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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
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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. 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
Parallel Lines and Transversals
Negative Exponent and Rational Exponent
Area of a Circle
2. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Comparing Fractions
Mixed Numbers and Improper Fractions
Adding and Subtraction Polynomials
3. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Characteristics of a Parallelogram
Determining Absolute Value
Adding and Subtraction Polynomials
Isosceles and Equilateral triangles
4. 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 and Subtraction Polynomials
Interior Angles of a Polygon
Exponential Growth
Area of a Triangle
5. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Interior Angles of a Polygon
Volume of a Rectangular Solid
Direct and Inverse Variation
Area of a Circle
6. Change in y/ change in x rise/run
Domain and Range of a Function
Determining Absolute Value
Using Two Points to Find the Slope
PEMDAS
7. 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
Counting Consecutive Integers
Area of a Triangle
Adding/Subtracting Signed Numbers
Solving a System of Equations
8. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Direct and Inverse Variation
Interior Angles of a Polygon
PEMDAS
9. 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
Tangency
Domain and Range of a Function
Function - Notation - and Evaulation
Average Formula -
10. The largest factor that two or more numbers have in common.
Greatest Common Factor
Reciprocal
Characteristics of a Square
Adding/Subtracting Fractions
11. 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
Finding the Original Whole
Characteristics of a Parallelogram
Intersection of sets
Raising Powers to Powers
12. 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
Intersecting Lines
Part-to-Part Ratios and Part-to-Whole Ratios
Characteristics of a Parallelogram
The 3-4-5 Triangle
13. To multiply fractions - multiply the numerators and multiply the denominators
Similar Triangles
Using an Equation to Find an Intercept
Multiplying Fractions
Circumference of a Circle
14. pr^2
Identifying the Parts and the Whole
Tangency
Area of a Circle
Finding the midpoint
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
Average Rate
Combined Percent Increase and Decrease
Length of an Arc
Percent Increase and Decrease
16. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Exponential Growth
The 3-4-5 Triangle
Counting the Possibilities
17. 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
Area of a Sector
Direct and Inverse Variation
Characteristics of a Square
Percent Increase and Decrease
18. 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.
Number Categories
Determining Absolute Value
Using the Average to Find the Sum
Even/Odd
19. Domain: all possible values of x for a function range: all possible outputs of a function
Solving a Quadratic Equation
Domain and Range of a Function
Interior and Exterior Angles of a Triangle
Volume of a Rectangular Solid
20. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Isosceles and Equilateral triangles
Characteristics of a Parallelogram
Evaluating an Expression
PEMDAS
21. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
(Least) Common Multiple
Using an Equation to Find the Slope
Multiplying Monomials
Characteristics of a Parallelogram
22. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Parallel Lines and Transversals
Setting up a Ratio
Comparing Fractions
Interior and Exterior Angles of a Triangle
23. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Median and Mode
Solving a System of Equations
Adding and Subtraction Polynomials
Negative Exponent and Rational Exponent
24. Part = Percent x Whole
Tangency
Adding and Subtraction Polynomials
Solving a Quadratic Equation
Percent Formula
25. To find the reciprocal of a fraction switch the numerator and the denominator
Combined Percent Increase and Decrease
Adding/Subtracting Fractions
Multiplying Fractions
Reciprocal
26. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Solving a Quadratic Equation
Using an Equation to Find the Slope
Using Two Points to Find the Slope
Percent Increase and Decrease
27. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Similar Triangles
Intersection of sets
Evaluating an Expression
Repeating Decimal
28. 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)
Domain and Range of a Function
Remainders
Combined Percent Increase and Decrease
Area of a Sector
29. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Intersecting Lines
Remainders
Mixed Numbers and Improper Fractions
30. 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
Volume of a Rectangular Solid
Rate
Average Rate
Reciprocal
31. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Median and Mode
Union of Sets
Remainders
Reciprocal
32. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Characteristics of a Rectangle
Multiples of 3 and 9
Volume of a Cylinder
Multiplying and Dividing Roots
33. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Even/Odd
Multiplying and Dividing Powers
Solving a Quadratic Equation
34. Subtract the smallest from the largest and add 1
Finding the midpoint
Finding the Missing Number
Counting Consecutive Integers
PEMDAS
35. The whole # left over after division
Reducing Fractions
Reciprocal
Remainders
Solving a System of Equations
36. 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
Using Two Points to Find the Slope
Multiplying Fractions
Negative Exponent and Rational Exponent
Repeating Decimal
37. Combine equations in such a way that one of the variables cancel out
Counting the Possibilities
(Least) Common Multiple
Solving a System of Equations
Characteristics of a Parallelogram
38. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Characteristics of a Parallelogram
Volume of a Cylinder
Multiplying and Dividing Roots
Length of an Arc
39. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average Formula -
Volume of a Cylinder
Finding the Distance Between Two Points
Reducing Fractions
40. 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
Reciprocal
Dividing Fractions
Domain and Range of a Function
Part-to-Part Ratios and Part-to-Whole Ratios
41. you can add/subtract when the part under the radical is the same
Pythagorean Theorem
Using an Equation to Find the Slope
Adding and Subtracting Roots
Percent Increase and Decrease
42. 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
Counting the Possibilities
Finding the midpoint
Using an Equation to Find the Slope
Solving an Inequality
43. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Relative Primes
Finding the midpoint
Interior Angles of a Polygon
Counting the Possibilities
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)
Tangency
Multiplying and Dividing Powers
Mixed Numbers and Improper Fractions
Length of an Arc
45. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Percent Increase and Decrease
Using Two Points to Find the Slope
Direct and Inverse Variation
Factor/Multiple
46. 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
Reducing Fractions
Using Two Points to Find the Slope
Average of Evenly Spaced Numbers
47. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Using the Average to Find the Sum
Average of Evenly Spaced Numbers
Intersecting Lines
Similar Triangles
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
Dividing Fractions
Multiplying Monomials
Exponential Growth
Characteristics of a Rectangle
49. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Similar Triangles
Determining Absolute Value
Area of a Triangle
Reducing Fractions
50. 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
Mixed Numbers and Improper Fractions
Raising Powers to Powers
Remainders
Solving a Quadratic Equation