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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. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Surface Area of a Rectangular Solid
Using the Average to Find the Sum
Volume of a Rectangular Solid
2. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Average Formula -
Negative Exponent and Rational Exponent
Interior Angles of a Polygon
Volume of a Rectangular Solid
3. Change in y/ change in x rise/run
Solving a Quadratic Equation
Using Two Points to Find the Slope
Repeating Decimal
Triangle Inequality Theorem
4. Surface Area = 2lw + 2wh + 2lh
Surface Area of a Rectangular Solid
Interior and Exterior Angles of a Triangle
Relative Primes
Percent Increase and Decrease
5. 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
Simplifying Square Roots
Average Rate
Factor/Multiple
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
Determining Absolute Value
Characteristics of a Square
The 5-12-13 Triangle
Raising Powers to Powers
7. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Average of Evenly Spaced Numbers
Greatest Common Factor
Evaluating an Expression
Mixed Numbers and Improper Fractions
8. 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)
Length of an Arc
Mixed Numbers and Improper Fractions
Rate
Average Rate
9. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Adding and Subtraction Polynomials
Intersection of sets
Counting Consecutive Integers
10. 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
Multiples of 2 and 4
Direct and Inverse Variation
Intersecting Lines
11. Subtract the smallest from the largest and add 1
Using an Equation to Find the Slope
Counting Consecutive Integers
Adding/Subtracting Signed Numbers
Area of a Circle
12. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Multiples of 3 and 9
Solving a Quadratic Equation
Interior and Exterior Angles of a Triangle
Setting up a Ratio
13. 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
Even/Odd
Solving a Quadratic Equation
Function - Notation - and Evaulation
Percent Formula
14. 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
Solving a Proportion
Reducing Fractions
Multiplying/Dividing Signed Numbers
Rate
15. To divide fractions - invert the second one and multiply
Percent Formula
Negative Exponent and Rational Exponent
Factor/Multiple
Dividing Fractions
16. 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
Reciprocal
Negative Exponent and Rational Exponent
Average of Evenly Spaced Numbers
Finding the Original Whole
17. 1. Re-express them with common denominators 2. Convert them to decimals
Average Formula -
Prime Factorization
The 5-12-13 Triangle
Comparing Fractions
18. 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
Reducing Fractions
Reciprocal
Interior and Exterior Angles of a Triangle
Multiplying Fractions
19. pr^2
Finding the Original Whole
Multiplying and Dividing Roots
Area of a Circle
Combined Percent Increase and Decrease
20. 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
Combined Percent Increase and Decrease
Intersection of sets
Using an Equation to Find an Intercept
21. The whole # left over after division
Probability
Using Two Points to Find the Slope
Similar Triangles
Remainders
22. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Average of Evenly Spaced Numbers
Interior and Exterior Angles of a Triangle
Evaluating an Expression
Parallel Lines and Transversals
23. 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 Signed Numbers
Domain and Range of a Function
Factor/Multiple
Combined Percent Increase and Decrease
24. 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
Relative Primes
Parallel Lines and Transversals
Rate
Mixed Numbers and Improper Fractions
25. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Solving a Quadratic Equation
Determining Absolute Value
Using an Equation to Find the Slope
Evaluating an Expression
26. 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
Multiplying and Dividing Roots
Multiplying Monomials
Using an Equation to Find an Intercept
Characteristics of a Rectangle
27. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Number Categories
Similar Triangles
(Least) Common Multiple
Characteristics of a Rectangle
28. 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
Solving an Inequality
(Least) Common Multiple
Direct and Inverse Variation
Finding the midpoint
29. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Finding the Missing Number
Average Rate
Adding and Subtracting monomials
Average of Evenly Spaced Numbers
30. 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
Volume of a Cylinder
Multiplying Fractions
Characteristics of a Parallelogram
31. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Domain and Range of a Function
Finding the Distance Between Two Points
Isosceles and Equilateral triangles
Reducing Fractions
32. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Finding the midpoint
Area of a Circle
Multiplying/Dividing Signed Numbers
Reducing Fractions
33. you can add/subtract when the part under the radical is the same
Solving a System of Equations
Direct and Inverse Variation
Interior Angles of a Polygon
Adding and Subtracting Roots
34. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Using an Equation to Find the Slope
Median and Mode
Parallel Lines and Transversals
Multiplying Monomials
35. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Relative Primes
Median and Mode
Using the Average to Find the Sum
Domain and Range of a Function
36. The largest factor that two or more numbers have in common.
Greatest Common Factor
Intersecting Lines
Counting Consecutive Integers
Volume of a Cylinder
37. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Similar Triangles
Length of an Arc
Multiples of 3 and 9
38. 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
Pythagorean Theorem
Rate
Volume of a Cylinder
Using an Equation to Find an Intercept
39. Combine like terms
Adding and Subtraction Polynomials
Length of an Arc
Negative Exponent and Rational Exponent
Remainders
40. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Exponential Growth
Prime Factorization
Length of an Arc
Area of a Circle
41. 2pr
Evaluating an Expression
Number Categories
Union of Sets
Circumference of a Circle
42. 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
Volume of a Cylinder
Multiples of 3 and 9
Characteristics of a Rectangle
Combined Percent Increase and Decrease
43. Multiply the exponents
Intersection of sets
Even/Odd
Raising Powers to Powers
Triangle Inequality Theorem
44. To multiply fractions - multiply the numerators and multiply the denominators
Negative Exponent and Rational Exponent
Solving a Proportion
Circumference of a Circle
Multiplying Fractions
45. 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 and Dividing Powers
Reciprocal
PEMDAS
Characteristics of a Parallelogram
46. 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
Counting the Possibilities
Determining Absolute Value
Multiples of 3 and 9
Evaluating an Expression
47. (average of the x coordinates - average of the y coordinates)
Domain and Range of a Function
Multiplying Monomials
Area of a Triangle
Finding the midpoint
48. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Intersection of sets
Adding and Subtracting monomials
Average of Evenly Spaced Numbers
Relative Primes
49. Domain: all possible values of x for a function range: all possible outputs of a function
Intersection of sets
Area of a Triangle
Domain and Range of a Function
Using the Average to Find the Sum
50. 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 and Subtracting monomials
Using an Equation to Find the Slope
Greatest Common Factor
Multiples of 3 and 9