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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 median is the value that falls in the middle of the set - the mode is the value that appears most often
Median and Mode
Adding and Subtracting Roots
The 3-4-5 Triangle
Combined Percent Increase and Decrease
2. 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
Average Rate
Triangle Inequality Theorem
PEMDAS
Characteristics of a Rectangle
3. 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.
Triangle Inequality Theorem
Percent Formula
Number Categories
Tangency
4. 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
Finding the Original Whole
Setting up a Ratio
Factor/Multiple
5. To multiply fractions - multiply the numerators and multiply the denominators
Part-to-Part Ratios and Part-to-Whole Ratios
Finding the Missing Number
Multiplying Fractions
Mixed Numbers and Improper Fractions
6. 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
Even/Odd
Simplifying Square Roots
Area of a Circle
Using an Equation to Find an Intercept
7. A square is a rectangle with four equal sides; Area of Square = side*side
Average Rate
Characteristics of a Square
Prime Factorization
Interior Angles of a Polygon
8. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Even/Odd
Interior and Exterior Angles of a Triangle
(Least) Common Multiple
Average Rate
9. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Intersecting Lines
Characteristics of a Square
Isosceles and Equilateral triangles
Reducing Fractions
10. Domain: all possible values of x for a function range: all possible outputs of a function
Solving a Quadratic Equation
Characteristics of a Parallelogram
Multiplying Fractions
Domain and Range of a Function
11. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Part-to-Part Ratios and Part-to-Whole Ratios
Characteristics of a Parallelogram
Negative Exponent and Rational Exponent
Finding the Distance Between Two Points
12. 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
Direct and Inverse Variation
Multiplying Monomials
Domain and Range of a Function
Characteristics of a Parallelogram
13. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Volume of a Cylinder
Direct and Inverse Variation
Percent Increase and Decrease
Union of Sets
14. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Intersection of sets
Finding the Distance Between Two Points
Using the Average to Find the Sum
Dividing Fractions
15. 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
Factor/Multiple
Exponential Growth
Percent Formula
Adding and Subtraction Polynomials
16. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Area of a Triangle
Negative Exponent and Rational Exponent
Remainders
Tangency
17. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Characteristics of a Rectangle
Parallel Lines and Transversals
The 5-12-13 Triangle
The 3-4-5 Triangle
18. 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
Percent Increase and Decrease
Using the Average to Find the Sum
Relative Primes
Mixed Numbers and Improper Fractions
19. Add the exponents and keep the same base
Function - Notation - and Evaulation
The 5-12-13 Triangle
Reducing Fractions
Multiplying and Dividing Powers
20. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Median and Mode
Repeating Decimal
PEMDAS
21. 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
The 5-12-13 Triangle
Adding and Subtracting Roots
Direct and Inverse Variation
Characteristics of a Rectangle
22. Change in y/ change in x rise/run
Using Two Points to Find the Slope
Similar Triangles
Number Categories
Finding the Distance Between Two Points
23. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Even/Odd
Multiples of 2 and 4
Pythagorean Theorem
24. Part = Percent x Whole
Comparing Fractions
Finding the Original Whole
Percent Formula
Characteristics of a Square
25. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Adding/Subtracting Fractions
Repeating Decimal
Rate
Factor/Multiple
26. To solve a proportion - cross multiply
Finding the Missing Number
Solving a Proportion
Circumference of a Circle
Relative Primes
27. 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
Adding and Subtracting Roots
Percent Formula
Repeating Decimal
28. If there are m ways one event can happen and n ways a second event can happen - then there are m × n ways for the 2 events to happen
Prime Factorization
Parallel Lines and Transversals
Mixed Numbers and Improper Fractions
Counting the Possibilities
29. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Similar Triangles
Exponential Growth
Solving a Quadratic Equation
Average Formula -
30. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Adding and Subtracting Roots
Remainders
Interior Angles of a Polygon
Adding/Subtracting Signed Numbers
31. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Adding and Subtraction Polynomials
Using an Equation to Find the Slope
Average of Evenly Spaced Numbers
Multiplying Monomials
32. Surface Area = 2lw + 2wh + 2lh
Isosceles and Equilateral triangles
Triangle Inequality Theorem
Surface Area of a Rectangular Solid
Function - Notation - and Evaulation
33. 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 and Subtraction Polynomials
Solving a Proportion
Multiplying and Dividing Powers
Rate
34. The whole # left over after division
Remainders
Reducing Fractions
Average of Evenly Spaced Numbers
Identifying the Parts and the Whole
35. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Multiples of 3 and 9
Surface Area of a Rectangular Solid
Circumference of a Circle
Solving a Quadratic Equation
36. Sum=(Average) x (Number of Terms)
Characteristics of a Parallelogram
Finding the Missing Number
Using the Average to Find the Sum
Triangle Inequality Theorem
37. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Reducing Fractions
Interior and Exterior Angles of a Triangle
Volume of a Rectangular Solid
Multiplying/Dividing Signed Numbers
38. 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
Percent Increase and Decrease
Adding/Subtracting Signed Numbers
Function - Notation - and Evaulation
Finding the Original Whole
39. 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
Surface Area of a Rectangular Solid
Comparing Fractions
Area of a Triangle
Multiples of 3 and 9
40. 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
Isosceles and Equilateral triangles
Percent Increase and Decrease
Factor/Multiple
Area of a Triangle
41. 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)
Number Categories
Multiplying Monomials
Area of a Sector
Combined Percent Increase and Decrease
42. 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
The 5-12-13 Triangle
Finding the Missing Number
Multiplying Monomials
Negative Exponent and Rational Exponent
43. The smallest multiple (other than zero) that two or more numbers have in common.
Even/Odd
Area of a Circle
Pythagorean Theorem
(Least) Common Multiple
44. 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
Function - Notation - and Evaulation
Multiples of 3 and 9
Triangle Inequality Theorem
Mixed Numbers and Improper Fractions
45. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Function - Notation - and Evaulation
Greatest Common Factor
Characteristics of a Square
Average of Evenly Spaced Numbers
46. The 3 angles of any triangle add up to 180 degrees - an exterior angles of a triangle is equal to the sum of the remote interior angles - the 3 exterior angles add up to 360 degrees
Domain and Range of a Function
Interior and Exterior Angles of a Triangle
Mixed Numbers and Improper Fractions
Percent Increase and Decrease
47. 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)
Solving a Quadratic Equation
Interior Angles of a Polygon
Adding and Subtracting monomials
Length of an Arc
48. 2pr
Setting up a Ratio
Reciprocal
Circumference of a Circle
Combined Percent Increase and Decrease
49. 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
Median and Mode
Average Formula -
Even/Odd
Intersecting Lines
50. To divide fractions - invert the second one and multiply
Isosceles and Equilateral triangles
PEMDAS
Intersecting Lines
Dividing Fractions