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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Study First
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. 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
Solving an Inequality
Adding/Subtracting Fractions
Counting the Possibilities
Volume of a Rectangular Solid
2. 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
Exponential Growth
Comparing Fractions
Determining Absolute Value
Finding the Missing Number
3. Part = Percent x Whole
Solving a System of Equations
Even/Odd
Percent Formula
Area of a Circle
4. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Median and Mode
Volume of a Cylinder
Negative Exponent and Rational Exponent
Average Rate
5. 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
Average Formula -
Volume of a Rectangular Solid
Characteristics of a Rectangle
Rate
6. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Adding and Subtracting Roots
Finding the Distance Between Two Points
Median and Mode
Solving a Quadratic Equation
7. (average of the x coordinates - average of the y coordinates)
Finding the midpoint
Dividing Fractions
Percent Increase and Decrease
Multiplying/Dividing Signed Numbers
8. A square is a rectangle with four equal sides; Area of Square = side*side
Area of a Circle
Combined Percent Increase and Decrease
Characteristics of a Square
Relative Primes
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
The 3-4-5 Triangle
Combined Percent Increase and Decrease
Evaluating an Expression
Finding the Missing Number
10. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Interior and Exterior Angles of a Triangle
Using an Equation to Find an Intercept
Direct and Inverse Variation
11. 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
Even/Odd
Raising Powers to Powers
Interior Angles of a Polygon
Triangle Inequality Theorem
12. The whole # left over after division
Remainders
Adding/Subtracting Fractions
Counting the Possibilities
Finding the Missing Number
13. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Characteristics of a Square
Using the Average to Find the Sum
Counting Consecutive Integers
14. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Remainders
Solving an Inequality
Pythagorean Theorem
15. 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
Even/Odd
Identifying the Parts and the Whole
Adding/Subtracting Signed Numbers
16. 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
Function - Notation - and Evaulation
Volume of a Cylinder
Solving a Proportion
The 5-12-13 Triangle
17. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Reducing Fractions
Remainders
Part-to-Part Ratios and Part-to-Whole Ratios
Finding the Distance Between Two Points
18. Factor out the perfect squares
Multiples of 3 and 9
Adding and Subtracting monomials
Percent Increase and Decrease
Simplifying Square Roots
19. 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
Multiples of 2 and 4
Triangle Inequality Theorem
Solving an Inequality
Similar Triangles
20. # 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
Part-to-Part Ratios and Part-to-Whole Ratios
Counting the Possibilities
Using the Average to Find the Sum
21. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Remainders
Volume of a Cylinder
Repeating Decimal
Average of Evenly Spaced Numbers
22. Surface Area = 2lw + 2wh + 2lh
Setting up a Ratio
Surface Area of a Rectangular Solid
Interior and Exterior Angles of a Triangle
Area of a Triangle
23. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Combined Percent Increase and Decrease
Multiplying and Dividing Roots
Average of Evenly Spaced Numbers
Solving a Quadratic Equation
24. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Multiplying and Dividing Powers
Rate
Average Rate
Volume of a Rectangular Solid
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
Function - Notation - and Evaulation
Greatest Common Factor
Median and Mode
Even/Odd
26. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Counting the Possibilities
Solving a System of Equations
Factor/Multiple
Intersection of sets
27. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Mixed Numbers and Improper Fractions
Multiples of 3 and 9
Determining Absolute Value
Characteristics of a Rectangle
28. 2pr
Adding and Subtracting Roots
Solving an Inequality
Even/Odd
Circumference of a Circle
29. The largest factor that two or more numbers have in common.
Greatest Common Factor
Tangency
Adding/Subtracting Fractions
Determining Absolute Value
30. Domain: all possible values of x for a function range: all possible outputs of a function
Characteristics of a Parallelogram
Multiples of 2 and 4
Simplifying Square Roots
Domain and Range of a Function
31. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Counting Consecutive Integers
Using an Equation to Find an Intercept
Multiples of 2 and 4
32. 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)
Reducing Fractions
Finding the Missing Number
Area of a Sector
Probability
33. pr^2
Area of a Circle
Multiples of 3 and 9
Reciprocal
Surface Area of a Rectangular Solid
34. 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
Isosceles and Equilateral triangles
Tangency
The 3-4-5 Triangle
Percent Formula
35. 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.
Percent Formula
Number Categories
Union of Sets
Solving a Proportion
36. 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
Area of a Triangle
Determining Absolute Value
Volume of a Cylinder
37. 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
Average Rate
Surface Area of a Rectangular Solid
Relative Primes
Interior and Exterior Angles of a Triangle
38. Multiply the exponents
Raising Powers to Powers
Adding and Subtraction Polynomials
Multiplying/Dividing Signed Numbers
Mixed Numbers and Improper Fractions
39. 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
Finding the Distance Between Two Points
Finding the midpoint
Multiplying/Dividing Signed Numbers
40. To divide fractions - invert the second one and multiply
Exponential Growth
Dividing Fractions
Prime Factorization
Part-to-Part Ratios and Part-to-Whole Ratios
41. For all right triangles: a^2+b^2=c^2
Average of Evenly Spaced Numbers
Pythagorean Theorem
Percent Formula
Adding and Subtraction Polynomials
42. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Direct and Inverse Variation
Average Formula -
Using an Equation to Find the Slope
Domain and Range of a Function
43. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Relative Primes
Multiplying and Dividing Powers
Prime Factorization
Determining Absolute Value
44. 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 a Quadratic Equation
Length of an Arc
Comparing Fractions
Adding and Subtracting monomials
45. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Direct and Inverse Variation
Characteristics of a Rectangle
Domain and Range of a Function
Multiplying and Dividing Roots
46. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them
Solving a System of Equations
Dividing Fractions
Even/Odd
Reducing Fractions
47. To multiply fractions - multiply the numerators and multiply the denominators
Average Rate
Multiplying Fractions
Using an Equation to Find an Intercept
Negative Exponent and Rational Exponent
48. Combine equations in such a way that one of the variables cancel out
Combined Percent Increase and Decrease
Solving a System of Equations
(Least) Common Multiple
Parallel Lines and Transversals
49. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Intersecting Lines
Union of Sets
Identifying the Parts and the Whole
Finding the midpoint
50. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Greatest Common Factor
Combined Percent Increase and Decrease
The 5-12-13 Triangle
Adding and Subtracting monomials