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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 evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Average Rate
The 5-12-13 Triangle
Evaluating an Expression
Identifying the Parts and the Whole
2. 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
Repeating Decimal
Pythagorean Theorem
Rate
Determining Absolute Value
3. Multiply the exponents
Even/Odd
Multiplying Monomials
Raising Powers to Powers
Parallel Lines and Transversals
4. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Percent Increase and Decrease
Evaluating an Expression
Counting the Possibilities
5. 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
Interior Angles of a Polygon
Finding the Missing Number
Volume of a Cylinder
Mixed Numbers and Improper Fractions
6. 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
Isosceles and Equilateral triangles
Using an Equation to Find an Intercept
Pythagorean Theorem
7. 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
Exponential Growth
The 5-12-13 Triangle
Volume of a Cylinder
The 3-4-5 Triangle
8. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Union of Sets
Characteristics of a Rectangle
Multiplying Monomials
Solving a System of Equations
9. 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 -
Finding the Original Whole
Length of an Arc
Simplifying Square Roots
10. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average Formula -
Prime Factorization
Using an Equation to Find an Intercept
Volume of a Cylinder
11. 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
Adding and Subtracting Roots
Similar Triangles
Interior Angles of a Polygon
12. To solve a proportion - cross multiply
Simplifying Square Roots
Interior and Exterior Angles of a Triangle
Direct and Inverse Variation
Solving a Proportion
13. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of
Exponential Growth
Area of a Triangle
Average Rate
Relative Primes
14. 1. Re-express them with common denominators 2. Convert them to decimals
Combined Percent Increase and Decrease
Exponential Growth
Multiples of 2 and 4
Comparing Fractions
15. 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
Function - Notation - and Evaulation
Characteristics of a Parallelogram
Greatest Common Factor
Characteristics of a Square
16. 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.
Adding and Subtracting Roots
Prime Factorization
Number Categories
Length of an Arc
17. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Repeating Decimal
Factor/Multiple
Area of a Circle
Multiplying and Dividing Roots
18. The largest factor that two or more numbers have in common.
Isosceles and Equilateral triangles
Finding the Original Whole
Intersecting Lines
Greatest Common Factor
19. 2pr
Triangle Inequality Theorem
Raising Powers to Powers
Remainders
Circumference of a Circle
20. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Isosceles and Equilateral triangles
Reducing Fractions
Multiplying Fractions
Tangency
21. 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
Setting up a Ratio
Solving an Inequality
Function - Notation - and Evaulation
Combined Percent Increase and Decrease
22. 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
Median and Mode
Using Two Points to Find the Slope
Simplifying Square Roots
23. To find the reciprocal of a fraction switch the numerator and the denominator
Multiples of 2 and 4
Reciprocal
Length of an Arc
Adding and Subtraction Polynomials
24. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Solving a System of Equations
Adding and Subtracting monomials
Characteristics of a Rectangle
Average Formula -
25. 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
Parallel Lines and Transversals
Volume of a Rectangular Solid
Union of Sets
Part-to-Part Ratios and Part-to-Whole Ratios
26. 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
Volume of a Cylinder
Multiples of 3 and 9
Similar Triangles
Area of a Triangle
27. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Characteristics of a Rectangle
Area of a Triangle
Multiplying Monomials
Multiples of 2 and 4
28. 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
Dividing Fractions
Solving a System of Equations
Multiplying and Dividing Roots
29. 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
The 3-4-5 Triangle
Solving a Quadratic Equation
Parallel Lines and Transversals
Part-to-Part Ratios and Part-to-Whole Ratios
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
Reciprocal
Using an Equation to Find the Slope
Intersecting Lines
Median and Mode
31. 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
Adding and Subtraction Polynomials
Simplifying Square Roots
Multiplying/Dividing Signed Numbers
Characteristics of a Rectangle
32. 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
Determining Absolute Value
Interior Angles of a Polygon
Remainders
33. Combine like terms
Triangle Inequality Theorem
Adding and Subtraction Polynomials
Finding the Missing Number
Characteristics of a Square
34. you can add/subtract when the part under the radical is the same
Average of Evenly Spaced Numbers
Identifying the Parts and the Whole
Adding and Subtracting Roots
The 3-4-5 Triangle
35. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Adding and Subtraction Polynomials
Area of a Sector
Parallel Lines and Transversals
36. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Comparing Fractions
Volume of a Cylinder
Similar Triangles
Union of Sets
37. 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
Interior Angles of a Polygon
Volume of a Rectangular Solid
Multiplying/Dividing Signed Numbers
Isosceles and Equilateral triangles
38. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Using an Equation to Find the Slope
Part-to-Part Ratios and Part-to-Whole Ratios
Intersection of sets
Setting up a Ratio
39. Subtract the smallest from the largest and add 1
Repeating Decimal
Counting Consecutive Integers
Average of Evenly Spaced Numbers
Remainders
40. Combine equations in such a way that one of the variables cancel out
Solving an Inequality
Solving a System of Equations
The 3-4-5 Triangle
Multiplying and Dividing Powers
41. Volume of a Cylinder = pr^2h
Repeating Decimal
Volume of a Cylinder
Counting the Possibilities
Pythagorean Theorem
42. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Negative Exponent and Rational Exponent
Probability
Intersecting Lines
Number Categories
43. For all right triangles: a^2+b^2=c^2
Comparing Fractions
Interior and Exterior Angles of a Triangle
Pythagorean Theorem
Percent Formula
44. 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
Number Categories
Relative Primes
Adding and Subtraction Polynomials
Identifying the Parts and the Whole
45. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Volume of a Rectangular Solid
Reducing Fractions
Isosceles and Equilateral triangles
Solving a Quadratic Equation
46. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Counting the Possibilities
The 5-12-13 Triangle
Area of a Sector
47. Probability= Favorable Outcomes/Total Possible Outcomes
Probability
Adding and Subtracting Roots
Direct and Inverse Variation
PEMDAS
48. Change in y/ change in x rise/run
Counting the Possibilities
Prime Factorization
Using Two Points to Find the Slope
Multiples of 2 and 4
49. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
The 5-12-13 Triangle
Number Categories
Intersection of sets
Solving a System of Equations
50. 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
Evaluating an Expression
Identifying the Parts and the Whole
Finding the midpoint
Even/Odd