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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
.
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. you can add/subtract when the part under the radical is the same
Counting the Possibilities
Remainders
Adding and Subtracting Roots
Direct and Inverse Variation
2. 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
Relative Primes
Median and Mode
PEMDAS
Adding/Subtracting Signed Numbers
3. 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
Adding/Subtracting Fractions
Counting the Possibilities
Solving a Quadratic Equation
Counting Consecutive Integers
4. Subtract the smallest from the largest and add 1
Repeating Decimal
Comparing Fractions
Counting Consecutive Integers
Isosceles and Equilateral triangles
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
Multiplying Fractions
Function - Notation - and Evaulation
Number Categories
Probability
6. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Characteristics of a Parallelogram
Solving a Quadratic Equation
Finding the Missing Number
7. 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
Finding the Original Whole
Interior Angles of a Polygon
Relative Primes
8. 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
Parallel Lines and Transversals
Counting the Possibilities
Using an Equation to Find an Intercept
Function - Notation - and Evaulation
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
Median and Mode
The 5-12-13 Triangle
Characteristics of a Rectangle
Finding the Missing Number
10. 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
Length of an Arc
Volume of a Cylinder
Factor/Multiple
11. 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
Average Rate
Solving a System of Equations
Adding/Subtracting Signed Numbers
Identifying the Parts and the Whole
12. 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
Interior and Exterior Angles of a Triangle
Adding and Subtraction Polynomials
Average Formula -
Combined Percent Increase and Decrease
13. To multiply fractions - multiply the numerators and multiply the denominators
Surface Area of a Rectangular Solid
Multiplying Fractions
Raising Powers to Powers
Repeating Decimal
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
The 3-4-5 Triangle
Finding the Distance Between Two Points
Finding the midpoint
Part-to-Part Ratios and Part-to-Whole Ratios
15. 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
Simplifying Square Roots
Negative Exponent and Rational Exponent
Solving a Quadratic Equation
16. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Rate
Using Two Points to Find the Slope
Average of Evenly Spaced Numbers
Adding/Subtracting Fractions
17. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Solving an Inequality
Determining Absolute Value
Intersection of sets
Union of Sets
18. Volume of a Cylinder = pr^2h
Relative Primes
Volume of a Cylinder
Counting Consecutive Integers
Pythagorean Theorem
19. To divide fractions - invert the second one and multiply
Finding the Missing Number
Reducing Fractions
Rate
Dividing Fractions
20. The smallest multiple (other than zero) that two or more numbers have in common.
Intersection of sets
The 3-4-5 Triangle
Average Formula -
(Least) Common Multiple
21. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Reciprocal
Union of Sets
Surface Area of a Rectangular Solid
PEMDAS
22. 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)
Identifying the Parts and the Whole
Interior Angles of a Polygon
Using an Equation to Find an Intercept
Length of an Arc
23. For all right triangles: a^2+b^2=c^2
Reciprocal
Adding/Subtracting Fractions
Finding the Original Whole
Pythagorean Theorem
24. 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
Prime Factorization
Finding the Original Whole
Direct and Inverse Variation
Negative Exponent and Rational Exponent
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
Function - Notation - and Evaulation
Using an Equation to Find an Intercept
(Least) Common Multiple
Adding and Subtracting monomials
26. 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
Median and Mode
Multiplying/Dividing Signed Numbers
Finding the Original Whole
27. Sum=(Average) x (Number of Terms)
Identifying the Parts and the Whole
Using the Average to Find the Sum
Raising Powers to Powers
Interior Angles of a Polygon
28. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Setting up a Ratio
PEMDAS
Comparing Fractions
Solving an Inequality
29. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Exponential Growth
Tangency
Direct and Inverse Variation
Characteristics of a Square
30. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Multiples of 3 and 9
Reciprocal
Factor/Multiple
Domain and Range of a Function
31. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Finding the Distance Between Two Points
Multiples of 2 and 4
Volume of a Rectangular Solid
Using an Equation to Find the Slope
32. 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
Tangency
Characteristics of a Rectangle
Interior and Exterior Angles of a Triangle
33. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Multiplying and Dividing Roots
PEMDAS
Adding/Subtracting Signed Numbers
Percent Increase and Decrease
34. 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
PEMDAS
Triangle Inequality Theorem
Solving a Quadratic Equation
Using an Equation to Find the Slope
35. 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
Adding/Subtracting Signed Numbers
Repeating Decimal
Raising Powers to Powers
Finding the Missing Number
36. 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
Using Two Points to Find the Slope
Prime Factorization
Intersecting Lines
37. 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
PEMDAS
Average Formula -
Interior and Exterior Angles of a Triangle
Surface Area of a Rectangular Solid
38. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Negative Exponent and Rational Exponent
Finding the midpoint
Intersection of sets
Characteristics of a Rectangle
39. 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
Determining Absolute Value
Percent Increase and Decrease
Finding the Original Whole
Using the Average to Find the Sum
40. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Union of Sets
Percent Increase and Decrease
Interior and Exterior Angles of a Triangle
Similar Triangles
41. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Union of Sets
Average of Evenly Spaced Numbers
Mixed Numbers and Improper Fractions
Counting the Possibilities
42. pr^2
Area of a Circle
Multiplying and Dividing Roots
Average Rate
Circumference of a Circle
43. 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
Multiples of 2 and 4
(Least) Common Multiple
Negative Exponent and Rational Exponent
Function - Notation - and Evaulation
44. Surface Area = 2lw + 2wh + 2lh
Average Formula -
Negative Exponent and Rational Exponent
Surface Area of a Rectangular Solid
Reciprocal
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
Solving a System of Equations
Characteristics of a Parallelogram
The 5-12-13 Triangle
Area of a Circle
46. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Dividing Fractions
Interior Angles of a Polygon
Combined Percent Increase and Decrease
47. 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 Signed Numbers
Area of a Triangle
Using Two Points to Find the Slope
Area of a Circle
48. 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
Multiplying Fractions
Finding the Missing Number
Comparing Fractions
49. Combine like terms
Adding and Subtraction Polynomials
Solving a System of Equations
Number Categories
Median and Mode
50. Multiply the exponents
Negative Exponent and Rational Exponent
Interior and Exterior Angles of a Triangle
Median and Mode
Raising Powers to Powers