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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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sat
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math
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
study here
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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. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
The 3-4-5 Triangle
Multiplying Monomials
Average of Evenly Spaced Numbers
Percent Formula
2. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Parallel Lines and Transversals
Probability
Evaluating an Expression
Factor/Multiple
3. To multiply fractions - multiply the numerators and multiply the denominators
Adding and Subtracting monomials
Using Two Points to Find the Slope
Multiplying Fractions
Mixed Numbers and Improper Fractions
4. 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
Dividing Fractions
Parallel Lines and Transversals
Direct and Inverse Variation
Multiplying/Dividing Signed Numbers
5. 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
Direct and Inverse Variation
Adding and Subtraction Polynomials
Using the Average to Find the Sum
6. Factor out the perfect squares
Number Categories
Simplifying Square Roots
(Least) Common Multiple
Percent Formula
7. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
PEMDAS
Setting up a Ratio
Using an Equation to Find the Slope
Surface Area of a Rectangular Solid
8. For all right triangles: a^2+b^2=c^2
Volume of a Cylinder
Exponential Growth
Pythagorean Theorem
Greatest Common Factor
9. 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
Similar Triangles
Intersecting Lines
Finding the Missing Number
Counting the Possibilities
10. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Characteristics of a Rectangle
Average of Evenly Spaced Numbers
Area of a Circle
Part-to-Part Ratios and Part-to-Whole Ratios
11. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Repeating Decimal
Simplifying Square Roots
Average Rate
Mixed Numbers and Improper Fractions
12. 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
Using an Equation to Find an Intercept
Multiples of 2 and 4
Probability
The 5-12-13 Triangle
13. Subtract the smallest from the largest and add 1
Volume of a Rectangular Solid
Evaluating an Expression
The 5-12-13 Triangle
Counting Consecutive Integers
14. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Raising Powers to Powers
Area of a Circle
Multiplying Monomials
15. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Average Rate
Setting up a Ratio
Similar Triangles
Percent Formula
16. 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
Characteristics of a Parallelogram
Isosceles and Equilateral triangles
Finding the Distance Between Two Points
Volume of a Cylinder
17. 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
Similar Triangles
Evaluating an Expression
Median and Mode
18. 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
Comparing Fractions
Multiplying and Dividing Roots
Interior and Exterior Angles of a Triangle
19. 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
Relative Primes
Mixed Numbers and Improper Fractions
Counting the Possibilities
Percent Formula
20. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Counting Consecutive Integers
Interior Angles of a Polygon
Intersecting Lines
Average Formula -
21. 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
Solving a System of Equations
Area of a Sector
Relative Primes
Adding and Subtracting Roots
22. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Evaluating an Expression
Pythagorean Theorem
Identifying the Parts and the Whole
Multiplying Monomials
23. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Volume of a Rectangular Solid
Triangle Inequality Theorem
Solving a Quadratic Equation
Union of Sets
24. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Multiplying Fractions
Exponential Growth
Area of a Circle
Union of Sets
25. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Factor/Multiple
Multiplying and Dividing Roots
Using the Average to Find the Sum
Identifying the Parts and the Whole
26. 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
Finding the Original Whole
Solving an Inequality
Evaluating an Expression
Repeating Decimal
27. 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
Mixed Numbers and Improper Fractions
Using an Equation to Find the Slope
Surface Area of a Rectangular Solid
Interior Angles of a Polygon
28. 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)
Similar Triangles
Length of an Arc
Isosceles and Equilateral triangles
Finding the Missing Number
29. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Adding/Subtracting Signed Numbers
PEMDAS
Volume of a Rectangular Solid
Adding/Subtracting Fractions
30. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Solving a System of Equations
Multiplying and Dividing Powers
Tangency
Solving a Proportion
31. Volume of a Cylinder = pr^2h
Similar Triangles
Factor/Multiple
Volume of a Cylinder
Solving a System of Equations
32. 2pr
Parallel Lines and Transversals
Area of a Circle
Median and Mode
Circumference of a Circle
33. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Finding the Original Whole
Intersection of sets
(Least) Common Multiple
Rate
34. 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
Finding the Distance Between Two Points
The 5-12-13 Triangle
Multiplying and Dividing Roots
The 3-4-5 Triangle
35. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Triangle Inequality Theorem
Adding/Subtracting Signed Numbers
Dividing Fractions
Setting up a Ratio
36. 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
Setting up a Ratio
Identifying the Parts and the Whole
Solving a Proportion
Adding/Subtracting Signed Numbers
37. A square is a rectangle with four equal sides; Area of Square = side*side
PEMDAS
Characteristics of a Square
Similar Triangles
Reducing Fractions
38. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Mixed Numbers and Improper Fractions
Parallel Lines and Transversals
Adding and Subtracting monomials
Isosceles and Equilateral triangles
39. Add the exponents and keep the same base
Multiplying/Dividing Signed Numbers
Adding/Subtracting Fractions
Multiplying and Dividing Powers
Mixed Numbers and Improper Fractions
40. 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
Union of Sets
Multiplying/Dividing Signed Numbers
Interior and Exterior Angles of a Triangle
Function - Notation - and Evaulation
41. 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
Dividing Fractions
Multiples of 3 and 9
Percent Increase and Decrease
Rate
42. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Number Categories
The 5-12-13 Triangle
Characteristics of a Square
43. 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
Raising Powers to Powers
Identifying the Parts and the Whole
Interior Angles of a Polygon
Triangle Inequality Theorem
44. 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
Interior and Exterior Angles of a Triangle
Interior Angles of a Polygon
Domain and Range of a Function
45. Combine like terms
Evaluating an Expression
Area of a Circle
Adding and Subtraction Polynomials
Parallel Lines and Transversals
46. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Identifying the Parts and the Whole
Interior Angles of a Polygon
Mixed Numbers and Improper Fractions
Similar Triangles
47. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Even/Odd
Prime Factorization
Multiples of 2 and 4
Raising Powers to Powers
48. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Multiplying Monomials
Multiplying and Dividing Roots
Direct and Inverse Variation
Intersecting Lines
49. The whole # left over after division
Area of a Triangle
Remainders
Characteristics of a Parallelogram
Multiples of 2 and 4
50. Domain: all possible values of x for a function range: all possible outputs of a function
Simplifying Square Roots
Determining Absolute Value
Union of Sets
Domain and Range of a Function