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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. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Isosceles and Equilateral triangles
Greatest Common Factor
Dividing Fractions
2. 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
Characteristics of a Rectangle
Isosceles and Equilateral triangles
Solving a Quadratic Equation
3. 1. Re-express them with common denominators 2. Convert them to decimals
Characteristics of a Rectangle
Comparing Fractions
Isosceles and Equilateral triangles
Pythagorean Theorem
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
Isosceles and Equilateral triangles
Multiplying/Dividing Signed Numbers
Adding/Subtracting Signed Numbers
Counting the Possibilities
5. 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
Length of an Arc
Function - Notation - and Evaulation
Percent Increase and Decrease
Remainders
6. The whole # left over after division
Reciprocal
Circumference of a Circle
Pythagorean Theorem
Remainders
7. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Using Two Points to Find the Slope
Interior Angles of a Polygon
Adding/Subtracting Fractions
Probability
8. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Area of a Triangle
Finding the midpoint
Factor/Multiple
Determining Absolute Value
9. 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
Identifying the Parts and the Whole
Multiplying/Dividing Signed Numbers
Characteristics of a Rectangle
Probability
10. 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
Relative Primes
Area of a Circle
Adding and Subtracting monomials
11. 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
PEMDAS
Using the Average to Find the Sum
Intersection of sets
12. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Solving a Quadratic Equation
The 5-12-13 Triangle
Characteristics of a Square
Raising Powers to Powers
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
Percent Formula
Intersecting Lines
Function - Notation - and Evaulation
Multiples of 2 and 4
14. A square is a rectangle with four equal sides; Area of Square = side*side
Negative Exponent and Rational Exponent
Characteristics of a Square
Mixed Numbers and Improper Fractions
Number Categories
15. Subtract the smallest from the largest and add 1
Isosceles and Equilateral triangles
Interior Angles of a Polygon
Counting Consecutive Integers
Solving a System of Equations
16. 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
The 5-12-13 Triangle
Domain and Range of a Function
Number Categories
17. 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
Area of a Circle
Characteristics of a Parallelogram
Evaluating an Expression
Number Categories
18. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Raising Powers to Powers
Using the Average to Find the Sum
Remainders
Multiples of 2 and 4
19. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Negative Exponent and Rational Exponent
Reducing Fractions
Solving a Quadratic Equation
Parallel Lines and Transversals
20. 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
Repeating Decimal
Probability
Combined Percent Increase and Decrease
Area of a Sector
21. 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
Direct and Inverse Variation
Triangle Inequality Theorem
Even/Odd
Raising Powers to Powers
22. 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)
Determining Absolute Value
Domain and Range of a Function
Area of a Sector
Characteristics of a Rectangle
23. To find the reciprocal of a fraction switch the numerator and the denominator
Interior Angles of a Polygon
Multiplying and Dividing Powers
Reciprocal
Dividing Fractions
24. 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 Parallelogram
Number Categories
Combined Percent Increase and Decrease
Relative Primes
25. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Percent Formula
Using the Average to Find the Sum
Multiplying and Dividing Roots
Setting up a Ratio
26. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Solving an Inequality
Raising Powers to Powers
Adding and Subtracting monomials
Prime Factorization
27. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Comparing Fractions
PEMDAS
Factor/Multiple
Multiplying and Dividing Powers
28. The largest factor that two or more numbers have in common.
Evaluating an Expression
The 3-4-5 Triangle
Greatest Common Factor
Average of Evenly Spaced Numbers
29. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Combined Percent Increase and Decrease
The 3-4-5 Triangle
Multiples of 3 and 9
30. Combine like terms
Adding and Subtraction Polynomials
Length of an Arc
Multiplying Fractions
Number Categories
31. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Characteristics of a Parallelogram
Multiples of 3 and 9
Counting the Possibilities
Identifying the Parts and the Whole
32. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Finding the Distance Between Two Points
Using Two Points to Find the Slope
Union of Sets
Remainders
33. Surface Area = 2lw + 2wh + 2lh
Surface Area of a Rectangular Solid
Domain and Range of a Function
Combined Percent Increase and Decrease
Area of a Circle
34. Add the exponents and keep the same base
Characteristics of a Square
Number Categories
Multiplying and Dividing Powers
Using Two Points to Find the Slope
35. 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
Parallel Lines and Transversals
Repeating Decimal
Solving a Quadratic Equation
Identifying the Parts and the Whole
36. Volume of a Cylinder = pr^2h
Combined Percent Increase and Decrease
Volume of a Cylinder
Factor/Multiple
Multiplying/Dividing Signed Numbers
37. (average of the x coordinates - average of the y coordinates)
Percent Increase and Decrease
Finding the midpoint
Prime Factorization
Solving an Inequality
38. 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
Adding and Subtracting Roots
Tangency
The 3-4-5 Triangle
Using Two Points to Find the Slope
39. 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
Solving a System of Equations
Adding and Subtracting monomials
Interior Angles of a Polygon
Triangle Inequality Theorem
40. 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
Setting up a Ratio
Average of Evenly Spaced Numbers
Counting the Possibilities
Mixed Numbers and Improper Fractions
41. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Factor/Multiple
Tangency
Comparing Fractions
Average of Evenly Spaced Numbers
42. The smallest multiple (other than zero) that two or more numbers have in common.
PEMDAS
Domain and Range of a Function
Length of an Arc
(Least) Common Multiple
43. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Prime Factorization
Average Formula -
Part-to-Part Ratios and Part-to-Whole Ratios
Relative Primes
44. Part = Percent x Whole
Raising Powers to Powers
Finding the Missing Number
Factor/Multiple
Percent Formula
45. Combine equations in such a way that one of the variables cancel out
Area of a Triangle
Using Two Points to Find the Slope
Dividing Fractions
Solving a System of Equations
46. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Intersection of sets
Multiples of 2 and 4
Average of Evenly Spaced Numbers
Reducing Fractions
47. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Rate
Determining Absolute Value
Volume of a Rectangular Solid
Remainders
48. 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
PEMDAS
Solving a Proportion
Finding the Missing Number
Multiplying Fractions
49. Change in y/ change in x rise/run
Using Two Points to Find the Slope
Dividing Fractions
Length of an Arc
Intersection of sets
50. To solve a proportion - cross multiply
Isosceles and Equilateral triangles
Solving a Proportion
Counting the Possibilities
PEMDAS