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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
.
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. 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
Characteristics of a Parallelogram
Circumference of a Circle
The 3-4-5 Triangle
Remainders
2. 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
Determining Absolute Value
Average Formula -
Area of a Circle
Isosceles and Equilateral triangles
3. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Greatest Common Factor
Adding and Subtracting monomials
Using an Equation to Find the Slope
Adding and Subtraction Polynomials
4. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Raising Powers to Powers
Remainders
Union of Sets
Greatest Common Factor
5. The whole # left over after division
Remainders
Reciprocal
Volume of a Rectangular Solid
Counting the Possibilities
6. 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
Adding/Subtracting Signed Numbers
Setting up a Ratio
Using an Equation to Find an Intercept
Solving an Inequality
7. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
PEMDAS
(Least) Common Multiple
Counting Consecutive Integers
8. Surface Area = 2lw + 2wh + 2lh
Surface Area of a Rectangular Solid
Rate
Function - Notation - and Evaulation
Prime Factorization
9. 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
Simplifying Square Roots
Adding and Subtracting monomials
Solving a Proportion
10. The largest factor that two or more numbers have in common.
PEMDAS
Circumference of a Circle
Greatest Common Factor
Evaluating an Expression
11. pr^2
Part-to-Part Ratios and Part-to-Whole Ratios
Determining Absolute Value
Area of a Circle
Percent Formula
12. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Number Categories
Parallel Lines and Transversals
Length of an Arc
Factor/Multiple
13. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Triangle Inequality Theorem
Intersecting Lines
Setting up a Ratio
Average Rate
14. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Average Rate
Solving a Quadratic Equation
Adding/Subtracting Fractions
Adding and Subtracting monomials
15. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Triangle Inequality Theorem
Interior Angles of a Polygon
Relative Primes
Length of an Arc
16. Combine like terms
Mixed Numbers and Improper Fractions
Adding and Subtraction Polynomials
Percent Formula
Prime Factorization
17. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
The 3-4-5 Triangle
Area of a Triangle
Intersection of sets
Union of Sets
18. 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
Multiplying/Dividing Signed Numbers
Negative Exponent and Rational Exponent
Determining Absolute Value
19. 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
Volume of a Rectangular Solid
Multiplying and Dividing Powers
Using an Equation to Find an Intercept
20. The smallest multiple (other than zero) that two or more numbers have in common.
Surface Area of a Rectangular Solid
Reciprocal
Number Categories
(Least) Common Multiple
21. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Simplifying Square Roots
Intersecting Lines
Average Rate
Adding and Subtracting monomials
22. 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
Interior and Exterior Angles of a Triangle
Average of Evenly Spaced Numbers
The 3-4-5 Triangle
Percent Increase and Decrease
23. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Area of a Sector
Area of a Circle
Parallel Lines and Transversals
Finding the Missing Number
24. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Exponential Growth
Median and Mode
Area of a Sector
25. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Finding the Missing Number
Area of a Sector
Factor/Multiple
26. 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
Factor/Multiple
Comparing Fractions
Intersection of sets
Repeating Decimal
27. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Setting up a Ratio
Greatest Common Factor
Average Formula -
Average Rate
28. 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
Multiples of 3 and 9
Function - Notation - and Evaulation
Probability
Adding/Subtracting Fractions
29. For all right triangles: a^2+b^2=c^2
Surface Area of a Rectangular Solid
Even/Odd
Number Categories
Pythagorean Theorem
30. 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.
Interior and Exterior Angles of a Triangle
Function - Notation - and Evaulation
Number Categories
Determining Absolute Value
31. 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
Finding the Distance Between Two Points
Counting the Possibilities
Using Two Points to Find the Slope
Identifying the Parts and the Whole
32. Domain: all possible values of x for a function range: all possible outputs of a function
Function - Notation - and Evaulation
Rate
Pythagorean Theorem
Domain and Range of a Function
33. 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
Multiplying Monomials
Identifying the Parts and the Whole
Relative Primes
Raising Powers to Powers
34. 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
Finding the midpoint
Negative Exponent and Rational Exponent
The 5-12-13 Triangle
Percent Formula
35. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Percent Formula
Determining Absolute Value
Even/Odd
(Least) Common Multiple
36. 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
Finding the midpoint
Rate
Identifying the Parts and the Whole
Interior Angles of a Polygon
37. 2pr
Circumference of a Circle
The 5-12-13 Triangle
Evaluating an Expression
Counting Consecutive Integers
38. To find the reciprocal of a fraction switch the numerator and the denominator
Prime Factorization
Finding the Distance Between Two Points
Domain and Range of a Function
Reciprocal
39. 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
Interior and Exterior Angles of a Triangle
Characteristics of a Parallelogram
(Least) Common Multiple
Dividing Fractions
40. 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
Volume of a Cylinder
Average of Evenly Spaced Numbers
Dividing Fractions
41. Factor out the perfect squares
Reducing Fractions
Simplifying Square Roots
Comparing Fractions
Average Rate
42. 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 a Proportion
Simplifying Square Roots
Characteristics of a Parallelogram
Identifying the Parts and the Whole
43. A square is a rectangle with four equal sides; Area of Square = side*side
Solving an Inequality
Intersecting Lines
Volume of a Rectangular Solid
Characteristics of a Square
44. 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
Multiplying and Dividing Roots
Solving a Proportion
Repeating Decimal
45. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Factor/Multiple
Determining Absolute Value
Adding/Subtracting Fractions
Even/Odd
46. 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
Percent Increase and Decrease
PEMDAS
Simplifying Square Roots
47. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Percent Increase and Decrease
Negative Exponent and Rational Exponent
Even/Odd
48. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Characteristics of a Parallelogram
Identifying the Parts and the Whole
Percent Increase and Decrease
49. 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
Area of a Triangle
Prime Factorization
Interior Angles of a Polygon
Even/Odd
50. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Characteristics of a Square
Average Formula -
Adding/Subtracting Signed Numbers