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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. 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
Reciprocal
Interior and Exterior Angles of a Triangle
Exponential Growth
Characteristics of a Rectangle
2. Combine equations in such a way that one of the variables cancel out
Intersecting Lines
Solving a System of Equations
Area of a Circle
Average of Evenly Spaced Numbers
3. 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
Characteristics of a Square
Adding/Subtracting Signed Numbers
Function - Notation - and Evaulation
4. Change in y/ change in x rise/run
Multiples of 2 and 4
Determining Absolute Value
Pythagorean Theorem
Using Two Points to Find the Slope
5. 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
Similar Triangles
Rate
Isosceles and Equilateral triangles
Mixed Numbers and Improper Fractions
6. 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
Triangle Inequality Theorem
Function - Notation - and Evaulation
Raising Powers to Powers
Multiplying/Dividing Signed Numbers
7. The largest factor that two or more numbers have in common.
(Least) Common Multiple
Relative Primes
Probability
Greatest Common Factor
8. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Domain and Range of a Function
Dividing Fractions
Probability
9. 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)
Area of a Sector
Using the Average to Find the Sum
Multiples of 3 and 9
Average of Evenly Spaced Numbers
10. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Determining Absolute Value
Percent Formula
Adding/Subtracting Fractions
Length of an Arc
11. 2pr
The 5-12-13 Triangle
Circumference of a Circle
Rate
Multiplying Fractions
12. Surface Area = 2lw + 2wh + 2lh
Multiplying Monomials
Adding/Subtracting Signed Numbers
Characteristics of a Square
Surface Area of a Rectangular Solid
13. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Volume of a Rectangular Solid
Prime Factorization
Finding the Distance Between Two Points
Reciprocal
14. 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
Simplifying Square Roots
Pythagorean Theorem
Even/Odd
15. Multiply the exponents
Intersecting Lines
Simplifying Square Roots
Raising Powers to Powers
Exponential Growth
16. 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
Even/Odd
Union of Sets
Exponential Growth
Probability
17. 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
Remainders
Isosceles and Equilateral triangles
Identifying the Parts and the Whole
18. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Intersection of sets
Mixed Numbers and Improper Fractions
Greatest Common Factor
Characteristics of a Rectangle
19. 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.
Probability
Number Categories
Setting up a Ratio
Reducing Fractions
20. 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
Adding and Subtracting monomials
Direct and Inverse Variation
Finding the midpoint
21. 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
Multiplying Monomials
Area of a Triangle
Mixed Numbers and Improper Fractions
Interior and Exterior Angles of a Triangle
22. 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
Circumference of a Circle
Multiplying and Dividing Powers
Solving an Inequality
The 5-12-13 Triangle
23. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Adding and Subtracting Roots
Multiplying and Dividing Roots
Volume of a Cylinder
24. 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
Using an Equation to Find the Slope
Exponential Growth
Interior and Exterior Angles of a Triangle
25. 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
Comparing Fractions
Area of a Sector
Counting Consecutive Integers
26. 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
Reducing Fractions
Combined Percent Increase and Decrease
The 5-12-13 Triangle
Greatest Common Factor
27. 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
Adding and Subtracting monomials
Interior Angles of a Polygon
Characteristics of a Parallelogram
Comparing Fractions
28. To multiply fractions - multiply the numerators and multiply the denominators
Reducing Fractions
Relative Primes
Multiplying Fractions
Union of Sets
29. Part = Percent x Whole
Percent Formula
(Least) Common Multiple
Multiplying/Dividing Signed Numbers
Finding the Missing Number
30. (average of the x coordinates - average of the y coordinates)
Union of Sets
Adding and Subtracting Roots
Pythagorean Theorem
Finding the midpoint
31. 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
The 3-4-5 Triangle
Solving a System of Equations
Evaluating an Expression
Part-to-Part Ratios and Part-to-Whole Ratios
32. The whole # left over after division
Reducing Fractions
Finding the midpoint
Remainders
Percent Increase and Decrease
33. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Combined Percent Increase and Decrease
Simplifying Square Roots
Adding and Subtracting monomials
Solving a Proportion
34. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Even/Odd
(Least) Common Multiple
Finding the Distance Between Two Points
Using Two Points to Find the Slope
35. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Multiplying Fractions
Prime Factorization
Using an Equation to Find the Slope
Intersection of sets
36. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Union of Sets
Triangle Inequality Theorem
Average Rate
Using an Equation to Find the Slope
37. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Solving an Inequality
Intersecting Lines
Characteristics of a Square
Finding the Distance Between Two Points
38. Volume of a Cylinder = pr^2h
Part-to-Part Ratios and Part-to-Whole Ratios
Percent Formula
Volume of a Cylinder
Negative Exponent and Rational Exponent
39. 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
Counting the Possibilities
PEMDAS
Average of Evenly Spaced Numbers
Union of Sets
40. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Multiplying and Dividing Powers
Intersection of sets
Adding/Subtracting Fractions
Finding the Distance Between Two Points
41. Add the exponents and keep the same base
Intersection of sets
Simplifying Square Roots
Finding the Distance Between Two Points
Multiplying and Dividing Powers
42. To find the reciprocal of a fraction switch the numerator and the denominator
Part-to-Part Ratios and Part-to-Whole Ratios
Number Categories
The 3-4-5 Triangle
Reciprocal
43. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Rate
Characteristics of a Square
Union of Sets
Identifying the Parts and the Whole
44. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Adding and Subtracting monomials
Direct and Inverse Variation
Parallel Lines and Transversals
Adding/Subtracting Fractions
45. 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
Average Formula -
Finding the Missing Number
Finding the Original Whole
Simplifying Square Roots
46. 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
Isosceles and Equilateral triangles
Using an Equation to Find an Intercept
Adding/Subtracting Fractions
Setting up a Ratio
47. 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
Using the Average to Find the Sum
The 5-12-13 Triangle
Triangle Inequality Theorem
Relative Primes
48. To solve a proportion - cross multiply
PEMDAS
Solving a Proportion
Counting the Possibilities
Pythagorean Theorem
49. The smallest multiple (other than zero) that two or more numbers have in common.
Solving a Proportion
Mixed Numbers and Improper Fractions
(Least) Common Multiple
Multiplying and Dividing Roots
50. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Solving a Proportion
Multiples of 3 and 9
Using the Average to Find the Sum
Counting the Possibilities