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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. 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
Average Rate
Intersecting Lines
Multiplying Monomials
2. 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
Percent Formula
Adding and Subtracting Roots
Solving a Proportion
The 3-4-5 Triangle
3. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Using Two Points to Find the Slope
Rate
Remainders
Finding the Distance Between Two Points
4. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Triangle Inequality Theorem
Using an Equation to Find the Slope
Pythagorean Theorem
Multiplying/Dividing Signed Numbers
5. Probability= Favorable Outcomes/Total Possible Outcomes
Probability
Direct and Inverse Variation
Union of Sets
Part-to-Part Ratios and Part-to-Whole Ratios
6. 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
Area of a Triangle
Multiplying and Dividing Powers
Negative Exponent and Rational Exponent
The 5-12-13 Triangle
7. 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
Number Categories
Multiplying and Dividing Roots
The 3-4-5 Triangle
8. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Factor/Multiple
Dividing Fractions
Length of an Arc
9. 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)
Circumference of a Circle
Surface Area of a Rectangular Solid
Length of an Arc
Area of a Sector
10. Volume of a Cylinder = pr^2h
Interior and Exterior Angles of a Triangle
Volume of a Cylinder
Reciprocal
Circumference of a Circle
11. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Solving a Quadratic Equation
Setting up a Ratio
Determining Absolute Value
Using the Average to Find the Sum
12. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Multiplying/Dividing Signed Numbers
Determining Absolute Value
Solving an Inequality
Probability
13. 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
Pythagorean Theorem
Average of Evenly Spaced Numbers
Average Rate
14. (average of the x coordinates - average of the y coordinates)
Tangency
Finding the midpoint
Factor/Multiple
Characteristics of a Rectangle
15. 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
Characteristics of a Square
Multiples of 3 and 9
Negative Exponent and Rational Exponent
Adding/Subtracting Signed Numbers
16. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Rate
Probability
Finding the Distance Between Two Points
Tangency
17. Part = Percent x Whole
Average Rate
Percent Formula
Similar Triangles
Relative Primes
18. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110
Combined Percent Increase and Decrease
Finding the Distance Between Two Points
Using an Equation to Find an Intercept
Evaluating an Expression
19. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Evaluating an Expression
Intersecting Lines
Solving a System of Equations
Finding the midpoint
20. The smallest multiple (other than zero) that two or more numbers have in common.
Median and Mode
(Least) Common Multiple
Adding and Subtraction Polynomials
Comparing Fractions
21. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Negative Exponent and Rational Exponent
Interior Angles of a Polygon
Identifying the Parts and the Whole
Reducing Fractions
22. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Percent Formula
Adding/Subtracting Fractions
Interior and Exterior Angles of a Triangle
The 3-4-5 Triangle
23. Domain: all possible values of x for a function range: all possible outputs of a function
Intersecting Lines
Part-to-Part Ratios and Part-to-Whole Ratios
Average Rate
Domain and Range of a Function
24. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Interior and Exterior Angles of a Triangle
Counting Consecutive Integers
Union of Sets
Volume of a Cylinder
25. To multiply fractions - multiply the numerators and multiply the denominators
Adding and Subtraction Polynomials
Identifying the Parts and the Whole
Multiples of 3 and 9
Multiplying Fractions
26. Add the exponents and keep the same base
Union of Sets
Simplifying Square Roots
Average Rate
Multiplying and Dividing Powers
27. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Solving an Inequality
Reducing Fractions
Multiplying and Dividing Powers
Part-to-Part Ratios and Part-to-Whole Ratios
28. 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
Area of a Triangle
Triangle Inequality Theorem
Identifying the Parts and the Whole
Isosceles and Equilateral triangles
29. 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
Negative Exponent and Rational Exponent
Determining Absolute Value
Relative Primes
30. you can add/subtract when the part under the radical is the same
Adding and Subtracting Roots
Using Two Points to Find the Slope
Prime Factorization
Pythagorean Theorem
31. The whole # left over after division
Characteristics of a Square
Using Two Points to Find the Slope
Remainders
Parallel Lines and Transversals
32. A square is a rectangle with four equal sides; Area of Square = side*side
Union of Sets
Multiples of 3 and 9
Greatest Common Factor
Characteristics of a Square
33. 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
Interior and Exterior Angles of a Triangle
Greatest Common Factor
Counting the Possibilities
Using an Equation to Find an Intercept
34. 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)
Negative Exponent and Rational Exponent
Length of an Arc
The 5-12-13 Triangle
Reciprocal
35. Surface Area = 2lw + 2wh + 2lh
Using an Equation to Find an Intercept
Surface Area of a Rectangular Solid
Using Two Points to Find the Slope
Average Rate
36. 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
Average of Evenly Spaced Numbers
Evaluating an Expression
(Least) Common Multiple
37. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Adding and Subtracting monomials
Circumference of a Circle
Finding the Distance Between Two Points
Multiplying Monomials
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
Characteristics of a Rectangle
Finding the Original Whole
Repeating Decimal
Reducing Fractions
39. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Setting up a Ratio
Multiples of 3 and 9
Intersection of sets
Number Categories
40. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Isosceles and Equilateral triangles
Probability
Tangency
Factor/Multiple
41. pr^2
Characteristics of a Parallelogram
Area of a Circle
Direct and Inverse Variation
Interior and Exterior Angles of a Triangle
42. To divide fractions - invert the second one and multiply
Evaluating an Expression
Domain and Range of a Function
Characteristics of a Square
Dividing Fractions
43. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Using an Equation to Find the Slope
Pythagorean Theorem
Volume of a Rectangular Solid
Interior and Exterior Angles of a Triangle
44. 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
Finding the Missing Number
Negative Exponent and Rational Exponent
(Least) Common Multiple
Adding/Subtracting Signed Numbers
45. 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 and Dividing Powers
Adding/Subtracting Fractions
Using an Equation to Find an Intercept
The 5-12-13 Triangle
46. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Function - Notation - and Evaulation
Counting the Possibilities
Average Formula -
Adding and Subtraction Polynomials
47. 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
The 5-12-13 Triangle
Determining Absolute Value
Simplifying Square Roots
Characteristics of a Parallelogram
48. 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
Even/Odd
Function - Notation - and Evaulation
The 5-12-13 Triangle
Multiples of 2 and 4
49. 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
Relative Primes
Probability
Reciprocal
50. For all right triangles: a^2+b^2=c^2
Interior Angles of a Polygon
Reciprocal
Factor/Multiple
Pythagorean Theorem