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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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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. 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
Combined Percent Increase and Decrease
Multiplying and Dividing Powers
Remainders
2. 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
Simplifying Square Roots
Median and Mode
Finding the Original Whole
Reciprocal
3. Domain: all possible values of x for a function range: all possible outputs of a function
Parallel Lines and Transversals
Area of a Sector
Solving a System of Equations
Domain and Range of a Function
4. 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
Function - Notation - and Evaulation
Rate
Interior and Exterior Angles of a Triangle
Relative Primes
5. Add the exponents and keep the same base
Multiplying and Dividing Powers
Using the Average to Find the Sum
Area of a Sector
Multiplying Fractions
6. 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
Median and Mode
Adding/Subtracting Signed Numbers
Interior Angles of a Polygon
Direct and Inverse Variation
7. 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
Isosceles and Equilateral triangles
Circumference of a Circle
(Least) Common Multiple
8. 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
Intersecting Lines
Union of Sets
Repeating Decimal
9. 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.
Prime Factorization
Number Categories
Simplifying Square Roots
Using an Equation to Find an Intercept
10. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Multiplying Fractions
Interior Angles of a Polygon
Area of a Sector
Average Formula -
11. 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
Multiples of 2 and 4
Tangency
Average of Evenly Spaced Numbers
Negative Exponent and Rational Exponent
12. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Counting the Possibilities
Reducing Fractions
Area of a Circle
Characteristics of a Rectangle
13. Part = Percent x Whole
Raising Powers to Powers
Using the Average to Find the Sum
Finding the midpoint
Percent Formula
14. (average of the x coordinates - average of the y coordinates)
Remainders
Dividing Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
Finding the midpoint
15. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Adding/Subtracting Signed Numbers
Median and Mode
Evaluating an Expression
16. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Similar Triangles
Finding the midpoint
Multiples of 3 and 9
PEMDAS
17. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Multiples of 2 and 4
Finding the Distance Between Two Points
Characteristics of a Parallelogram
18. 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
Area of a Triangle
Probability
Using an Equation to Find an Intercept
Prime Factorization
19. you can add/subtract when the part under the radical is the same
The 3-4-5 Triangle
Negative Exponent and Rational Exponent
Adding and Subtracting Roots
Simplifying Square Roots
20. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Area of a Sector
Characteristics of a Parallelogram
Multiplying and Dividing Roots
21. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Surface Area of a Rectangular Solid
Solving a Quadratic Equation
Average Formula -
Average Rate
22. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Multiplying Monomials
Exponential Growth
Solving an Inequality
Tangency
23. 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
Area of a Sector
Function - Notation - and Evaulation
Probability
Characteristics of a Square
24. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Adding and Subtraction Polynomials
Rate
Number Categories
Determining Absolute Value
25. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Solving an Inequality
Parallel Lines and Transversals
Percent Formula
Volume of a Cylinder
26. pr^2
Solving a Proportion
Setting up a Ratio
Area of a Circle
Adding and Subtraction Polynomials
27. 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
Counting the Possibilities
Intersection of sets
Circumference of a Circle
Interior and Exterior Angles of a Triangle
28. To divide fractions - invert the second one and multiply
Negative Exponent and Rational Exponent
Percent Increase and Decrease
Dividing Fractions
Interior and Exterior Angles of a Triangle
29. 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
Domain and Range of a Function
Determining Absolute Value
Reducing Fractions
30. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
The 5-12-13 Triangle
Median and Mode
Using Two Points to Find the Slope
31. 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
Union of Sets
Average Rate
Exponential Growth
32. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Identifying the Parts and the Whole
Interior and Exterior Angles of a Triangle
Average Formula -
Determining Absolute Value
33. 1. Re-express them with common denominators 2. Convert them to decimals
Adding/Subtracting Signed Numbers
Comparing Fractions
Finding the Original Whole
Counting the Possibilities
34. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Average of Evenly Spaced Numbers
Using an Equation to Find the Slope
Multiplying Fractions
Determining Absolute Value
35. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Probability
Adding and Subtracting monomials
Finding the Original Whole
Characteristics of a Parallelogram
36. 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 an Equation to Find the Slope
Dividing Fractions
Area of a Sector
(Least) Common Multiple
37. 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
Adding/Subtracting Signed Numbers
Multiplying Monomials
Simplifying Square Roots
Repeating Decimal
38. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Identifying the Parts and the Whole
Intersecting Lines
Average Rate
Direct and Inverse Variation
39. Subtract the smallest from the largest and add 1
Raising Powers to Powers
Multiplying/Dividing Signed Numbers
Median and Mode
Counting Consecutive Integers
40. The largest factor that two or more numbers have in common.
Reciprocal
Percent Formula
Domain and Range of a Function
Greatest Common Factor
41. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Function - Notation - and Evaulation
Factor/Multiple
Area of a Triangle
Similar Triangles
42. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Volume of a Rectangular Solid
Characteristics of a Rectangle
Adding/Subtracting Signed Numbers
Exponential Growth
43. 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
Counting Consecutive Integers
Using an Equation to Find the Slope
Finding the midpoint
Combined Percent Increase and Decrease
44. Change in y/ change in x rise/run
Adding/Subtracting Signed Numbers
Number Categories
Surface Area of a Rectangular Solid
Using Two Points to Find the Slope
45. Combine like terms
Adding and Subtracting Roots
Multiples of 2 and 4
Adding and Subtraction Polynomials
Simplifying Square Roots
46. The smallest multiple (other than zero) that two or more numbers have in common.
Multiples of 2 and 4
Multiplying Monomials
Combined Percent Increase and Decrease
(Least) Common Multiple
47. To multiply fractions - multiply the numerators and multiply the denominators
Triangle Inequality Theorem
Adding and Subtraction Polynomials
Multiplying Fractions
Volume of a Cylinder
48. To solve a proportion - cross multiply
Area of a Sector
Pythagorean Theorem
Solving a Proportion
Solving an Inequality
49. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Direct and Inverse Variation
Average Rate
Adding/Subtracting Fractions
Multiples of 2 and 4
50. 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
Negative Exponent and Rational Exponent
Counting the Possibilities
Adding/Subtracting Fractions
Even/Odd