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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
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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. To solve a proportion - cross multiply
Solving a Proportion
Counting Consecutive Integers
Multiplying/Dividing Signed Numbers
Multiplying Fractions
2. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Length of an Arc
Area of a Triangle
Solving a Proportion
3. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Probability
Characteristics of a Parallelogram
Determining Absolute Value
Multiplying and Dividing Powers
4. Combine equations in such a way that one of the variables cancel out
Solving an Inequality
Solving a System of Equations
Solving a Proportion
Direct and Inverse Variation
5. 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 monomials
Mixed Numbers and Improper Fractions
Multiplying Fractions
The 3-4-5 Triangle
6. The largest factor that two or more numbers have in common.
Interior and Exterior Angles of a Triangle
Average of Evenly Spaced Numbers
Greatest Common Factor
Multiplying and Dividing Powers
7. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Intersection of sets
Counting Consecutive Integers
Adding/Subtracting Signed Numbers
Solving a System of Equations
8. 1. Re-express them with common denominators 2. Convert them to decimals
Counting the Possibilities
Parallel Lines and Transversals
Isosceles and Equilateral triangles
Comparing Fractions
9. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Prime Factorization
Circumference of a Circle
Characteristics of a Square
Multiplying Monomials
10. 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
Rate
Greatest Common Factor
Comparing Fractions
11. 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
Multiplying Monomials
Repeating Decimal
Even/Odd
Average of Evenly Spaced Numbers
12. 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
Counting Consecutive Integers
Raising Powers to Powers
13. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Median and Mode
Percent Formula
Using Two Points to Find the Slope
Similar Triangles
14. you can add/subtract when the part under the radical is the same
Adding and Subtracting Roots
Raising Powers to Powers
Finding the Missing Number
Greatest Common Factor
15. 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
Similar Triangles
Finding the Missing Number
Reciprocal
Tangency
16. 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
Rate
Median and Mode
Triangle Inequality Theorem
Adding/Subtracting Signed Numbers
17. The whole # left over after division
Interior Angles of a Polygon
Adding/Subtracting Fractions
Percent Formula
Remainders
18. 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
Multiplying and Dividing Roots
Solving a Proportion
Counting the Possibilities
19. 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
Using the Average to Find the Sum
Multiplying Monomials
Repeating Decimal
Prime Factorization
20. Probability= Favorable Outcomes/Total Possible Outcomes
Probability
Adding/Subtracting Signed Numbers
Length of an Arc
Solving a System of Equations
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
Using an Equation to Find the Slope
Direct and Inverse Variation
Interior Angles of a Polygon
Percent Increase and Decrease
22. 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
The 5-12-13 Triangle
Negative Exponent and Rational Exponent
Exponential Growth
Adding/Subtracting Fractions
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
Multiples of 2 and 4
Using an Equation to Find an Intercept
Characteristics of a Parallelogram
Intersecting Lines
24. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Probability
Interior Angles of a Polygon
Adding and Subtraction Polynomials
Greatest Common Factor
25. 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
Isosceles and Equilateral triangles
Reducing Fractions
Area of a Circle
26. 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
Average Formula -
Volume of a Rectangular Solid
Direct and Inverse Variation
(Least) Common Multiple
27. Volume of a Cylinder = pr^2h
Solving a Quadratic Equation
Volume of a Cylinder
Greatest Common Factor
Counting the Possibilities
28. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average Formula -
Identifying the Parts and the Whole
Comparing Fractions
Factor/Multiple
29. Domain: all possible values of x for a function range: all possible outputs of a function
Union of Sets
Probability
Domain and Range of a Function
Finding the Missing Number
30. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Multiplying Monomials
Triangle Inequality Theorem
Adding/Subtracting Fractions
31. 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)
Using the Average to Find the Sum
Median and Mode
Area of a Sector
Union of Sets
32. Combine like terms
Part-to-Part Ratios and Part-to-Whole Ratios
The 3-4-5 Triangle
Adding and Subtraction Polynomials
(Least) Common Multiple
33. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Intersection of sets
Solving a Quadratic Equation
Parallel Lines and Transversals
Tangency
34. 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
Identifying the Parts and the Whole
The 3-4-5 Triangle
Probability
Adding and Subtracting Roots
35. (average of the x coordinates - average of the y coordinates)
(Least) Common Multiple
Remainders
Multiplying Fractions
Finding the midpoint
36. # 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
Dividing Fractions
Characteristics of a Rectangle
Surface Area of a Rectangular Solid
37. For all right triangles: a^2+b^2=c^2
Intersection of sets
Volume of a Rectangular Solid
Similar Triangles
Pythagorean Theorem
38. 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
Evaluating an Expression
Part-to-Part Ratios and Part-to-Whole Ratios
Finding the midpoint
Characteristics of a Square
39. Part = Percent x Whole
Parallel Lines and Transversals
Volume of a Rectangular Solid
Percent Formula
Reducing Fractions
40. To multiply fractions - multiply the numerators and multiply the denominators
(Least) Common Multiple
The 3-4-5 Triangle
Union of Sets
Multiplying Fractions
41. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Finding the Distance Between Two Points
Similar Triangles
Finding the Missing Number
Solving an Inequality
42. 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
Solving a Proportion
Solving an Inequality
Parallel Lines and Transversals
43. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Direct and Inverse Variation
Multiples of 2 and 4
Isosceles and Equilateral triangles
Adding and Subtracting Roots
44. 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
Mixed Numbers and Improper Fractions
Solving a System of Equations
Finding the Original Whole
Adding/Subtracting Fractions
45. To find the reciprocal of a fraction switch the numerator and the denominator
Multiples of 3 and 9
Evaluating an Expression
Area of a Triangle
Reciprocal
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
Relative Primes
Finding the Missing Number
Surface Area of a Rectangular Solid
Exponential Growth
47. 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)
Counting Consecutive Integers
Average Rate
Length of an Arc
Characteristics of a Parallelogram
48. Add the exponents and keep the same base
Repeating Decimal
Mixed Numbers and Improper Fractions
Average of Evenly Spaced Numbers
Multiplying and Dividing Powers
49. 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
The 5-12-13 Triangle
Interior and Exterior Angles of a Triangle
Finding the midpoint
Percent Formula
50. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Function - Notation - and Evaulation
Adding and Subtracting Roots
Parallel Lines and Transversals