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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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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. 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
Dividing Fractions
Multiplying Fractions
2. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Multiples of 2 and 4
Union of Sets
Percent Formula
Adding and Subtracting monomials
3. 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
Identifying the Parts and the Whole
Factor/Multiple
Setting up a Ratio
Number Categories
4. 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
Determining Absolute Value
Prime Factorization
The 3-4-5 Triangle
The 5-12-13 Triangle
5. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Prime Factorization
Using Two Points to Find the Slope
Negative Exponent and Rational Exponent
Adding/Subtracting Signed Numbers
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
Intersecting Lines
Relative Primes
Area of a Triangle
Counting the Possibilities
7. Probability= Favorable Outcomes/Total Possible Outcomes
Probability
Multiples of 2 and 4
Solving a Proportion
Median and Mode
8. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Dividing Fractions
The 3-4-5 Triangle
Adding/Subtracting Fractions
9. 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
Isosceles and Equilateral triangles
Percent Increase and Decrease
Finding the midpoint
Interior and Exterior Angles of a Triangle
10. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Finding the Original Whole
Solving a System of Equations
Percent Increase and Decrease
11. For all right triangles: a^2+b^2=c^2
Using the Average to Find the Sum
Area of a Sector
Pythagorean Theorem
Simplifying Square Roots
12. Multiply the exponents
Dividing Fractions
Solving a System of Equations
PEMDAS
Raising Powers to Powers
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.
Relative Primes
Characteristics of a Square
Solving an Inequality
Number Categories
14. 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
Adding and Subtracting monomials
Parallel Lines and Transversals
Average Rate
15. 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
Volume of a Rectangular Solid
PEMDAS
16. 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
Multiplying Monomials
Solving a Proportion
Negative Exponent and Rational Exponent
Intersecting Lines
17. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Multiplying and Dividing Roots
Using Two Points to Find the Slope
Union of Sets
18. A square is a rectangle with four equal sides; Area of Square = side*side
Volume of a Rectangular Solid
Characteristics of a Square
Combined Percent Increase and Decrease
Relative Primes
19. 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)
Length of an Arc
Even/Odd
Area of a Triangle
Solving a System of Equations
20. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Interior Angles of a Polygon
Multiplying Monomials
Counting Consecutive Integers
Similar Triangles
21. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Intersecting Lines
Adding and Subtracting monomials
Identifying the Parts and the Whole
Determining Absolute Value
22. 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
Finding the midpoint
Adding/Subtracting Signed Numbers
Greatest Common Factor
Factor/Multiple
23. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Reducing Fractions
Percent Increase and Decrease
Intersection of sets
Solving a System of Equations
24. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
(Least) Common Multiple
Average Formula -
Counting Consecutive Integers
Length of an Arc
25. To divide fractions - invert the second one and multiply
Multiples of 2 and 4
Characteristics of a Parallelogram
Dividing Fractions
Adding and Subtracting monomials
26. 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
Combined Percent Increase and Decrease
Finding the Distance Between Two Points
Using Two Points to Find the Slope
27. 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
Adding and Subtracting monomials
Tangency
Adding and Subtraction Polynomials
Combined Percent Increase and Decrease
28. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Exponential Growth
The 3-4-5 Triangle
Multiples of 2 and 4
Volume of a Cylinder
29. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Distance Between Two Points
Counting Consecutive Integers
Raising Powers to Powers
Dividing Fractions
30. Change in y/ change in x rise/run
Finding the midpoint
Using Two Points to Find the Slope
PEMDAS
Combined Percent Increase and Decrease
31. 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
Repeating Decimal
Rate
Remainders
Surface Area of a Rectangular Solid
32. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Counting Consecutive Integers
Interior Angles of a Polygon
Area of a Sector
Volume of a Cylinder
33. 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
Multiplying Fractions
Surface Area of a Rectangular Solid
Finding the Distance Between Two Points
The 3-4-5 Triangle
34. you can add/subtract when the part under the radical is the same
Finding the Missing Number
Interior Angles of a Polygon
Adding and Subtracting Roots
Factor/Multiple
35. 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
Function - Notation - and Evaulation
Adding and Subtracting monomials
Using an Equation to Find an Intercept
Interior Angles of a Polygon
36. 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
Counting the Possibilities
Length of an Arc
Using an Equation to Find an Intercept
Average Formula -
37. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Remainders
Multiplying and Dividing Roots
Interior and Exterior Angles of a Triangle
Comparing Fractions
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
Area of a Circle
Percent Formula
Finding the Original Whole
Setting up a Ratio
39. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Solving an Inequality
PEMDAS
Parallel Lines and Transversals
Characteristics of a Parallelogram
40. 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
Similar Triangles
Solving an Inequality
(Least) Common Multiple
Multiplying Monomials
41. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Multiplying and Dividing Roots
Prime Factorization
Multiples of 2 and 4
Parallel Lines and Transversals
42. Combine equations in such a way that one of the variables cancel out
Function - Notation - and Evaulation
Triangle Inequality Theorem
Multiplying and Dividing Powers
Solving a System of Equations
43. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Multiples of 2 and 4
Part-to-Part Ratios and Part-to-Whole Ratios
Adding/Subtracting Fractions
Relative Primes
44. 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
Percent Formula
Parallel Lines and Transversals
Direct and Inverse Variation
Greatest Common Factor
45. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Number Categories
Multiplying and Dividing Roots
Multiplying Fractions
Intersecting Lines
46. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Multiplying and Dividing Roots
Median and Mode
Solving a Proportion
47. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Median and Mode
Characteristics of a Parallelogram
Average Formula -
Area of a Triangle
48. The largest factor that two or more numbers have in common.
Exponential Growth
Percent Increase and Decrease
Greatest Common Factor
Average Rate
49. 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
Surface Area of a Rectangular Solid
Average Formula -
Tangency
50. Part = Percent x Whole
Prime Factorization
Percent Formula
The 3-4-5 Triangle
Multiplying and Dividing Powers