Inverse Variation
Characteristics of a Square
23. 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
Volume of a Cylinder
Using an Equation to Find an Intercept
Probability
Surface Area of a Rectangular Solid
24. 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.
Rate
Simplifying Square Roots
Number Categories
Percent Formula
25. 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
Evaluating an Expression
Setting up a Ratio
Using the Average to Find the Sum
Function - Notation - and Evaulation
26. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Median and Mode
Average Rate
Dividing Fractions
Adding and Subtracting monomials
27. Multiply the exponents
Circumference of a Circle
Relative Primes
Pythagorean Theorem
Raising Powers to Powers
28. For all right triangles: a^2+b^2=c^2
Average of Evenly Spaced Numbers
Pythagorean Theorem
Solving an Inequality
Direct and Inverse Variation
29. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Characteristics of a Parallelogram
Counting the Possibilities
Finding the Missing Number
Parallel Lines and Transversals
30. 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
Reciprocal
The 5-12-13 Triangle
Repeating Decimal
PEMDAS
31. 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
Similar Triangles
Triangle Inequality Theorem
Part-to-Part Ratios and Part-to-Whole Ratios
Setting up a Ratio
32. The largest factor that two or more numbers have in common.
Greatest Common Factor
Domain and Range of a Function
Determining Absolute Value
Volume of a Cylinder
33. Sum=(Average) x (Number of Terms)
Percent Increase and Decrease
Finding the Missing Number
Pythagorean Theorem
Using the Average to Find the Sum
34. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
The 5-12-13 Triangle
Area of a Sector
Raising Powers to Powers
35. 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
Identifying the Parts and the Whole
Adding/Subtracting Signed Numbers
Percent Increase and Decrease
Characteristics of a Parallelogram
36. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Isosceles and Equilateral triangles
Multiplying and Dividing Roots
Determining Absolute Value
Length of an Arc
37. 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
Repeating Decimal
Multiplying and Dividing Roots
Counting the Possibilities
Solving a Quadratic Equation
38. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Greatest Common Factor
Union of Sets
PEMDAS
Mixed Numbers and Improper Fractions
39. The smallest multiple (other than zero) that two or more numbers have in common.
Solving a Proportion
Characteristics of a Square
(Least) Common Multiple
Domain and Range of a Function
40. 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
Number Categories
Finding the Original Whole
Interior and Exterior Angles of a Triangle
Area of a Circle
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
Finding the Missing Number
Multiples of 2 and 4
Adding and Subtraction Polynomials
Average Formula -
42. To divide fractions - invert the second one and multiply
Dividing Fractions
Prime Factorization
Comparing Fractions
Adding/Subtracting Fractions
43. A square is a rectangle with four equal sides; Area of Square = side*side
(Least) Common Multiple
Counting Consecutive Integers
Characteristics of a Parallelogram
Characteristics of a Square
44. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
(Least) Common Multiple
Finding the Original Whole
Remainders
Intersecting Lines
45. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Using Two Points to Find the Slope
Area of a Triangle
Factor/Multiple
Finding the Original Whole
46. 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
Using Two Points to Find the Slope
Triangle Inequality Theorem
Determining Absolute Value
47. 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
Combined Percent Increase and Decrease
Finding the midpoint
Mixed Numbers and Improper Fractions
Even/Odd
48. Probability= Favorable Outcomes/Total Possible Outcomes
Interior Angles of a Polygon
Characteristics of a Rectangle
Probability
Multiplying/Dividing Signed Numbers
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
Determining Absolute Value
Combined Percent Increase and Decrease
Negative Exponent and Rational Exponent
Even/Odd
50. 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
Intersection of sets
Isosceles and Equilateral triangles
Setting up a Ratio
Solving a Quadratic Equation