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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. For all right triangles: a^2+b^2=c^2
Counting Consecutive Integers
Pythagorean Theorem
Average Rate
Percent Formula
2. 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
Adding/Subtracting Signed Numbers
Area of a Circle
Finding the Missing Number
Relative Primes
3. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Characteristics of a Rectangle
Characteristics of a Square
Average Formula -
The 5-12-13 Triangle
4. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Dividing Fractions
Identifying the Parts and the Whole
Intersecting Lines
Tangency
5. Factor out the perfect squares
Solving a Proportion
Probability
Simplifying Square Roots
Surface Area of a Rectangular Solid
6. 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
Intersecting Lines
Prime Factorization
Solving an Inequality
Factor/Multiple
7. Surface Area = 2lw + 2wh + 2lh
Surface Area of a Rectangular Solid
Raising Powers to Powers
Median and Mode
Direct and Inverse Variation
8. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Setting up a Ratio
Solving an Inequality
Volume of a Rectangular Solid
9. Volume of a Cylinder = pr^2h
Multiples of 2 and 4
Area of a Sector
Volume of a Cylinder
Parallel Lines and Transversals
10. To solve a proportion - cross multiply
(Least) Common Multiple
Solving a Proportion
Multiples of 3 and 9
The 3-4-5 Triangle
11. 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
Percent Increase and Decrease
Percent Formula
Adding and Subtracting Roots
Characteristics of a Square
12. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Counting Consecutive Integers
Interior Angles of a Polygon
Even/Odd
Parallel Lines and Transversals
13. 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
Pythagorean Theorem
Remainders
Multiplying/Dividing Signed Numbers
14. 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
Pythagorean Theorem
Rate
Probability
Multiplying Fractions
15. 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
Function - Notation - and Evaulation
Finding the Original Whole
Counting the Possibilities
Percent Increase and Decrease
16. 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
Using Two Points to Find the Slope
Multiplying/Dividing Signed Numbers
Even/Odd
Multiples of 3 and 9
17. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Adding/Subtracting Signed Numbers
Multiplying Fractions
Solving a Proportion
18. 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
Adding and Subtracting monomials
Finding the Original Whole
Domain and Range of a Function
Surface Area of a Rectangular Solid
19. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Determining Absolute Value
Area of a Sector
Union of Sets
Counting the Possibilities
20. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Multiples of 2 and 4
Prime Factorization
Multiplying and Dividing Powers
Repeating Decimal
21. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Solving a System of Equations
Adding/Subtracting Signed Numbers
Characteristics of a Square
22. Sum=(Average) x (Number of Terms)
Even/Odd
Using the Average to Find the Sum
PEMDAS
Prime Factorization
23. Multiply the exponents
Raising Powers to Powers
The 5-12-13 Triangle
Circumference of a Circle
Multiplying Fractions
24. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Finding the midpoint
Domain and Range of a Function
Intersection of sets
Volume of a Rectangular Solid
25. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Average Rate
Direct and Inverse Variation
Adding and Subtraction Polynomials
Multiples of 3 and 9
26. The whole # left over after division
Solving an Inequality
Multiplying Monomials
The 3-4-5 Triangle
Remainders
27. To divide fractions - invert the second one and multiply
Identifying the Parts and the Whole
Multiplying Monomials
Dividing Fractions
Average of Evenly Spaced Numbers
28. 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
Dividing Fractions
Parallel Lines and Transversals
Repeating Decimal
Length of an Arc
29. 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
Median and Mode
Determining Absolute Value
Multiplying/Dividing Signed Numbers
Direct and Inverse Variation
30. Combine like terms
Characteristics of a Parallelogram
Part-to-Part Ratios and Part-to-Whole Ratios
Intersecting Lines
Adding and Subtraction Polynomials
31. you can add/subtract when the part under the radical is the same
Part-to-Part Ratios and Part-to-Whole Ratios
Function - Notation - and Evaulation
Median and Mode
Adding and Subtracting Roots
32. 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
Average Formula -
Area of a Triangle
Union of Sets
Number Categories
33. 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 Formula -
The 5-12-13 Triangle
Multiples of 2 and 4
34. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Multiplying Monomials
Parallel Lines and Transversals
Factor/Multiple
Remainders
35. The smallest multiple (other than zero) that two or more numbers have in common.
Multiplying and Dividing Powers
(Least) Common Multiple
Intersection of sets
Determining Absolute Value
36. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Counting Consecutive Integers
Median and Mode
Volume of a Cylinder
Percent Increase and Decrease
37. 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
Tangency
Using an Equation to Find the Slope
Using Two Points to Find the Slope
38. 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
Finding the Missing Number
Function - Notation - and Evaulation
Domain and Range of a Function
Area of a Circle
39. 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
Finding the Original Whole
Using an Equation to Find an Intercept
Average of Evenly Spaced Numbers
Union of Sets
40. 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
Mixed Numbers and Improper Fractions
Reducing Fractions
Volume of a Cylinder
Part-to-Part Ratios and Part-to-Whole Ratios
41. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
The 5-12-13 Triangle
Average Rate
Mixed Numbers and Improper Fractions
Combined Percent Increase and Decrease
42. 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
Negative Exponent and Rational Exponent
Multiplying Monomials
Surface Area of a Rectangular Solid
Finding the Original Whole
43. 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
Relative Primes
Interior Angles of a Polygon
Triangle Inequality Theorem
44. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Union of Sets
Identifying the Parts and the Whole
Counting the Possibilities
45. pr^2
Repeating Decimal
Tangency
Area of a Circle
Mixed Numbers and Improper Fractions
46. 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
Multiplying Fractions
Setting up a Ratio
Area of a Sector
47. 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
Multiplying Monomials
Even/Odd
Volume of a Rectangular Solid
The 5-12-13 Triangle
48. 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
Counting the Possibilities
Average Rate
Isosceles and Equilateral triangles
Solving an Inequality
49. 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
Volume of a Cylinder
Multiplying Fractions
Triangle Inequality Theorem
Interior and Exterior Angles of a Triangle
50. 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
Adding/Subtracting Signed Numbers
PEMDAS
Solving a System of Equations
Characteristics of a Rectangle