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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. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Multiples of 2 and 4
Multiplying and Dividing Roots
Average Formula -
Area of a Circle
2. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Percent Increase and Decrease
Number Categories
Interior and Exterior Angles of a Triangle
3. To solve a proportion - cross multiply
Adding and Subtraction Polynomials
Pythagorean Theorem
Average Rate
Solving a Proportion
4. 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
Tangency
Finding the midpoint
Solving a Proportion
5. 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
Finding the Original Whole
Counting Consecutive Integers
Mixed Numbers and Improper Fractions
6. 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
Intersecting Lines
Multiplying Fractions
Rate
Area of a Triangle
7. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Even/Odd
Finding the Original Whole
Characteristics of a Rectangle
Average of Evenly Spaced Numbers
8. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Average Rate
Circumference of a Circle
Multiplying and Dividing Powers
Mixed Numbers and Improper Fractions
9. 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
Determining Absolute Value
Pythagorean Theorem
Mixed Numbers and Improper Fractions
Repeating Decimal
10. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Distance Between Two Points
Finding the Missing Number
Solving a Proportion
Factor/Multiple
11. 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
Similar Triangles
Multiplying and Dividing Roots
The 3-4-5 Triangle
(Least) Common Multiple
12. 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
Adding/Subtracting Signed Numbers
Volume of a Rectangular Solid
Intersection of sets
Determining Absolute Value
13. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Area of a Sector
Average of Evenly Spaced Numbers
Solving a System of Equations
Adding and Subtracting monomials
14. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Greatest Common Factor
Simplifying Square Roots
Using the Average to Find the Sum
15. 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
Volume of a Cylinder
Average Rate
Solving an Inequality
Factor/Multiple
16. 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
Finding the Missing Number
Isosceles and Equilateral triangles
Average Rate
(Least) Common Multiple
17. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Median and Mode
Using Two Points to Find the Slope
Adding and Subtracting Roots
Setting up a Ratio
18. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Prime Factorization
Union of Sets
Average of Evenly Spaced Numbers
Multiplying and Dividing Roots
19. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Domain and Range of a Function
Length of an Arc
Intersecting Lines
Using an Equation to Find the Slope
20. Combine like terms
Exponential Growth
Domain and Range of a Function
Combined Percent Increase and Decrease
Adding and Subtraction Polynomials
21. Surface Area = 2lw + 2wh + 2lh
Solving a Proportion
Even/Odd
Surface Area of a Rectangular Solid
Multiplying Fractions
22. The whole # left over after division
Negative Exponent and Rational Exponent
Remainders
Multiples of 3 and 9
Using Two Points to Find the Slope
23. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Negative Exponent and Rational Exponent
Using an Equation to Find the Slope
Multiples of 3 and 9
Average Formula -
24. 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 Monomials
Function - Notation - and Evaulation
Finding the Original Whole
Using the Average to Find the Sum
25. 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
Using Two Points to Find the Slope
Adding and Subtraction Polynomials
Volume of a Cylinder
Percent Increase and Decrease
26. Add the exponents and keep the same base
Repeating Decimal
Prime Factorization
Multiplying and Dividing Powers
Circumference of a Circle
27. 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
Parallel Lines and Transversals
Interior and Exterior Angles of a Triangle
Comparing Fractions
Prime Factorization
28. 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
Determining Absolute Value
Surface Area of a Rectangular Solid
Even/Odd
29. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Mixed Numbers and Improper Fractions
Volume of a Cylinder
Triangle Inequality Theorem
30. Domain: all possible values of x for a function range: all possible outputs of a function
Reciprocal
Multiples of 2 and 4
Adding/Subtracting Fractions
Domain and Range of a Function
31. Part = Percent x Whole
Probability
Percent Formula
Evaluating an Expression
Average of Evenly Spaced Numbers
32. 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
The 5-12-13 Triangle
Mixed Numbers and Improper Fractions
Using Two Points to Find the Slope
Adding and Subtracting Roots
33. To divide fractions - invert the second one and multiply
Union of Sets
Multiplying Monomials
Identifying the Parts and the Whole
Dividing Fractions
34. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Identifying the Parts and the Whole
Relative Primes
Union of Sets
Area of a Triangle
35. pr^2
Domain and Range of a Function
Area of a Circle
Adding and Subtracting Roots
(Least) Common Multiple
36. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Using Two Points to Find the Slope
Finding the Original Whole
Solving a System of Equations
Median and Mode
37. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Volume of a Rectangular Solid
Even/Odd
Counting Consecutive Integers
38. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Repeating Decimal
Finding the Missing Number
Even/Odd
Reducing Fractions
39. 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
Characteristics of a Rectangle
Simplifying Square Roots
Negative Exponent and Rational Exponent
Using the Average to Find the Sum
40. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Evaluating an Expression
Factor/Multiple
Circumference of a Circle
Multiplying Fractions
41. 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
Intersection of sets
Adding and Subtracting Roots
Similar Triangles
42. 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
Direct and Inverse Variation
Factor/Multiple
The 5-12-13 Triangle
Percent Increase and Decrease
43. 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
Even/Odd
Using an Equation to Find an Intercept
Average Formula -
The 3-4-5 Triangle
44. 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
Comparing Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
Multiples of 2 and 4
PEMDAS
45. 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
Finding the midpoint
Even/Odd
Combined Percent Increase and Decrease
Area of a Sector
46. 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
Pythagorean Theorem
Direct and Inverse Variation
Using the Average to Find the Sum
Exponential Growth
47. Change in y/ change in x rise/run
Adding/Subtracting Signed Numbers
Median and Mode
Percent Increase and Decrease
Using Two Points to Find the Slope
48. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Adding/Subtracting Signed Numbers
Interior Angles of a Polygon
Percent Formula
Multiples of 2 and 4
49. 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
Dividing Fractions
Multiplying Monomials
Interior Angles of a Polygon
Identifying the Parts and the Whole
50. 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)
Number Categories
Length of an Arc
Evaluating an Expression
Identifying the Parts and the Whole