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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. 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
Average of Evenly Spaced Numbers
Similar Triangles
Length of an Arc
2. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Prime Factorization
Characteristics of a Square
Area of a Triangle
3. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Percent Increase and Decrease
Multiples of 3 and 9
Area of a Circle
Average Rate
4. 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
Multiples of 2 and 4
Factor/Multiple
Volume of a Cylinder
5. 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
The 5-12-13 Triangle
Function - Notation - and Evaulation
Direct and Inverse Variation
Adding/Subtracting Fractions
6. The whole # left over after division
Remainders
Part-to-Part Ratios and Part-to-Whole Ratios
Rate
Prime Factorization
7. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Percent Formula
Solving an Inequality
Prime Factorization
8. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Multiples of 3 and 9
Multiples of 2 and 4
Area of a Sector
Interior Angles of a Polygon
9. 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
Average of Evenly Spaced Numbers
Triangle Inequality Theorem
Multiples of 2 and 4
10. Change in y/ change in x rise/run
Interior Angles of a Polygon
Greatest Common Factor
Using Two Points to Find the Slope
Determining Absolute Value
11. 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
Comparing Fractions
Combined Percent Increase and Decrease
Multiplying and Dividing Roots
Finding the midpoint
12. Volume of a Cylinder = pr^2h
Interior and Exterior Angles of a Triangle
Adding and Subtracting monomials
Volume of a Cylinder
Volume of a Rectangular Solid
13. 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
Multiples of 3 and 9
Combined Percent Increase and Decrease
Greatest Common Factor
Exponential Growth
14. pr^2
Interior Angles of a Polygon
Area of a Circle
Direct and Inverse Variation
Relative Primes
15. 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
Evaluating an Expression
Mixed Numbers and Improper Fractions
Multiples of 2 and 4
16. 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
Domain and Range of a Function
Volume of a Rectangular Solid
Adding/Subtracting Signed Numbers
Rate
17. you can add/subtract when the part under the radical is the same
Volume of a Cylinder
Finding the Distance Between Two Points
Adding and Subtracting Roots
Reciprocal
18. Factor out the perfect squares
Simplifying Square Roots
Intersection of sets
Multiples of 2 and 4
Greatest Common Factor
19. 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
Finding the Missing Number
Identifying the Parts and the Whole
Reciprocal
Multiples of 3 and 9
20. 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
Solving a System of Equations
The 5-12-13 Triangle
Negative Exponent and Rational Exponent
Greatest Common Factor
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
Similar Triangles
Relative Primes
Multiples of 3 and 9
Isosceles and Equilateral triangles
22. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Using an Equation to Find the Slope
Finding the Distance Between Two Points
Area of a Circle
Intersecting Lines
23. To solve a proportion - cross multiply
Finding the Original Whole
Average of Evenly Spaced Numbers
Solving a Proportion
Circumference of a Circle
24. 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
Solving an Inequality
Length of an Arc
Negative Exponent and Rational Exponent
Characteristics of a Parallelogram
25. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Area of a Triangle
Finding the Missing Number
Adding and Subtracting monomials
Adding/Subtracting Signed Numbers
26. 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
Solving a Quadratic Equation
Using Two Points to Find the Slope
The 5-12-13 Triangle
27. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Reducing Fractions
Multiplying and Dividing Roots
Relative Primes
Average Formula -
28. 2pr
PEMDAS
(Least) Common Multiple
Interior and Exterior Angles of a Triangle
Circumference of a Circle
29. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Using Two Points to Find the Slope
Domain and Range of a Function
Rate
30. 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
Multiplying/Dividing Signed Numbers
Average of Evenly Spaced Numbers
Solving a Proportion
Repeating Decimal
31. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Mixed Numbers and Improper Fractions
Using Two Points to Find the Slope
Determining Absolute Value
32. 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
Finding the Distance Between Two Points
Adding and Subtraction Polynomials
Characteristics of a Parallelogram
Rate
33. 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 Fractions
Adding/Subtracting Signed Numbers
Length of an Arc
Factor/Multiple
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)
Multiplying Monomials
PEMDAS
Exponential Growth
Length of an Arc
35. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Evaluating an Expression
Length of an Arc
Finding the Distance Between Two Points
Tangency
36. 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
Negative Exponent and Rational Exponent
Finding the Original Whole
Circumference of a Circle
37. 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
Repeating Decimal
Multiples of 3 and 9
The 3-4-5 Triangle
Greatest Common Factor
38. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Adding and Subtracting Roots
Volume of a Cylinder
Using an Equation to Find the Slope
Determining Absolute Value
39. The largest factor that two or more numbers have in common.
PEMDAS
Reducing Fractions
Finding the Missing Number
Greatest Common Factor
40. 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)
Adding and Subtracting Roots
Area of a Sector
Intersecting Lines
Remainders
41. Sum=(Average) x (Number of Terms)
Determining Absolute Value
Using Two Points to Find the Slope
Using the Average to Find the Sum
Characteristics of a Rectangle
42. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Solving a Quadratic Equation
Volume of a Rectangular Solid
Isosceles and Equilateral triangles
Domain and Range of a Function
43. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Isosceles and Equilateral triangles
Prime Factorization
Comparing Fractions
Evaluating an Expression
44. For all right triangles: a^2+b^2=c^2
Intersection of sets
Multiplying and Dividing Powers
Multiplying and Dividing Roots
Pythagorean Theorem
45. Probability= Favorable Outcomes/Total Possible Outcomes
Relative Primes
Probability
Parallel Lines and Transversals
Multiplying/Dividing Signed Numbers
46. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Domain and Range of a Function
Counting the Possibilities
Average of Evenly Spaced Numbers
Characteristics of a Square
47. To divide fractions - invert the second one and multiply
Multiplying Monomials
Percent Formula
Dividing Fractions
Percent Increase and Decrease
48. 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.
Intersecting Lines
Setting up a Ratio
Number Categories
Counting the Possibilities
49. A square is a rectangle with four equal sides; Area of Square = side*side
Median and Mode
Identifying the Parts and the Whole
Relative Primes
Characteristics of a Square
50. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Characteristics of a Parallelogram
Adding/Subtracting Fractions
Using an Equation to Find an Intercept
Remainders