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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. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Distance Between Two Points
Solving an Inequality
Volume of a Cylinder
Comparing Fractions
2. 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
Multiplying Monomials
Reducing Fractions
Volume of a Cylinder
Combined Percent Increase and Decrease
3. Part = Percent x Whole
PEMDAS
Area of a Circle
Length of an Arc
Percent Formula
4. 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
Triangle Inequality Theorem
Part-to-Part Ratios and Part-to-Whole Ratios
Characteristics of a Square
5. 1. Re-express them with common denominators 2. Convert them to decimals
Intersecting Lines
Comparing Fractions
Union of Sets
Setting up a Ratio
6. 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
Multiplying and Dividing Powers
Finding the Original Whole
Percent Formula
Characteristics of a Square
7. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Multiplying and Dividing Powers
Intersecting Lines
Using an Equation to Find the Slope
Function - Notation - and Evaulation
8. 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
Using an Equation to Find the Slope
Direct and Inverse Variation
Interior and Exterior Angles of a Triangle
Reciprocal
9. 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
Characteristics of a Parallelogram
Characteristics of a Square
Average Formula -
Counting Consecutive Integers
10. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
PEMDAS
Even/Odd
Setting up a Ratio
Using an Equation to Find the Slope
11. 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
Area of a Sector
Isosceles and Equilateral triangles
The 5-12-13 Triangle
Adding and Subtracting Roots
12. 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
Interior and Exterior Angles of a Triangle
Relative Primes
Solving an Inequality
Factor/Multiple
13. 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
Repeating Decimal
Average Rate
Parallel Lines and Transversals
Multiples of 2 and 4
14. pr^2
Characteristics of a Square
Solving a Quadratic Equation
Area of a Circle
Using an Equation to Find an Intercept
15. 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.
Finding the Missing Number
Characteristics of a Rectangle
Adding and Subtracting monomials
Number Categories
16. 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
The 3-4-5 Triangle
Direct and Inverse Variation
Multiples of 2 and 4
17. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Reducing Fractions
Counting Consecutive Integers
Determining Absolute Value
Similar Triangles
18. 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
Characteristics of a Rectangle
Using an Equation to Find the Slope
Direct and Inverse Variation
Intersecting Lines
19. 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
Percent Formula
Triangle Inequality Theorem
Volume of a Rectangular Solid
Identifying the Parts and the Whole
20. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying and Dividing Roots
Average Rate
Function - Notation - and Evaulation
Multiplying Fractions
21. To divide fractions - invert the second one and multiply
Domain and Range of a Function
Characteristics of a Rectangle
Dividing Fractions
Intersecting Lines
22. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Isosceles and Equilateral triangles
The 3-4-5 Triangle
Evaluating an Expression
Percent Increase and Decrease
23. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Intersecting Lines
Factor/Multiple
Finding the Original Whole
Circumference of a Circle
24. The whole # left over after division
Simplifying Square Roots
Solving an Inequality
Remainders
Average Rate
25. Combine like terms
Using the Average to Find the Sum
Multiplying Fractions
Intersecting Lines
Adding and Subtraction Polynomials
26. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Multiplying and Dividing Roots
The 3-4-5 Triangle
Solving an Inequality
Interior and Exterior Angles of a Triangle
27. For all right triangles: a^2+b^2=c^2
Median and Mode
Multiples of 3 and 9
Finding the midpoint
Pythagorean Theorem
28. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Finding the Missing Number
Determining Absolute Value
Length of an Arc
29. A square is a rectangle with four equal sides; Area of Square = side*side
Finding the midpoint
Characteristics of a Square
Length of an Arc
Reducing Fractions
30. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Multiplying and Dividing Powers
Using Two Points to Find the Slope
Similar Triangles
Domain and Range of a Function
31. Surface Area = 2lw + 2wh + 2lh
Prime Factorization
Adding/Subtracting Signed Numbers
Solving an Inequality
Surface Area of a Rectangular Solid
32. To find the reciprocal of a fraction switch the numerator and the denominator
Area of a Sector
Finding the midpoint
Reciprocal
Even/Odd
33. 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
Volume of a Rectangular Solid
Determining Absolute Value
Adding/Subtracting Signed Numbers
Dividing Fractions
34. 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
Percent Increase and Decrease
Parallel Lines and Transversals
PEMDAS
Function - Notation - and Evaulation
35. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Average of Evenly Spaced Numbers
Relative Primes
Factor/Multiple
Length of an Arc
36. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Intersecting Lines
Characteristics of a Rectangle
Tangency
Factor/Multiple
37. Combine equations in such a way that one of the variables cancel out
PEMDAS
Multiples of 2 and 4
Solving a System of Equations
The 3-4-5 Triangle
38. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Similar Triangles
Multiples of 2 and 4
Repeating Decimal
Using an Equation to Find the Slope
39. Factor out the perfect squares
Part-to-Part Ratios and Part-to-Whole Ratios
Simplifying Square Roots
Adding and Subtracting Roots
Characteristics of a Rectangle
40. Change in y/ change in x rise/run
Multiplying Fractions
Domain and Range of a Function
Even/Odd
Using Two Points to Find the Slope
41. 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
Percent Increase and Decrease
Adding and Subtraction Polynomials
Solving an Inequality
Multiples of 3 and 9
42. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Negative Exponent and Rational Exponent
Intersecting Lines
Adding and Subtracting monomials
43. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Multiples of 2 and 4
Mixed Numbers and Improper Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
44. Add the exponents and keep the same base
Using an Equation to Find an Intercept
Exponential Growth
Multiplying and Dividing Powers
Raising Powers to Powers
45. 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
Counting the Possibilities
Domain and Range of a Function
Finding the Missing Number
Average Formula -
46. 2pr
Finding the Missing Number
Circumference of a Circle
Volume of a Rectangular Solid
Counting the Possibilities
47. 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)
Length of an Arc
Using Two Points to Find the Slope
Characteristics of a Square
Percent Increase and Decrease
48. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Using Two Points to Find the Slope
Median and Mode
Simplifying Square Roots
Union of Sets
49. Sum=(Average) x (Number of Terms)
Area of a Triangle
Combined Percent Increase and Decrease
Adding and Subtracting Roots
Using the Average to Find the Sum
50. 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
Number Categories
Part-to-Part Ratios and Part-to-Whole Ratios
Negative Exponent and Rational Exponent
Finding the Missing Number