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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. Multiply the exponents
Union of Sets
Average Formula -
Raising Powers to Powers
Counting Consecutive Integers
2. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Finding the Missing Number
Parallel Lines and Transversals
Area of a Triangle
Median and Mode
3. Surface Area = 2lw + 2wh + 2lh
Probability
Prime Factorization
Identifying the Parts and the Whole
Surface Area of a Rectangular Solid
4. 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
Adding/Subtracting Fractions
Evaluating an Expression
Dividing Fractions
Isosceles and Equilateral triangles
5. # 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
Solving a Quadratic Equation
Reciprocal
Finding the midpoint
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
Adding/Subtracting Signed Numbers
(Least) Common Multiple
Area of a Circle
Comparing Fractions
7. 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
(Least) Common Multiple
Adding/Subtracting Fractions
Function - Notation - and Evaulation
Multiplying Fractions
8. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Reducing Fractions
Solving a Quadratic Equation
Volume of a Rectangular Solid
Prime Factorization
9. Sum=(Average) x (Number of Terms)
Average Formula -
Characteristics of a Square
Using the Average to Find the Sum
Solving an Inequality
10. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Part-to-Part Ratios and Part-to-Whole Ratios
Identifying the Parts and the Whole
Adding and Subtracting monomials
Setting up a Ratio
11. For all right triangles: a^2+b^2=c^2
Number Categories
Pythagorean Theorem
Surface Area of a Rectangular Solid
Percent Formula
12. Probability= Favorable Outcomes/Total Possible Outcomes
Mixed Numbers and Improper Fractions
Characteristics of a Parallelogram
Isosceles and Equilateral triangles
Probability
13. To divide fractions - invert the second one and multiply
Solving a Proportion
Circumference of a Circle
Dividing Fractions
The 5-12-13 Triangle
14. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Average Rate
Solving a Quadratic Equation
Average Formula -
Multiplying/Dividing Signed Numbers
15. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Volume of a Rectangular Solid
Average of Evenly Spaced Numbers
Intersection of sets
The 5-12-13 Triangle
16. 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
Adding and Subtracting Roots
Median and Mode
Percent Increase and Decrease
Multiplying/Dividing Signed Numbers
17. 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
Tangency
Area of a Sector
Using the Average to Find the Sum
18. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Characteristics of a Square
Exponential Growth
Greatest Common Factor
Average Formula -
19. 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
Prime Factorization
Relative Primes
Adding and Subtraction Polynomials
Exponential Growth
20. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Using Two Points to Find the Slope
Adding/Subtracting Signed Numbers
Multiplying/Dividing Signed Numbers
Adding/Subtracting Fractions
21. Part = Percent x Whole
Percent Formula
Direct and Inverse Variation
Adding and Subtracting Roots
Multiples of 2 and 4
22. The largest factor that two or more numbers have in common.
Exponential Growth
Tangency
Prime Factorization
Greatest Common Factor
23. 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
Raising Powers to Powers
Using an Equation to Find the Slope
Combined Percent Increase and Decrease
Tangency
24. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Adding and Subtracting Roots
Setting up a Ratio
Part-to-Part Ratios and Part-to-Whole Ratios
Using an Equation to Find the Slope
25. 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)
Characteristics of a Square
Area of a Sector
Using Two Points to Find the Slope
Multiples of 3 and 9
26. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Multiplying/Dividing Signed Numbers
Multiplying and Dividing Powers
Exponential Growth
27. 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
Surface Area of a Rectangular Solid
Mixed Numbers and Improper Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
PEMDAS
28. 1. Re-express them with common denominators 2. Convert them to decimals
Raising Powers to Powers
Comparing Fractions
Number Categories
Rate
29. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Average of Evenly Spaced Numbers
Multiples of 2 and 4
Using the Average to Find the Sum
Union of Sets
30. To solve a proportion - cross multiply
Solving a Proportion
Dividing Fractions
Simplifying Square Roots
Area of a Sector
31. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Intersecting Lines
Average of Evenly Spaced Numbers
Tangency
Multiplying/Dividing Signed Numbers
32. 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
Characteristics of a Rectangle
Triangle Inequality Theorem
(Least) Common Multiple
Area of a Triangle
33. 2pr
Circumference of a Circle
Number Categories
Average Rate
Remainders
34. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Volume of a Rectangular Solid
Remainders
Setting up a Ratio
Mixed Numbers and Improper Fractions
35. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Percent Increase and Decrease
Average of Evenly Spaced Numbers
Simplifying Square Roots
36. 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
Negative Exponent and Rational Exponent
Finding the Missing Number
Percent Increase and Decrease
37. Factor out the perfect squares
Rate
Counting Consecutive Integers
Finding the Missing Number
Simplifying Square Roots
38. 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
Identifying the Parts and the Whole
Average Formula -
The 3-4-5 Triangle
Finding the Original Whole
39. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
PEMDAS
Median and Mode
Multiplying/Dividing Signed Numbers
40. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Setting up a Ratio
Relative Primes
Reciprocal
41. 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
PEMDAS
Solving an Inequality
Mixed Numbers and Improper Fractions
Negative Exponent and Rational Exponent
42. 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
Identifying the Parts and the Whole
Adding and Subtracting Roots
The 3-4-5 Triangle
Parallel Lines and Transversals
43. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Volume of a Cylinder
Multiplying and Dividing Roots
Solving a Quadratic Equation
Dividing Fractions
44. Combine like terms
Using an Equation to Find the Slope
Adding and Subtraction Polynomials
Rate
Intersection of sets
45. 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
The 5-12-13 Triangle
Negative Exponent and Rational Exponent
Setting up a Ratio
Mixed Numbers and Improper Fractions
46. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Simplifying Square Roots
Identifying the Parts and the Whole
Probability
Reducing Fractions
47. 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
Mixed Numbers and Improper Fractions
Combined Percent Increase and Decrease
Using an Equation to Find an Intercept
Characteristics of a Rectangle
48. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Dividing Fractions
Adding and Subtracting Roots
Average Rate
Function - Notation - and Evaulation
49. 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
Remainders
Parallel Lines and Transversals
Relative Primes
Multiples of 2 and 4
50. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Average Formula -
Setting up a Ratio
Tangency
Pythagorean Theorem