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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. 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
Probability
Isosceles and Equilateral triangles
Rate
2. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Pythagorean Theorem
Adding and Subtracting monomials
Intersection of sets
3. 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
Finding the Missing Number
Adding and Subtraction Polynomials
Length of an Arc
4. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Finding the midpoint
Parallel Lines and Transversals
Function - Notation - and Evaulation
Similar Triangles
5. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Mixed Numbers and Improper Fractions
Dividing Fractions
Median and Mode
Raising Powers to Powers
6. 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.
Multiplying and Dividing Roots
Characteristics of a Parallelogram
Number Categories
Even/Odd
7. The largest factor that two or more numbers have in common.
Rate
PEMDAS
Mixed Numbers and Improper Fractions
Greatest Common Factor
8. Add the exponents and keep the same base
Multiplying and Dividing Powers
Pythagorean Theorem
The 3-4-5 Triangle
Negative Exponent and Rational Exponent
9. To solve a proportion - cross multiply
Reducing Fractions
Triangle Inequality Theorem
Solving a Proportion
The 5-12-13 Triangle
10. 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
Percent Increase and Decrease
Adding and Subtraction Polynomials
Finding the Original Whole
Part-to-Part Ratios and Part-to-Whole Ratios
11. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Domain and Range of a Function
Multiplying and Dividing Roots
Circumference of a Circle
Adding and Subtracting monomials
12. 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
Repeating Decimal
Area of a Sector
Average Formula -
Intersection of sets
13. 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
Area of a Triangle
Combined Percent Increase and Decrease
Adding and Subtracting monomials
Repeating Decimal
14. 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
Rate
The 5-12-13 Triangle
Solving an Inequality
Using an Equation to Find the Slope
15. Combine like terms
Reducing Fractions
Repeating Decimal
Parallel Lines and Transversals
Adding and Subtraction Polynomials
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
Number Categories
Percent Formula
Finding the midpoint
Exponential Growth
17. 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
Solving a Proportion
Rate
Interior and Exterior Angles of a Triangle
18. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Intersecting Lines
Raising Powers to Powers
Finding the midpoint
Using an Equation to Find the Slope
19. 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
Union of Sets
Direct and Inverse Variation
Intersecting Lines
Determining Absolute Value
20. 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
Probability
Dividing Fractions
Negative Exponent and Rational Exponent
Identifying the Parts and the Whole
21. Sum=(Average) x (Number of Terms)
Volume of a Cylinder
Volume of a Rectangular Solid
Counting Consecutive Integers
Using the Average to Find the Sum
22. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Reciprocal
Using an Equation to Find an Intercept
Factor/Multiple
Direct and Inverse Variation
23. 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
Intersection of sets
Using an Equation to Find an Intercept
Pythagorean Theorem
24. For all right triangles: a^2+b^2=c^2
Solving a System of Equations
Finding the Original Whole
Pythagorean Theorem
Evaluating an Expression
25. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Counting the Possibilities
Determining Absolute Value
Multiplying and Dividing Roots
Parallel Lines and Transversals
26. A square is a rectangle with four equal sides; Area of Square = side*side
Average Rate
Characteristics of a Square
Prime Factorization
Adding and Subtracting monomials
27. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Distance Between Two Points
Function - Notation - and Evaulation
Adding/Subtracting Fractions
Using an Equation to Find an Intercept
28. 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
Using an Equation to Find an Intercept
Characteristics of a Rectangle
Multiples of 2 and 4
29. The smallest multiple (other than zero) that two or more numbers have in common.
PEMDAS
Factor/Multiple
Determining Absolute Value
(Least) Common Multiple
30. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Adding/Subtracting Signed Numbers
Setting up a Ratio
Multiples of 3 and 9
Repeating Decimal
31. you can add/subtract when the part under the radical is the same
Interior and Exterior Angles of a Triangle
Length of an Arc
Adding and Subtracting monomials
Adding and Subtracting Roots
32. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Solving a System of Equations
Factor/Multiple
(Least) Common Multiple
33. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Area of a Circle
Multiples of 2 and 4
Tangency
Volume of a Cylinder
34. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Determining Absolute Value
Probability
PEMDAS
Using an Equation to Find the Slope
35. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Pythagorean Theorem
Characteristics of a Parallelogram
Combined Percent Increase and Decrease
36. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Percent Increase and Decrease
Raising Powers to Powers
PEMDAS
Tangency
37. 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
Determining Absolute Value
Volume of a Rectangular Solid
Area of a Circle
The 3-4-5 Triangle
38. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Average Rate
Setting up a Ratio
Area of a Circle
Interior Angles of a Polygon
39. 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
Percent Increase and Decrease
PEMDAS
Pythagorean Theorem
Counting the Possibilities
40. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
PEMDAS
Area of a Triangle
Reducing Fractions
Percent Increase and Decrease
41. The whole # left over after division
Multiplying Fractions
Remainders
Function - Notation - and Evaulation
Finding the Missing Number
42. 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
Area of a Sector
Function - Notation - and Evaulation
Factor/Multiple
Counting Consecutive Integers
43. 2pr
Using Two Points to Find the Slope
Circumference of a Circle
Multiplying Monomials
Multiplying and Dividing Roots
44. 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
(Least) Common Multiple
Even/Odd
Using an Equation to Find the Slope
Characteristics of a Square
45. 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
Volume of a Rectangular Solid
Characteristics of a Parallelogram
The 5-12-13 Triangle
Multiplying/Dividing Signed Numbers
46. (average of the x coordinates - average of the y coordinates)
Pythagorean Theorem
Finding the midpoint
Using the Average to Find the Sum
PEMDAS
47. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Number Categories
Interior and Exterior Angles of a Triangle
Length of an Arc
Intersecting Lines
48. 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
Intersecting Lines
Counting the Possibilities
Solving an Inequality
49. To find the reciprocal of a fraction switch the numerator and the denominator
Prime Factorization
Reciprocal
Comparing Fractions
Using an Equation to Find the Slope
50. Multiply the exponents
Area of a Triangle
Similar Triangles
Interior and Exterior Angles of a Triangle
Raising Powers to Powers