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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
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. 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
Solving a Quadratic Equation
Triangle Inequality Theorem
Relative Primes
2. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Median and Mode
Finding the Original Whole
Evaluating an Expression
Triangle Inequality Theorem
3. Surface Area = 2lw + 2wh + 2lh
Adding and Subtracting Roots
Counting Consecutive Integers
Using Two Points to Find the Slope
Surface Area of a Rectangular Solid
4. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Characteristics of a Rectangle
Percent Formula
Comparing Fractions
Determining Absolute Value
5. The largest factor that two or more numbers have in common.
Solving a Proportion
Greatest Common Factor
Average of Evenly Spaced Numbers
The 3-4-5 Triangle
6. Add the exponents and keep the same base
Even/Odd
Multiplying and Dividing Powers
Similar Triangles
Using an Equation to Find an Intercept
7. Combine equations in such a way that one of the variables cancel out
Pythagorean Theorem
Multiples of 3 and 9
Solving a System of Equations
Median and Mode
8. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Repeating Decimal
Triangle Inequality Theorem
Multiplying Fractions
Factor/Multiple
9. 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
Negative Exponent and Rational Exponent
Multiples of 3 and 9
Number Categories
The 5-12-13 Triangle
10. 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
Surface Area of a Rectangular Solid
Characteristics of a Square
Solving an Inequality
Area of a Triangle
11. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Interior Angles of a Polygon
Median and Mode
The 5-12-13 Triangle
Prime Factorization
12. To multiply fractions - multiply the numerators and multiply the denominators
Union of Sets
Pythagorean Theorem
Probability
Multiplying Fractions
13. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Greatest Common Factor
Using an Equation to Find an Intercept
Probability
14. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Repeating Decimal
Median and Mode
Simplifying Square Roots
Interior and Exterior Angles of a Triangle
15. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Determining Absolute Value
Volume of a Rectangular Solid
Similar Triangles
Characteristics of a Rectangle
16. 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
Triangle Inequality Theorem
Average Formula -
Multiples of 3 and 9
Using an Equation to Find an Intercept
17. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Relative Primes
Using the Average to Find the Sum
Average Rate
Characteristics of a Rectangle
18. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Even/Odd
Multiples of 3 and 9
Evaluating an Expression
Interior and Exterior Angles of a Triangle
19. To divide fractions - invert the second one and multiply
Dividing Fractions
Evaluating an Expression
Median and Mode
Volume of a Rectangular Solid
20. 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
Multiplying/Dividing Signed Numbers
Remainders
Circumference of a Circle
Prime Factorization
21. 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
Evaluating an Expression
Counting Consecutive Integers
Characteristics of a Parallelogram
The 5-12-13 Triangle
22. 2pr
Circumference of a Circle
Adding/Subtracting Signed Numbers
Exponential Growth
Finding the midpoint
23. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Characteristics of a Rectangle
Parallel Lines and Transversals
Reducing Fractions
Prime Factorization
24. 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
Intersection of sets
Factor/Multiple
Prime Factorization
The 3-4-5 Triangle
25. you can add/subtract when the part under the radical is the same
Characteristics of a Parallelogram
Percent Formula
Intersecting Lines
Adding and Subtracting Roots
26. 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
Multiplying/Dividing Signed Numbers
Solving a Proportion
Characteristics of a Parallelogram
Parallel Lines and Transversals
27. 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
Greatest Common Factor
Identifying the Parts and the Whole
Solving a Quadratic Equation
Function - Notation - and Evaulation
28. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Percent Increase and Decrease
Finding the Distance Between Two Points
Exponential Growth
Domain and Range of a Function
29. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Multiples of 2 and 4
Solving a System of Equations
Setting up a Ratio
30. 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
Average Rate
Adding/Subtracting Signed Numbers
Multiplying Fractions
Adding and Subtraction Polynomials
31. 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
Area of a Sector
Counting Consecutive Integers
Rate
Repeating Decimal
32. (average of the x coordinates - average of the y coordinates)
Factor/Multiple
Characteristics of a Parallelogram
Finding the midpoint
Volume of a Cylinder
33. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Tangency
Prime Factorization
Finding the Original Whole
Negative Exponent and Rational Exponent
34. Subtract the smallest from the largest and add 1
The 3-4-5 Triangle
Comparing Fractions
Counting Consecutive Integers
Adding and Subtracting monomials
35. pr^2
Finding the Original Whole
Finding the Missing Number
Repeating Decimal
Area of a Circle
36. 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
Interior and Exterior Angles of a Triangle
Multiplying Monomials
Intersection of sets
Multiplying and Dividing Powers
37. 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
Characteristics of a Square
Triangle Inequality Theorem
Relative Primes
Counting Consecutive Integers
38. Volume of a Cylinder = pr^2h
Adding and Subtracting Roots
Volume of a Cylinder
Area of a Sector
Percent Increase and Decrease
39. 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.
Reciprocal
Domain and Range of a Function
Number Categories
Union of Sets
40. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Dividing Fractions
Finding the midpoint
Interior and Exterior Angles of a Triangle
Solving a Quadratic Equation
41. 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
Triangle Inequality Theorem
Characteristics of a Rectangle
Percent Increase and Decrease
42. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Reducing Fractions
Characteristics of a Parallelogram
Average Formula -
Simplifying Square Roots
43. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Solving an Inequality
Dividing Fractions
Finding the Original Whole
Average of Evenly Spaced Numbers
44. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Identifying the Parts and the Whole
The 5-12-13 Triangle
Remainders
Setting up a Ratio
45. 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
Using an Equation to Find the Slope
Counting the Possibilities
Average Rate
Reducing Fractions
46. 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
Circumference of a Circle
Mixed Numbers and Improper Fractions
Union of Sets
47. 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 Fractions
Simplifying Square Roots
Even/Odd
48. 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
Evaluating an Expression
Repeating Decimal
The 3-4-5 Triangle
(Least) Common Multiple
49. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Volume of a Rectangular Solid
Finding the Original Whole
Multiples of 3 and 9
Multiplying Fractions
50. Change in y/ change in x rise/run
Average Formula -
Adding and Subtracting monomials
Number Categories
Using Two Points to Find the Slope