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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. Subtract the smallest from the largest and add 1
Mixed Numbers and Improper Fractions
PEMDAS
Counting Consecutive Integers
Using an Equation to Find the Slope
2. 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
Domain and Range of a Function
Multiplying Monomials
Percent Formula
3. Factor out the perfect squares
Simplifying Square Roots
Multiplying Fractions
Multiplying and Dividing Powers
Greatest Common Factor
4. you can add/subtract when the part under the radical is the same
Adding and Subtracting Roots
Finding the Missing Number
Domain and Range of a Function
The 3-4-5 Triangle
5. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Using the Average to Find the Sum
Combined Percent Increase and Decrease
Average Rate
6. 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
Characteristics of a Parallelogram
Even/Odd
Average Rate
Intersection of sets
7. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Rate
Reciprocal
Evaluating an Expression
Prime Factorization
8. 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
Area of a Triangle
Solving a Quadratic Equation
Prime Factorization
9. 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
Adding and Subtraction Polynomials
Evaluating an Expression
Characteristics of a Rectangle
10. 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
Interior Angles of a Polygon
The 5-12-13 Triangle
Raising Powers to Powers
11. 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
Rate
Evaluating an Expression
Part-to-Part Ratios and Part-to-Whole Ratios
Dividing Fractions
12. Combine equations in such a way that one of the variables cancel out
Reducing Fractions
Adding/Subtracting Fractions
Solving a System of Equations
Using Two Points to Find the Slope
13. 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.
Identifying the Parts and the Whole
Number Categories
Multiplying and Dividing Roots
Union of Sets
14. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Percent Formula
Area of a Sector
Evaluating an Expression
Average Formula -
15. For all right triangles: a^2+b^2=c^2
Surface Area of a Rectangular Solid
Negative Exponent and Rational Exponent
Pythagorean Theorem
Area of a Triangle
16. To multiply fractions - multiply the numerators and multiply the denominators
Area of a Triangle
Direct and Inverse Variation
Multiplying Fractions
Simplifying Square Roots
17. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Exponential Growth
Finding the Missing Number
Average of Evenly Spaced Numbers
Similar Triangles
18. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Adding and Subtracting monomials
Multiplying/Dividing Signed Numbers
Function - Notation - and Evaulation
Union of Sets
19. The whole # left over after division
Characteristics of a Square
Remainders
Dividing Fractions
Evaluating an Expression
20. 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
Direct and Inverse Variation
Multiplying/Dividing Signed Numbers
Multiples of 2 and 4
Median and Mode
21. 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
Average Formula -
Probability
Negative Exponent and Rational Exponent
Determining Absolute Value
22. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Determining Absolute Value
Similar Triangles
(Least) Common Multiple
23. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Remainders
Counting the Possibilities
Average of Evenly Spaced Numbers
24. Change in y/ change in x rise/run
Part-to-Part Ratios and Part-to-Whole Ratios
Using Two Points to Find the Slope
Multiplying Fractions
Intersection of sets
25. 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
Finding the Missing Number
Average Rate
Direct and Inverse Variation
Multiplying Fractions
26. 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
Counting Consecutive Integers
The 5-12-13 Triangle
Solving a Proportion
Adding and Subtracting monomials
27. Add the exponents and keep the same base
Identifying the Parts and the Whole
Interior and Exterior Angles of a Triangle
Multiplying and Dividing Powers
Adding and Subtracting Roots
28. To solve an inequality do whatever is necessary to both sides to isolate the variable. When you multiply or divide both sides by a negative number you must reverse the sign
Interior and Exterior Angles of a Triangle
Reciprocal
Solving an Inequality
PEMDAS
29. Surface Area = 2lw + 2wh + 2lh
Percent Increase and Decrease
Negative Exponent and Rational Exponent
Surface Area of a Rectangular Solid
Intersecting Lines
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
Tangency
Repeating Decimal
Greatest Common Factor
Simplifying Square Roots
31. The smallest multiple (other than zero) that two or more numbers have in common.
Negative Exponent and Rational Exponent
Counting Consecutive Integers
(Least) Common Multiple
Even/Odd
32. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Multiples of 3 and 9
Reducing Fractions
Area of a Circle
Combined Percent Increase and Decrease
33. 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
Intersection of sets
Rate
Triangle Inequality Theorem
Mixed Numbers and Improper Fractions
34. To find the reciprocal of a fraction switch the numerator and the denominator
Characteristics of a Square
Relative Primes
Reciprocal
Area of a Triangle
35. 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
Even/Odd
Average Rate
Finding the Original Whole
Reciprocal
36. Volume of a Cylinder = pr^2h
Finding the Distance Between Two Points
Characteristics of a Rectangle
Volume of a Cylinder
Percent Increase and Decrease
37. Multiply the exponents
Solving a Proportion
Adding and Subtracting monomials
Function - Notation - and Evaulation
Raising Powers to Powers
38. (average of the x coordinates - average of the y coordinates)
Solving a Proportion
Finding the midpoint
The 3-4-5 Triangle
Identifying the Parts and the Whole
39. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Circumference of a Circle
Finding the Distance Between Two Points
Reducing Fractions
Greatest Common Factor
40. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Even/Odd
Evaluating an Expression
Multiples of 2 and 4
(Least) Common Multiple
41. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Relative Primes
Isosceles and Equilateral triangles
Adding and Subtracting monomials
Median and Mode
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
Evaluating an Expression
Reducing Fractions
Counting the Possibilities
43. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Median and Mode
Relative Primes
Volume of a Rectangular Solid
(Least) Common Multiple
44. 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
Negative Exponent and Rational Exponent
Multiplying and Dividing Roots
Exponential Growth
Median and Mode
45. Sum=(Average) x (Number of Terms)
Mixed Numbers and Improper Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
Using the Average to Find the Sum
Multiplying and Dividing Powers
46. 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
Union of Sets
Identifying the Parts and the Whole
Domain and Range of a Function
Volume of a Cylinder
47. Part = Percent x Whole
Raising Powers to Powers
Percent Formula
Combined Percent Increase and Decrease
Reducing Fractions
48. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Characteristics of a Square
Setting up a Ratio
Average Rate
Parallel Lines and Transversals
49. 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
Finding the Distance Between Two Points
Multiples of 2 and 4
(Least) Common Multiple
50. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Counting Consecutive Integers
Domain and Range of a Function
Area of a Triangle
PEMDAS