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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. (average of the x coordinates - average of the y coordinates)
Using an Equation to Find the Slope
Volume of a Rectangular Solid
The 5-12-13 Triangle
Finding the midpoint
2. 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 and Dividing Roots
Combined Percent Increase and Decrease
Average of Evenly Spaced Numbers
Length of an Arc
3. The largest factor that two or more numbers have in common.
Interior Angles of a Polygon
Adding and Subtracting Roots
Greatest Common Factor
Finding the Original Whole
4. 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
Prime Factorization
Circumference of a Circle
Solving a Proportion
The 3-4-5 Triangle
5. The whole # left over after division
Remainders
Using the Average to Find the Sum
Multiples of 3 and 9
Finding the Missing Number
6. 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
Multiples of 3 and 9
The 5-12-13 Triangle
Exponential Growth
Part-to-Part Ratios and Part-to-Whole Ratios
7. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Multiples of 2 and 4
Factor/Multiple
Identifying the Parts and the Whole
Area of a Triangle
8. 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
Multiplying Fractions
Circumference of a Circle
Even/Odd
Negative Exponent and Rational Exponent
9. 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
Setting up a Ratio
Finding the midpoint
Adding/Subtracting Signed Numbers
Isosceles and Equilateral triangles
10. 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
Solving a System of Equations
The 5-12-13 Triangle
Using an Equation to Find the Slope
Rate
11. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Number Categories
Average of Evenly Spaced Numbers
Repeating Decimal
Intersecting Lines
12. Volume of a Cylinder = pr^2h
Median and Mode
Adding and Subtracting monomials
Volume of a Cylinder
Greatest Common Factor
13. 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
Using an Equation to Find an Intercept
Multiplying/Dividing Signed Numbers
Volume of a Cylinder
Triangle Inequality Theorem
14. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Reducing Fractions
Relative Primes
Remainders
PEMDAS
15. Sum=(Average) x (Number of Terms)
Solving an Inequality
Multiplying Monomials
Using the Average to Find the Sum
Remainders
16. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Percent Increase and Decrease
Factor/Multiple
Adding and Subtracting Roots
17. 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 Formula -
Average Rate
Counting the Possibilities
Function - Notation - and Evaulation
18. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Adding and Subtracting Roots
Evaluating an Expression
Dividing Fractions
Function - Notation - and Evaulation
19. 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
PEMDAS
Factor/Multiple
Even/Odd
Finding the Distance Between Two Points
20. 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)
Negative Exponent and Rational Exponent
Solving an Inequality
Rate
Area of a Sector
21. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Area of a Triangle
Mixed Numbers and Improper Fractions
Evaluating an Expression
Adding/Subtracting Fractions
22. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Percent Increase and Decrease
Number Categories
Reducing Fractions
Finding the Missing Number
23. pr^2
Characteristics of a Parallelogram
Area of a Circle
Identifying the Parts and the Whole
(Least) Common Multiple
24. 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
Mixed Numbers and Improper Fractions
The 3-4-5 Triangle
Solving an Inequality
25. 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
Intersecting Lines
Exponential Growth
Multiplying/Dividing Signed Numbers
Characteristics of a Parallelogram
26. Subtract the smallest from the largest and add 1
Volume of a Cylinder
Dividing Fractions
Identifying the Parts and the Whole
Counting Consecutive Integers
27. 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
(Least) Common Multiple
Relative Primes
Part-to-Part Ratios and Part-to-Whole Ratios
Characteristics of a Rectangle
28. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Using an Equation to Find the Slope
Tangency
Average Formula -
Multiplying and Dividing Powers
29. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Solving a Quadratic Equation
Multiplying Monomials
(Least) Common Multiple
Average of Evenly Spaced Numbers
30. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Dividing Fractions
Multiples of 2 and 4
Finding the midpoint
31. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Characteristics of a Parallelogram
Solving a Quadratic Equation
Multiplying/Dividing Signed Numbers
Multiplying Fractions
32. Part = Percent x Whole
Union of Sets
Direct and Inverse Variation
Multiplying Fractions
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
Number Categories
Average of Evenly Spaced Numbers
Greatest Common Factor
Using Two Points to Find the Slope
34. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Finding the Original Whole
Volume of a Cylinder
Union of Sets
Adding/Subtracting Signed Numbers
35. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Interior Angles of a Polygon
Raising Powers to Powers
PEMDAS
Prime Factorization
36. 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
Solving a Quadratic Equation
The 5-12-13 Triangle
Reducing Fractions
37. 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)
Volume of a Rectangular Solid
Function - Notation - and Evaulation
Multiplying Monomials
Length of an Arc
38. To solve a proportion - cross multiply
Remainders
Counting Consecutive Integers
Evaluating an Expression
Solving a Proportion
39. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Reciprocal
Median and Mode
Greatest Common Factor
(Least) Common Multiple
40. Combine like terms
Pythagorean Theorem
Negative Exponent and Rational Exponent
Circumference of a Circle
Adding and Subtraction Polynomials
41. For all right triangles: a^2+b^2=c^2
Raising Powers to Powers
Pythagorean Theorem
Average Formula -
Adding/Subtracting Signed Numbers
42. Probability= Favorable Outcomes/Total Possible Outcomes
Number Categories
Probability
Area of a Triangle
Mixed Numbers and Improper Fractions
43. 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
Parallel Lines and Transversals
Average Formula -
Multiples of 3 and 9
Mixed Numbers and Improper Fractions
44. To multiply fractions - multiply the numerators and multiply the denominators
Adding/Subtracting Signed Numbers
The 5-12-13 Triangle
Multiplying Fractions
Combined Percent Increase and Decrease
45. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Multiples of 2 and 4
Even/Odd
Multiples of 3 and 9
Determining Absolute Value
46. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Multiplying and Dividing Powers
Using an Equation to Find the Slope
The 3-4-5 Triangle
(Least) Common Multiple
47. 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
Pythagorean Theorem
Percent Increase and Decrease
Adding and Subtraction Polynomials
Reducing Fractions
48. 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
Counting the Possibilities
Using an Equation to Find an Intercept
Solving an Inequality
Solving a Quadratic Equation
49. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Volume of a Rectangular Solid
Probability
Finding the Original Whole
Multiples of 2 and 4
50. To divide fractions - invert the second one and multiply
Dividing Fractions
Average Formula -
Similar Triangles
The 3-4-5 Triangle