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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. Volume of a Cylinder = pr^2h
Characteristics of a Parallelogram
Solving a Quadratic Equation
Volume of a Cylinder
Using an Equation to Find an Intercept
2. 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
Direct and Inverse Variation
The 5-12-13 Triangle
Adding and Subtraction Polynomials
Multiplying and Dividing Powers
3. To find the reciprocal of a fraction switch the numerator and the denominator
Finding the Missing Number
Reducing Fractions
Probability
Reciprocal
4. 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
Factor/Multiple
Adding/Subtracting Signed Numbers
Mixed Numbers and Improper Fractions
(Least) Common Multiple
5. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Counting the Possibilities
Determining Absolute Value
Similar Triangles
Tangency
6. 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
Even/Odd
Intersection of sets
Average Rate
Area of a Triangle
7. 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
Using Two Points to Find the Slope
Adding/Subtracting Fractions
Even/Odd
Finding the Missing Number
8. 2pr
Isosceles and Equilateral triangles
Circumference of a Circle
Solving an Inequality
Greatest Common Factor
9. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Multiplying and Dividing Powers
Surface Area of a Rectangular Solid
Interior Angles of a Polygon
(Least) Common Multiple
10. Add the exponents and keep the same base
Exponential Growth
Greatest Common Factor
Multiplying and Dividing Powers
Average of Evenly Spaced Numbers
11. Part = Percent x Whole
Probability
Percent Formula
Adding/Subtracting Signed Numbers
Evaluating an Expression
12. 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)
Average Formula -
Length of an Arc
Multiples of 3 and 9
Characteristics of a Square
13. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Characteristics of a Square
Median and Mode
Prime Factorization
Average of Evenly Spaced Numbers
14. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Similar Triangles
Median and Mode
Finding the Original Whole
Finding the Distance Between Two Points
15. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Volume of a Rectangular Solid
Number Categories
Using the Average to Find the Sum
16. Factor out the perfect squares
Union of Sets
Identifying the Parts and the Whole
Function - Notation - and Evaulation
Simplifying Square Roots
17. 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
Determining Absolute Value
Finding the Original Whole
Length of an Arc
Counting Consecutive Integers
18. 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
Rate
Multiplying Fractions
Counting Consecutive Integers
19. 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
Pythagorean Theorem
Part-to-Part Ratios and Part-to-Whole Ratios
Evaluating an Expression
Direct and Inverse Variation
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
Identifying the Parts and the Whole
Setting up a Ratio
Direct and Inverse Variation
Multiples of 2 and 4
21. 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
Even/Odd
Tangency
Finding the midpoint
Solving an Inequality
22. 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
Area of a Sector
Adding and Subtraction Polynomials
Using the Average to Find the Sum
23. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Direct and Inverse Variation
Repeating Decimal
Pythagorean Theorem
Setting up a Ratio
24. To solve a proportion - cross multiply
Counting Consecutive Integers
Interior Angles of a Polygon
Solving a Proportion
Using Two Points to Find the Slope
25. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Rate
PEMDAS
Determining Absolute Value
Average Formula -
26. 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
Negative Exponent and Rational Exponent
Multiplying Fractions
Multiplying/Dividing Signed Numbers
Intersection of sets
27. 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
Finding the midpoint
Solving an Inequality
Percent Formula
Mixed Numbers and Improper Fractions
28. 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
Finding the Missing Number
Area of a Triangle
Volume of a Cylinder
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
Surface Area of a Rectangular Solid
Direct and Inverse Variation
(Least) Common Multiple
30. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Greatest Common Factor
Intersecting Lines
(Least) Common Multiple
Using an Equation to Find the Slope
31. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Multiplying/Dividing Signed Numbers
Solving a System of Equations
Combined Percent Increase and Decrease
32. 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
Probability
Area of a Triangle
Multiplying Monomials
Solving a System of Equations
33. Probability= Favorable Outcomes/Total Possible Outcomes
Tangency
Using an Equation to Find an Intercept
Probability
Adding/Subtracting Fractions
34. Change in y/ change in x rise/run
Relative Primes
Using an Equation to Find an Intercept
Using Two Points to Find the Slope
Negative Exponent and Rational Exponent
35. 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
The 5-12-13 Triangle
Finding the Distance Between Two Points
Raising Powers to Powers
Isosceles and Equilateral triangles
36. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Setting up a Ratio
Adding/Subtracting Fractions
Adding and Subtracting monomials
Percent Formula
37. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Length of an Arc
Combined Percent Increase and Decrease
Characteristics of a Square
38. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Multiplying and Dividing Powers
Factor/Multiple
Using the Average to Find the Sum
Volume of a Rectangular Solid
39. pr^2
Repeating Decimal
Triangle Inequality Theorem
Multiples of 3 and 9
Area of a Circle
40. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Union of Sets
Solving a Proportion
Pythagorean Theorem
41. you can add/subtract when the part under the radical is the same
Combined Percent Increase and Decrease
Using an Equation to Find the Slope
Even/Odd
Adding and Subtracting Roots
42. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Part-to-Part Ratios and Part-to-Whole Ratios
Characteristics of a Rectangle
Percent Formula
Combined Percent Increase and Decrease
43. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Multiplying and Dividing Roots
Parallel Lines and Transversals
Interior and Exterior Angles of a Triangle
Similar Triangles
44. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Multiplying and Dividing Roots
Domain and Range of a Function
Tangency
Direct and Inverse Variation
45. The smallest multiple (other than zero) that two or more numbers have in common.
The 3-4-5 Triangle
(Least) Common Multiple
Using the Average to Find the Sum
Even/Odd
46. Combine equations in such a way that one of the variables cancel out
Triangle Inequality Theorem
Relative Primes
Intersecting Lines
Solving a System of Equations
47. 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 and Subtracting monomials
Negative Exponent and Rational Exponent
Dividing Fractions
Circumference of a Circle
48. The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides
Triangle Inequality Theorem
Isosceles and Equilateral triangles
Determining Absolute Value
Volume of a Rectangular Solid
49. The largest factor that two or more numbers have in common.
Greatest Common Factor
Comparing Fractions
Prime Factorization
Average Rate
50. Multiply the exponents
Solving an Inequality
Determining Absolute Value
Raising Powers to Powers
Counting the Possibilities