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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Study First
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. The whole # left over after division
The 5-12-13 Triangle
Counting the Possibilities
Remainders
Setting up a Ratio
2. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Percent Increase and Decrease
Triangle Inequality Theorem
Setting up a Ratio
3. 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
Even/Odd
Mixed Numbers and Improper Fractions
PEMDAS
Part-to-Part Ratios and Part-to-Whole Ratios
4. 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
Raising Powers to Powers
Intersecting Lines
Greatest Common Factor
Repeating Decimal
5. 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
Circumference of a Circle
Multiplying/Dividing Signed Numbers
Average Rate
Parallel Lines and Transversals
6. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Using an Equation to Find an Intercept
The 5-12-13 Triangle
Simplifying Square Roots
Adding/Subtracting Fractions
7. 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
Adding/Subtracting Signed Numbers
The 5-12-13 Triangle
Similar Triangles
Rate
8. Change in y/ change in x rise/run
Area of a Triangle
Using Two Points to Find the Slope
Probability
Surface Area of a Rectangular Solid
9. 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
Finding the Original Whole
Combined Percent Increase and Decrease
Volume of a Cylinder
Triangle Inequality Theorem
10. pr^2
Direct and Inverse Variation
Finding the Distance Between Two Points
Finding the Original Whole
Area of a Circle
11. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Greatest Common Factor
Interior and Exterior Angles of a Triangle
Volume of a Rectangular Solid
Using an Equation to Find an Intercept
12. 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
Domain and Range of a Function
Tangency
Identifying the Parts and the Whole
Function - Notation - and Evaulation
13. 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)
Pythagorean Theorem
Solving a Proportion
Length of an Arc
Dividing Fractions
14. Volume of a Cylinder = pr^2h
Interior Angles of a Polygon
Determining Absolute Value
Volume of a Cylinder
Characteristics of a Parallelogram
15. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Parallel Lines and Transversals
Union of Sets
Function - Notation - and Evaulation
Finding the Distance Between Two Points
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
Using the Average to Find the Sum
Area of a Circle
Multiples of 3 and 9
Even/Odd
17. Surface Area = 2lw + 2wh + 2lh
Counting Consecutive Integers
Average Formula -
Even/Odd
Surface Area of a Rectangular Solid
18. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Greatest Common Factor
Evaluating an Expression
Surface Area of a Rectangular Solid
19. 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
Adding/Subtracting Fractions
Prime Factorization
Percent Increase and Decrease
Counting Consecutive Integers
20. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa
Multiples of 3 and 9
Adding/Subtracting Fractions
Average Formula -
Direct and Inverse Variation
21. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Multiples of 2 and 4
Union of Sets
Multiplying and Dividing Roots
Using an Equation to Find the Slope
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)
Area of a Sector
Combined Percent Increase and Decrease
Exponential Growth
Average Rate
23. 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
Similar Triangles
Solving an Inequality
Solving a System of Equations
Solving a Proportion
24. 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
Multiplying/Dividing Signed Numbers
Average Rate
Adding/Subtracting Signed Numbers
Using Two Points to Find the Slope
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
Setting up a Ratio
Area of a Circle
Tangency
Exponential Growth
26. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Simplifying Square Roots
Prime Factorization
Multiples of 2 and 4
Reciprocal
27. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average Formula -
Pythagorean Theorem
Intersecting Lines
Exponential Growth
28. The smallest multiple (other than zero) that two or more numbers have in common.
Prime Factorization
(Least) Common Multiple
Exponential Growth
Multiplying and Dividing Roots
29. 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
Circumference of a Circle
Rate
Identifying the Parts and the Whole
Finding the Original Whole
30. (average of the x coordinates - average of the y coordinates)
Finding the midpoint
Solving a Proportion
Reducing Fractions
Function - Notation - and Evaulation
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
Intersection of sets
Finding the Original Whole
Using an Equation to Find an Intercept
Solving an Inequality
32. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Domain and Range of a Function
Pythagorean Theorem
Determining Absolute Value
Parallel Lines and Transversals
33. Probability= Favorable Outcomes/Total Possible Outcomes
Length of an Arc
Solving a Proportion
(Least) Common Multiple
Probability
34. 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
Counting Consecutive Integers
Negative Exponent and Rational Exponent
Mixed Numbers and Improper Fractions
Even/Odd
35. 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.
PEMDAS
Tangency
Number Categories
(Least) Common Multiple
36. To multiply fractions - multiply the numerators and multiply the denominators
Area of a Sector
Finding the Original Whole
Multiples of 3 and 9
Multiplying Fractions
37. 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
Median and Mode
Area of a Triangle
Direct and Inverse Variation
Exponential Growth
38. 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
Finding the Original Whole
Average of Evenly Spaced Numbers
Domain and Range of a Function
39. Combine equations in such a way that one of the variables cancel out
Even/Odd
Intersection of sets
Solving a System of Equations
Solving an Inequality
40. To solve a proportion - cross multiply
Relative Primes
Counting the Possibilities
Even/Odd
Solving a Proportion
41. 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
Remainders
Finding the Missing Number
Union of Sets
Using the Average to Find the Sum
42. Part = Percent x Whole
Median and Mode
Multiplying/Dividing Signed Numbers
The 5-12-13 Triangle
Percent Formula
43. 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
Rate
Multiplying and Dividing Roots
Negative Exponent and Rational Exponent
Mixed Numbers and Improper Fractions
44. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Area of a Circle
Function - Notation - and Evaulation
Combined Percent Increase and Decrease
45. Domain: all possible values of x for a function range: all possible outputs of a function
Exponential Growth
Domain and Range of a Function
Interior and Exterior Angles of a Triangle
Length of an Arc
46. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
The 3-4-5 Triangle
Function - Notation - and Evaulation
Counting Consecutive Integers
47. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Average of Evenly Spaced Numbers
Multiples of 2 and 4
PEMDAS
Combined Percent Increase and Decrease
48. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Adding/Subtracting Fractions
Remainders
Reducing Fractions
Prime Factorization
49. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Parallel Lines and Transversals
Circumference of a Circle
Adding and Subtracting Roots
Similar Triangles
50. Subtract the smallest from the largest and add 1
Multiples of 3 and 9
Simplifying Square Roots
Average Rate
Counting Consecutive Integers