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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 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Multiples of 2 and 4
Exponential Growth
Multiples of 3 and 9
Multiplying Fractions
2. 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
Adding and Subtraction Polynomials
Interior and Exterior Angles of a Triangle
Solving an Inequality
Volume of a Rectangular Solid
3. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Circumference of a Circle
Percent Formula
Interior Angles of a Polygon
PEMDAS
4. 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
Multiplying/Dividing Signed Numbers
Number Categories
Raising Powers to Powers
Rate
5. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Finding the Distance Between Two Points
Solving a Proportion
Reducing Fractions
Relative Primes
6. 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 Fractions
Multiplying Fractions
Comparing Fractions
Adding/Subtracting Signed Numbers
7. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Similar Triangles
Negative Exponent and Rational Exponent
Area of a Circle
Simplifying Square Roots
8. 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
Using Two Points to Find the Slope
PEMDAS
Mixed Numbers and Improper Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
9. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Interior Angles of a Polygon
Exponential Growth
Part-to-Part Ratios and Part-to-Whole Ratios
10. 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
Finding the midpoint
Relative Primes
Triangle Inequality Theorem
Characteristics of a Parallelogram
11. Combine like terms
Remainders
Triangle Inequality Theorem
Adding and Subtraction Polynomials
Using an Equation to Find the Slope
12. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Multiples of 2 and 4
Area of a Triangle
Using an Equation to Find the Slope
Characteristics of a Square
13. you can add/subtract when the part under the radical is the same
Probability
Multiplying and Dividing Powers
Adding and Subtracting Roots
Comparing Fractions
14. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Comparing Fractions
The 5-12-13 Triangle
Simplifying Square Roots
Average Rate
15. 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
Finding the Distance Between Two Points
Area of a Circle
Repeating Decimal
Number Categories
16. 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)
Volume of a Rectangular Solid
Repeating Decimal
Length of an Arc
Exponential Growth
17. 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.
Intersection of sets
Number Categories
Setting up a Ratio
Solving an Inequality
18. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Rate
Using an Equation to Find the Slope
Intersection of sets
Multiplying Monomials
19. Probability= Favorable Outcomes/Total Possible Outcomes
Length of an Arc
Probability
Reducing Fractions
Average Rate
20. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Using the Average to Find the Sum
Identifying the Parts and the Whole
The 3-4-5 Triangle
Multiplying and Dividing Roots
21. 2pr
Circumference of a Circle
Characteristics of a Square
Counting Consecutive Integers
Volume of a Rectangular Solid
22. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Solving an Inequality
Counting Consecutive Integers
The 5-12-13 Triangle
23. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Volume of a Rectangular Solid
Interior and Exterior Angles of a Triangle
Finding the Distance Between Two Points
Multiples of 3 and 9
24. 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
Setting up a Ratio
Average of Evenly Spaced Numbers
Function - Notation - and Evaulation
Greatest Common Factor
25. 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
Setting up a Ratio
Solving a Quadratic Equation
Relative Primes
26. pr^2
Part-to-Part Ratios and Part-to-Whole Ratios
Area of a Circle
Parallel Lines and Transversals
Adding and Subtracting Roots
27. 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
Finding the Original Whole
Greatest Common Factor
Direct and Inverse Variation
Counting Consecutive Integers
28. 1. Re-express them with common denominators 2. Convert them to decimals
Relative Primes
Finding the Distance Between Two Points
Area of a Sector
Comparing Fractions
29. To multiply fractions - multiply the numerators and multiply the denominators
Adding/Subtracting Fractions
Solving a System of Equations
Dividing Fractions
Multiplying Fractions
30. 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
Characteristics of a Rectangle
Evaluating an Expression
Using an Equation to Find an Intercept
PEMDAS
31. The largest factor that two or more numbers have in common.
Greatest Common Factor
Area of a Triangle
Characteristics of a Rectangle
Adding/Subtracting Fractions
32. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
PEMDAS
Repeating Decimal
Using an Equation to Find an Intercept
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
Similar Triangles
Finding the midpoint
Tangency
Adding and Subtracting monomials
34. Factor out the perfect squares
Simplifying Square Roots
Rate
PEMDAS
Even/Odd
35. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Characteristics of a Square
Average of Evenly Spaced Numbers
Factor/Multiple
The 3-4-5 Triangle
36. 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
Identifying the Parts and the Whole
Percent Formula
Relative Primes
Evaluating an Expression
37. 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
Comparing Fractions
Parallel Lines and Transversals
Remainders
38. 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
Isosceles and Equilateral triangles
Exponential Growth
Reducing Fractions
Area of a Triangle
39. 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
Finding the Original Whole
Interior and Exterior Angles of a Triangle
Multiplying/Dividing Signed Numbers
Intersecting Lines
40. Combine equations in such a way that one of the variables cancel out
Number Categories
Triangle Inequality Theorem
Probability
Solving a System of Equations
41. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Average Rate
Multiples of 2 and 4
PEMDAS
Percent Increase and Decrease
42. Surface Area = 2lw + 2wh + 2lh
Union of Sets
Surface Area of a Rectangular Solid
Relative Primes
Setting up a Ratio
43. The whole # left over after division
Number Categories
Parallel Lines and Transversals
Remainders
Reducing Fractions
44. A square is a rectangle with four equal sides; Area of Square = side*side
Tangency
Isosceles and Equilateral triangles
Characteristics of a Square
Setting up a Ratio
45. 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
Parallel Lines and Transversals
Isosceles and Equilateral triangles
Comparing Fractions
46. To find the reciprocal of a fraction switch the numerator and the denominator
Percent Formula
Adding and Subtraction Polynomials
Surface Area of a Rectangular Solid
Reciprocal
47. The smallest multiple (other than zero) that two or more numbers have in common.
Using Two Points to Find the Slope
Tangency
PEMDAS
(Least) Common Multiple
48. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average Formula -
Reciprocal
Volume of a Rectangular Solid
Similar Triangles
49. 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
Identifying the Parts and the Whole
Setting up a Ratio
Negative Exponent and Rational Exponent
Solving a System of Equations
50. To divide fractions - invert the second one and multiply
Dividing Fractions
Mixed Numbers and Improper Fractions
Multiples of 2 and 4
Prime Factorization