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Test your basic knowledge |
SAT Math: Concepts And Tricks
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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. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average Formula -
Adding and Subtraction Polynomials
Direct and Inverse Variation
Identifying the Parts and the Whole
2. 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
Counting Consecutive Integers
Number Categories
Factor/Multiple
Identifying the Parts and the Whole
3. 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
Average of Evenly Spaced Numbers
Counting the Possibilities
Median and Mode
Adding/Subtracting Fractions
4. To solve a proportion - cross multiply
Solving a Proportion
Exponential Growth
Adding and Subtraction Polynomials
Identifying the Parts and the Whole
5. 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
Area of a Circle
Finding the Missing Number
Finding the Original Whole
Direct and Inverse Variation
6. 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
Negative Exponent and Rational Exponent
Triangle Inequality Theorem
Finding the midpoint
Volume of a Cylinder
7. The whole # left over after division
Remainders
Number Categories
Solving a System of Equations
Setting up a Ratio
8. 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
Adding/Subtracting Signed Numbers
Multiples of 3 and 9
Part-to-Part Ratios and Part-to-Whole Ratios
Area of a Triangle
9. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Interior Angles of a Polygon
Circumference of a Circle
Evaluating an Expression
Intersection of sets
10. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Repeating Decimal
Similar Triangles
Identifying the Parts and the Whole
Prime Factorization
11. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Characteristics of a Parallelogram
Volume of a Rectangular Solid
Finding the midpoint
Area of a Sector
12. 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
Part-to-Part Ratios and Part-to-Whole Ratios
(Least) Common Multiple
Percent Formula
13. Change in y/ change in x rise/run
Volume of a Cylinder
Using Two Points to Find the Slope
Evaluating an Expression
The 3-4-5 Triangle
14. For all right triangles: a^2+b^2=c^2
Interior Angles of a Polygon
Pythagorean Theorem
Median and Mode
Reciprocal
15. 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
Triangle Inequality Theorem
Reciprocal
Interior Angles of a Polygon
Finding the Distance Between Two Points
16. 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
Isosceles and Equilateral triangles
Adding/Subtracting Signed Numbers
Solving an Inequality
Adding and Subtraction Polynomials
17. 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
Area of a Sector
Domain and Range of a Function
Probability
Part-to-Part Ratios and Part-to-Whole Ratios
18. 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
Identifying the Parts and the Whole
Characteristics of a Parallelogram
Characteristics of a Rectangle
Multiplying and Dividing Powers
19. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Multiplying/Dividing Signed Numbers
Determining Absolute Value
Pythagorean Theorem
20. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Relative Primes
Multiplying and Dividing Roots
Adding/Subtracting Fractions
Negative Exponent and Rational Exponent
21. Probability= Favorable Outcomes/Total Possible Outcomes
Domain and Range of a Function
Probability
Even/Odd
The 5-12-13 Triangle
22. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Interior Angles of a Polygon
Comparing Fractions
Relative Primes
23. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Adding/Subtracting Signed Numbers
Average of Evenly Spaced Numbers
Number Categories
Multiplying/Dividing Signed Numbers
24. 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)
Multiplying Monomials
Union of Sets
Volume of a Rectangular Solid
Length of an Arc
25. you can add/subtract when the part under the radical is the same
Tangency
Factor/Multiple
Adding and Subtracting Roots
The 5-12-13 Triangle
26. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Reducing Fractions
Multiplying Monomials
Determining Absolute Value
27. 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
Domain and Range of a Function
Percent Increase and Decrease
Percent Formula
Union of Sets
28. The largest factor that two or more numbers have in common.
Characteristics of a Square
Reciprocal
Greatest Common Factor
Solving a Proportion
29. 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
Using an Equation to Find an Intercept
Reciprocal
Probability
Finding the Distance Between Two Points
30. 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
Solving a System of Equations
Adding/Subtracting Signed Numbers
Union of Sets
31. Factor out the perfect squares
Simplifying Square Roots
Finding the Distance Between Two Points
Isosceles and Equilateral triangles
Interior Angles of a Polygon
32. 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
Number Categories
Using the Average to Find the Sum
Isosceles and Equilateral triangles
Intersecting Lines
33. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Solving a Proportion
Multiplying and Dividing Powers
Number Categories
34. 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 and Subtracting monomials
Finding the Missing Number
Circumference of a Circle
Intersection of sets
35. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Adding and Subtracting Roots
Solving a Quadratic Equation
Length of an Arc
Circumference of a Circle
36. Combine like terms
Volume of a Cylinder
Evaluating an Expression
Solving a System of Equations
Adding and Subtraction Polynomials
37. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Multiples of 3 and 9
Average Rate
Average Formula -
Probability
38. 1. Re-express them with common denominators 2. Convert them to decimals
Using the Average to Find the Sum
Median and Mode
Adding and Subtracting Roots
Comparing Fractions
39. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Using the Average to Find the Sum
Adding/Subtracting Fractions
Isosceles and Equilateral triangles
Multiplying and Dividing Powers
40. To divide fractions - invert the second one and multiply
Solving a System of Equations
Finding the midpoint
Dividing Fractions
Area of a Triangle
41. Domain: all possible values of x for a function range: all possible outputs of a function
Triangle Inequality Theorem
Area of a Circle
Raising Powers to Powers
Domain and Range of a Function
42. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Simplifying Square Roots
Prime Factorization
Evaluating an Expression
Average Rate
43. Multiply the exponents
Volume of a Cylinder
Raising Powers to Powers
Using the Average to Find the Sum
Evaluating an Expression
44. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Factor/Multiple
PEMDAS
Average Formula -
Reciprocal
45. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Identifying the Parts and the Whole
Length of an Arc
Factor/Multiple
Area of a Triangle
46. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Area of a Circle
Characteristics of a Rectangle
Solving a Quadratic Equation
Evaluating an Expression
47. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Adding/Subtracting Fractions
Multiples of 2 and 4
Remainders
Solving an Inequality
48. 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
Counting Consecutive Integers
Intersecting Lines
Exponential Growth
Area of a Circle
49. 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
Interior and Exterior Angles of a Triangle
Repeating Decimal
Domain and Range of a Function
Probability
50. 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
Adding/Subtracting Fractions
Area of a Sector
Solving an Inequality