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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. Part = Percent x Whole
Using the Average to Find the Sum
Percent Formula
Repeating Decimal
The 3-4-5 Triangle
2. 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
Finding the Original Whole
Area of a Triangle
Solving a Proportion
3. 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
Isosceles and Equilateral triangles
Percent Formula
The 5-12-13 Triangle
4. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Mixed Numbers and Improper Fractions
Interior Angles of a Polygon
Circumference of a Circle
Intersecting Lines
5. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Finding the Original Whole
Median and Mode
Using an Equation to Find an Intercept
Average of Evenly Spaced Numbers
6. Subtract the smallest from the largest and add 1
The 5-12-13 Triangle
Counting Consecutive Integers
Intersecting Lines
Length of an Arc
7. 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
Solving an Inequality
Using an Equation to Find an Intercept
Determining Absolute Value
Identifying the Parts and the Whole
8. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Solving a System of Equations
Similar Triangles
Percent Formula
Finding the Missing Number
9. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Adding and Subtraction Polynomials
Finding the Distance Between Two Points
Using the Average to Find the Sum
Evaluating an Expression
10. 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
Prime Factorization
The 3-4-5 Triangle
PEMDAS
Relative Primes
11. 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 Rate
Union of Sets
Counting the Possibilities
Characteristics of a Parallelogram
12. pr^2
Counting the Possibilities
Percent Formula
Area of a Circle
The 5-12-13 Triangle
13. Multiply the exponents
Counting the Possibilities
Mixed Numbers and Improper Fractions
Remainders
Raising Powers to Powers
14. 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
Isosceles and Equilateral triangles
Domain and Range of a Function
Finding the midpoint
15. 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
Average of Evenly Spaced Numbers
Volume of a Cylinder
Circumference of a Circle
Isosceles and Equilateral triangles
16. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Average Formula -
(Least) Common Multiple
Part-to-Part Ratios and Part-to-Whole Ratios
17. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Multiplying Fractions
Circumference of a Circle
Reducing Fractions
Mixed Numbers and Improper Fractions
18. Add the exponents and keep the same base
Negative Exponent and Rational Exponent
Parallel Lines and Transversals
Solving a System of Equations
Multiplying and Dividing Powers
19. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Function - Notation - and Evaulation
Union of Sets
(Least) Common Multiple
PEMDAS
20. 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
Pythagorean Theorem
Repeating Decimal
Adding/Subtracting Signed Numbers
Remainders
21. Factor out the perfect squares
Part-to-Part Ratios and Part-to-Whole Ratios
Surface Area of a Rectangular Solid
Simplifying Square Roots
Reciprocal
22. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Probability
Multiples of 2 and 4
Remainders
Intersecting Lines
23. The median is the value that falls in the middle of the set - the mode is the value that appears most often
(Least) Common Multiple
Multiples of 2 and 4
Median and Mode
Using Two Points to Find the Slope
24. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Isosceles and Equilateral triangles
Direct and Inverse Variation
Intersection of sets
Greatest Common Factor
25. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Percent Formula
Solving a System of Equations
Adding and Subtracting Roots
Multiplying Monomials
26. A square is a rectangle with four equal sides; Area of Square = side*side
Remainders
Counting the Possibilities
Adding/Subtracting Signed Numbers
Characteristics of a Square
27. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Mixed Numbers and Improper Fractions
Length of an Arc
The 3-4-5 Triangle
Adding/Subtracting Fractions
28. To find the reciprocal of a fraction switch the numerator and the denominator
Direct and Inverse Variation
Reciprocal
Reducing Fractions
Percent Formula
29. Combine equations in such a way that one of the variables cancel out
Remainders
Factor/Multiple
Using the Average to Find the Sum
Solving a System of Equations
30. 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
Characteristics of a Rectangle
Union of Sets
(Least) Common Multiple
Interior and Exterior Angles of a Triangle
31. 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
Volume of a Cylinder
Multiplying Fractions
Solving an Inequality
32. 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
Triangle Inequality Theorem
Counting the Possibilities
Negative Exponent and Rational Exponent
33. Sum=(Average) x (Number of Terms)
Volume of a Cylinder
The 5-12-13 Triangle
Function - Notation - and Evaulation
Using the Average to Find the Sum
34. 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
Prime Factorization
Similar Triangles
Interior and Exterior Angles of a Triangle
35. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Characteristics of a Parallelogram
Volume of a Rectangular Solid
Prime Factorization
Even/Odd
36. 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
Circumference of a Circle
Counting Consecutive Integers
PEMDAS
Part-to-Part Ratios and Part-to-Whole Ratios
37. 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
Adding/Subtracting Signed Numbers
Average Formula -
Simplifying Square Roots
38. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Probability
Dividing Fractions
Comparing Fractions
Tangency
39. 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
Multiplying and Dividing Roots
Percent Formula
Even/Odd
The 5-12-13 Triangle
40. For all right triangles: a^2+b^2=c^2
Solving an Inequality
Pythagorean Theorem
Isosceles and Equilateral triangles
Repeating Decimal
41. 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
Counting Consecutive Integers
Multiplying/Dividing Signed Numbers
Isosceles and Equilateral triangles
42. 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
Simplifying Square Roots
Finding the Missing Number
Multiplying Fractions
Exponential Growth
43. The smallest multiple (other than zero) that two or more numbers have in common.
(Least) Common Multiple
Greatest Common Factor
Finding the Distance Between Two Points
Length of an Arc
44. 1. Re-express them with common denominators 2. Convert them to decimals
Solving a Proportion
Finding the midpoint
Comparing Fractions
Negative Exponent and Rational Exponent
45. (average of the x coordinates - average of the y coordinates)
Percent Increase and Decrease
Solving a Proportion
Intersecting Lines
Finding the midpoint
46. 2pr
Multiples of 3 and 9
Using Two Points to Find the Slope
Circumference of a Circle
Counting the Possibilities
47. 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
Remainders
Repeating Decimal
Exponential Growth
Finding the Distance Between Two Points
48. 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
Percent Formula
Finding the Original Whole
Volume of a Cylinder
Probability
49. 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 Cylinder
Median and Mode
Rate
Area of a Triangle
50. To solve a proportion - cross multiply
Counting Consecutive Integers
Solving a Proportion
Combined Percent Increase and Decrease
Multiples of 2 and 4