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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. 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)
Adding and Subtracting Roots
Characteristics of a Rectangle
Area of a Triangle
Length of an Arc
2. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Surface Area of a Rectangular Solid
Isosceles and Equilateral triangles
Function - Notation - and Evaulation
3. To multiply fractions - multiply the numerators and multiply the denominators
Finding the midpoint
Counting the Possibilities
Multiplying Fractions
Percent Formula
4. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Characteristics of a Square
Multiples of 3 and 9
Using the Average to Find the Sum
5. 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
Using the Average to Find the Sum
(Least) Common Multiple
Finding the Original Whole
Interior and Exterior Angles of a Triangle
6. 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
Area of a Triangle
The 5-12-13 Triangle
Tangency
Percent Increase and Decrease
7. To divide fractions - invert the second one and multiply
Evaluating an Expression
Exponential Growth
Dividing Fractions
Adding and Subtracting Roots
8. To multiply or divide integers - firstly ignore the sign and compute the problem - given 2 negatives make a positive - 2 positives make a positive - and one negative - and one positive make a negative attach the correct sign
Part-to-Part Ratios and Part-to-Whole Ratios
Multiplying/Dividing Signed Numbers
Relative Primes
Circumference of a Circle
9. A square is a rectangle with four equal sides; Area of Square = side*side
Finding the Missing Number
Multiplying Monomials
Characteristics of a Square
Intersection of sets
10. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Intersecting Lines
Multiplying Monomials
Percent Increase and Decrease
Surface Area of a Rectangular Solid
11. 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
Union of Sets
Determining Absolute Value
Interior and Exterior Angles of a Triangle
Multiplying/Dividing Signed Numbers
12. 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
Mixed Numbers and Improper Fractions
Area of a Triangle
Multiplying and Dividing Powers
Using the Average to Find the Sum
13. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Using an Equation to Find the Slope
Remainders
Solving a System of Equations
Average Formula -
14. Sum=(Average) x (Number of Terms)
Intersection of sets
Using the Average to Find the Sum
Adding/Subtracting Signed Numbers
Exponential Growth
15. 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
Domain and Range of a Function
Median and Mode
Isosceles and Equilateral triangles
Using an Equation to Find an Intercept
16. pr^2
Intersecting Lines
Mixed Numbers and Improper Fractions
Simplifying Square Roots
Area of a Circle
17. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Circumference of a Circle
Solving a Quadratic Equation
Remainders
18. Surface Area = 2lw + 2wh + 2lh
Domain and Range of a Function
Surface Area of a Rectangular Solid
Adding and Subtracting monomials
Solving an Inequality
19. 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
Finding the midpoint
Identifying the Parts and the Whole
Adding and Subtracting Roots
Probability
20. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Intersecting Lines
Direct and Inverse Variation
Percent Increase and Decrease
Finding the Distance Between Two Points
21. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Factor/Multiple
Using an Equation to Find the Slope
Function - Notation - and Evaulation
Multiplying Monomials
22. 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
Multiples of 2 and 4
Mixed Numbers and Improper Fractions
Adding/Subtracting Signed Numbers
Intersecting Lines
23. 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
Adding and Subtracting Roots
Mixed Numbers and Improper Fractions
Tangency
Area of a Triangle
24. Multiply the exponents
Counting Consecutive Integers
Counting the Possibilities
Raising Powers to Powers
Similar Triangles
25. 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
Remainders
Finding the Missing Number
Adding and Subtraction Polynomials
Exponential Growth
26. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Median and Mode
Prime Factorization
Length of an Arc
Counting Consecutive Integers
27. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Parallel Lines and Transversals
Tangency
Length of an Arc
Using an Equation to Find an Intercept
28. 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
Remainders
Multiplying and Dividing Powers
Using an Equation to Find an Intercept
Using the Average to Find the Sum
29. 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.
Number Categories
Adding and Subtracting monomials
Solving a Quadratic Equation
Average of Evenly Spaced Numbers
30. 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
Determining Absolute Value
Average Formula -
Evaluating an Expression
31. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Solving a Proportion
(Least) Common Multiple
Circumference of a Circle
Average of Evenly Spaced Numbers
32. 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
Pythagorean Theorem
Adding and Subtracting monomials
Multiples of 3 and 9
Counting the Possibilities
33. The whole # left over after division
Remainders
Parallel Lines and Transversals
Using an Equation to Find the Slope
Relative Primes
34. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Determining Absolute Value
Average Rate
Rate
Volume of a Rectangular Solid
35. 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
The 3-4-5 Triangle
Union of Sets
Average of Evenly Spaced Numbers
36. 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
Adding and Subtracting Roots
Interior and Exterior Angles of a Triangle
Pythagorean Theorem
Part-to-Part Ratios and Part-to-Whole Ratios
37. 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
Median and Mode
Even/Odd
Using an Equation to Find the Slope
38. Volume of a Cylinder = pr^2h
Simplifying Square Roots
Raising Powers to Powers
Volume of a Cylinder
Relative Primes
39. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Using an Equation to Find an Intercept
Interior Angles of a Polygon
Area of a Triangle
Average Formula -
40. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Solving a System of Equations
Intersecting Lines
Multiplying Fractions
Evaluating an Expression
41. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Counting Consecutive Integers
Isosceles and Equilateral triangles
Domain and Range of a Function
Setting up a Ratio
42. The largest factor that two or more numbers have in common.
Solving a Proportion
Tangency
Characteristics of a Rectangle
Greatest Common Factor
43. Domain: all possible values of x for a function range: all possible outputs of a function
Counting Consecutive Integers
Reducing Fractions
Adding/Subtracting Signed Numbers
Domain and Range of a Function
44. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Circumference of a Circle
Tangency
(Least) Common Multiple
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
Combined Percent Increase and Decrease
Using an Equation to Find an Intercept
Even/Odd
Union of Sets
46. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Counting Consecutive Integers
Determining Absolute Value
Comparing Fractions
Prime Factorization
47. 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
Solving a Proportion
Using an Equation to Find an Intercept
Number Categories
48. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Negative Exponent and Rational Exponent
Isosceles and Equilateral triangles
Median and Mode
Intersection of sets
49. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Adding/Subtracting Fractions
Area of a Triangle
Pythagorean Theorem
Adding and Subtracting monomials
50. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Median and Mode
Solving a Quadratic Equation
Multiplying/Dividing Signed Numbers