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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. Combine equations in such a way that one of the variables cancel out
Triangle Inequality Theorem
Mixed Numbers and Improper Fractions
Average of Evenly Spaced Numbers
Solving a System of Equations
2. Combine like terms
PEMDAS
Adding and Subtraction Polynomials
Counting Consecutive Integers
Direct and Inverse Variation
3. The whole # left over after division
Area of a Triangle
Adding and Subtracting Roots
Average Rate
Remainders
4. To find the reciprocal of a fraction switch the numerator and the denominator
Reducing Fractions
Reciprocal
Area of a Triangle
Volume of a Cylinder
5. 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
Multiplying/Dividing Signed Numbers
Combined Percent Increase and Decrease
Solving an Inequality
Factor/Multiple
6. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Area of a Circle
Multiples of 3 and 9
Average of Evenly Spaced Numbers
Using an Equation to Find the Slope
7. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50
Percent Increase and Decrease
Surface Area of a Rectangular Solid
Identifying the Parts and the Whole
Circumference of a Circle
8. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Simplifying Square Roots
Adding/Subtracting Fractions
Using the Average to Find the Sum
Reciprocal
9. 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
Raising Powers to Powers
Mixed Numbers and Improper Fractions
Tangency
The 5-12-13 Triangle
10. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Similar Triangles
Solving an Inequality
Parallel Lines and Transversals
Simplifying Square Roots
11. For all right triangles: a^2+b^2=c^2
Using Two Points to Find the Slope
Pythagorean Theorem
Multiples of 2 and 4
Multiples of 3 and 9
12. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Raising Powers to Powers
Rate
Length of an Arc
Tangency
13. 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
Identifying the Parts and the Whole
Triangle Inequality Theorem
Adding/Subtracting Signed Numbers
Exponential Growth
14. To multiply fractions - multiply the numerators and multiply the denominators
Finding the Original Whole
Adding/Subtracting Signed Numbers
Multiplying Fractions
Multiples of 2 and 4
15. Probability= Favorable Outcomes/Total Possible Outcomes
Rate
Negative Exponent and Rational Exponent
Solving a Quadratic Equation
Probability
16. 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
Using an Equation to Find an Intercept
Rate
Negative Exponent and Rational Exponent
Mixed Numbers and Improper Fractions
17. you can add/subtract when the part under the radical is the same
Prime Factorization
Raising Powers to Powers
Adding and Subtracting Roots
Number Categories
18. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Relative Primes
Average Formula -
Interior Angles of a Polygon
Area of a Circle
19. 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.
Comparing Fractions
Counting Consecutive Integers
Multiples of 2 and 4
Number Categories
20. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Tangency
PEMDAS
Prime Factorization
Interior Angles of a Polygon
21. Volume of a Cylinder = pr^2h
Adding and Subtraction Polynomials
Volume of a Cylinder
Identifying the Parts and the Whole
Union of Sets
22. 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
Setting up a Ratio
Area of a Sector
Average Formula -
23. 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)
Tangency
Factor/Multiple
Area of a Sector
Number Categories
24. 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
Multiplying/Dividing Signed Numbers
Raising Powers to Powers
Interior and Exterior Angles of a Triangle
25. Add the exponents and keep the same base
Pythagorean Theorem
Exponential Growth
Average Rate
Multiplying and Dividing Powers
26. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Factor/Multiple
Union of Sets
Part-to-Part Ratios and Part-to-Whole Ratios
Multiplying and Dividing Powers
27. 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
Even/Odd
Using Two Points to Find the Slope
Isosceles and Equilateral triangles
Comparing Fractions
28. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Reciprocal
Raising Powers to Powers
The 5-12-13 Triangle
29. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Pythagorean Theorem
Multiplying Monomials
Solving a System of Equations
Circumference of a Circle
30. 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
Interior Angles of a Polygon
Using the Average to Find the Sum
Function - Notation - and Evaulation
Multiplying Fractions
31. 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
The 3-4-5 Triangle
Using an Equation to Find an Intercept
Exponential Growth
Remainders
32. (average of the x coordinates - average of the y coordinates)
Finding the Distance Between Two Points
Part-to-Part Ratios and Part-to-Whole Ratios
Finding the midpoint
Percent Formula
33. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Negative Exponent and Rational Exponent
Average of Evenly Spaced Numbers
Remainders
Adding and Subtracting Roots
34. pr^2
Factor/Multiple
Domain and Range of a Function
Area of a Circle
Probability
35. A square is a rectangle with four equal sides; Area of Square = side*side
Pythagorean Theorem
Solving a Proportion
Characteristics of a Square
Characteristics of a Rectangle
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
Multiples of 2 and 4
Area of a Triangle
Part-to-Part Ratios and Part-to-Whole Ratios
Percent Increase and Decrease
37. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Mixed Numbers and Improper Fractions
Reducing Fractions
Solving a System of Equations
Multiplying and Dividing Roots
38. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Prime Factorization
Using an Equation to Find the Slope
Surface Area of a Rectangular Solid
Raising Powers to Powers
39. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Characteristics of a Rectangle
The 5-12-13 Triangle
Average Formula -
Remainders
40. To divide fractions - invert the second one and multiply
Triangle Inequality Theorem
Multiples of 3 and 9
Dividing Fractions
PEMDAS
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
Similar Triangles
Circumference of a Circle
Finding the Missing Number
Setting up a Ratio
42. 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
Relative Primes
Characteristics of a Square
The 5-12-13 Triangle
Even/Odd
43. 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
Solving an Inequality
Finding the Original Whole
Counting the Possibilities
Pythagorean Theorem
44. 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
Adding/Subtracting Signed Numbers
Solving a System of Equations
Adding/Subtracting Fractions
45. 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
Multiplying and Dividing Roots
Domain and Range of a Function
Median and Mode
46. 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
Average Formula -
Multiplying/Dividing Signed Numbers
Identifying the Parts and the Whole
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)
Solving a System of Equations
Length of an Arc
Characteristics of a Square
Multiplying Fractions
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
Adding and Subtraction Polynomials
Reciprocal
Using an Equation to Find an Intercept
Adding and Subtracting monomials
49. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
PEMDAS
Percent Formula
Even/Odd
Solving a Quadratic Equation
50. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Probability
Multiples of 2 and 4
Exponential Growth
Relative Primes