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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.
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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. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Finding the Missing Number
Median and Mode
Percent Formula
Multiples of 2 and 4
2. 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
Circumference of a Circle
Average Rate
Multiples of 2 and 4
Identifying the Parts and the Whole
3. 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
Probability
Direct and Inverse Variation
Average Formula -
Isosceles and Equilateral triangles
4. 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
Multiplying/Dividing Signed Numbers
Average Formula -
Average Rate
5. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Exponential Growth
Average Rate
Simplifying Square Roots
Multiples of 3 and 9
6. 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
Multiples of 3 and 9
Adding/Subtracting Signed Numbers
(Least) Common Multiple
Solving an Inequality
7. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Characteristics of a Square
Median and Mode
Repeating Decimal
Volume of a Cylinder
8. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
PEMDAS
Characteristics of a Square
Average Rate
9. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Similar Triangles
Characteristics of a Square
Area of a Circle
Prime Factorization
10. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Combined Percent Increase and Decrease
Setting up a Ratio
Volume of a Rectangular Solid
Factor/Multiple
11. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Mixed Numbers and Improper Fractions
Reducing Fractions
Finding the midpoint
Function - Notation - and Evaulation
12. (average of the x coordinates - average of the y coordinates)
Reciprocal
The 5-12-13 Triangle
Intersection of sets
Finding the midpoint
13. 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
Area of a Circle
The 5-12-13 Triangle
Rate
Multiples of 2 and 4
14. 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
Percent Formula
Using the Average to Find the Sum
Finding the midpoint
Mixed Numbers and Improper Fractions
15. 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
Rate
Even/Odd
Domain and Range of a Function
16. 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
Similar Triangles
Adding/Subtracting Fractions
Average Rate
17. Subtract the smallest from the largest and add 1
Characteristics of a Square
Counting Consecutive Integers
Simplifying Square Roots
Finding the Original Whole
18. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Part-to-Part Ratios and Part-to-Whole Ratios
Percent Increase and Decrease
Using an Equation to Find the Slope
Area of a Triangle
19. Add the exponents and keep the same base
Counting the Possibilities
Adding and Subtracting monomials
The 5-12-13 Triangle
Multiplying and Dividing Powers
20. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Average of Evenly Spaced Numbers
Dividing Fractions
PEMDAS
Intersection of sets
21. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Pythagorean Theorem
Average of Evenly Spaced Numbers
Parallel Lines and Transversals
Setting up a Ratio
22. Volume of a Cylinder = pr^2h
Finding the midpoint
Counting the Possibilities
Solving a Quadratic Equation
Volume of a Cylinder
23. 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
Characteristics of a Parallelogram
Similar Triangles
Relative Primes
24. Sum=(Average) x (Number of Terms)
Solving a Proportion
Solving an Inequality
Using the Average to Find the Sum
Similar Triangles
25. To divide fractions - invert the second one and multiply
Simplifying Square Roots
Dividing Fractions
Even/Odd
Relative Primes
26. you can add/subtract when the part under the radical is the same
Union of Sets
Using an Equation to Find the Slope
Adding and Subtracting Roots
Circumference of a Circle
27. 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
Determining Absolute Value
Solving a Quadratic Equation
Simplifying Square Roots
Area of a Triangle
28. 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
Using the Average to Find the Sum
Prime Factorization
Using an Equation to Find the Slope
Interior and Exterior Angles of a Triangle
29. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Rate
Using the Average to Find the Sum
Comparing Fractions
30. 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
Using the Average to Find the Sum
Area of a Triangle
Similar Triangles
Repeating Decimal
31. 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 Subtraction Polynomials
Finding the Original Whole
Reciprocal
Counting Consecutive Integers
32. 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
Triangle Inequality Theorem
Circumference of a Circle
Using Two Points to Find the Slope
Percent Increase and Decrease
33. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Using an Equation to Find the Slope
Isosceles and Equilateral triangles
Direct and Inverse Variation
Setting up a Ratio
34. 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
Direct and Inverse Variation
Characteristics of a Parallelogram
Counting Consecutive Integers
Multiplying Fractions
35. 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
Area of a Triangle
Counting Consecutive Integers
Determining Absolute Value
36. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Multiples of 3 and 9
Parallel Lines and Transversals
Multiplying and Dividing Roots
Finding the Distance Between Two Points
37. 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
Using Two Points to Find the Slope
(Least) Common Multiple
Rate
Characteristics of a Square
38. Probability= Favorable Outcomes/Total Possible Outcomes
Probability
Area of a Triangle
Evaluating an Expression
Average Rate
39. 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
Average of Evenly Spaced Numbers
Isosceles and Equilateral triangles
Adding and Subtraction Polynomials
Characteristics of a Square
40. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Percent Formula
Finding the Distance Between Two Points
Solving a Quadratic Equation
Repeating Decimal
41. 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
Mixed Numbers and Improper Fractions
Solving a Proportion
Dividing Fractions
Triangle Inequality Theorem
42. 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
Union of Sets
Prime Factorization
Reciprocal
43. Surface Area = 2lw + 2wh + 2lh
Repeating Decimal
The 5-12-13 Triangle
Volume of a Cylinder
Surface Area of a Rectangular Solid
44. To multiply fractions - multiply the numerators and multiply the denominators
Circumference of a Circle
Multiplying/Dividing Signed Numbers
Multiplying Fractions
Combined Percent Increase and Decrease
45. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Average of Evenly Spaced Numbers
Multiplying/Dividing Signed Numbers
Characteristics of a Parallelogram
Volume of a Rectangular Solid
46. 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
Multiplying Fractions
Using an Equation to Find an Intercept
Simplifying Square Roots
The 3-4-5 Triangle
47. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Length of an Arc
Circumference of a Circle
Evaluating an Expression
Percent Formula
48. The largest factor that two or more numbers have in common.
Average Rate
Circumference of a Circle
Greatest Common Factor
Factor/Multiple
49. Factor out the perfect squares
Percent Formula
Simplifying Square Roots
Volume of a Rectangular Solid
Prime Factorization
50. To find the reciprocal of a fraction switch the numerator and the denominator
Solving a System of Equations
Reciprocal
Average Rate
Adding and Subtraction Polynomials
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