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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. 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
Counting the Possibilities
Adding and Subtracting monomials
Multiplying Monomials
2. (average of the x coordinates - average of the y coordinates)
Intersection of sets
Average of Evenly Spaced Numbers
Finding the midpoint
Identifying the Parts and the Whole
3. 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
Evaluating an Expression
Solving a System of Equations
Adding/Subtracting Fractions
4. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Intersecting Lines
Average Rate
Surface Area of a Rectangular Solid
Volume of a Rectangular Solid
5. Surface Area = 2lw + 2wh + 2lh
Average Formula -
Finding the midpoint
Adding/Subtracting Fractions
Surface Area of a Rectangular Solid
6. To find the reciprocal of a fraction switch the numerator and the denominator
Part-to-Part Ratios and Part-to-Whole Ratios
Repeating Decimal
Reciprocal
Setting up a Ratio
7. 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
Raising Powers to Powers
Area of a Triangle
Using an Equation to Find an Intercept
Area of a Circle
8. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Interior Angles of a Polygon
(Least) Common Multiple
Percent Increase and Decrease
Identifying the Parts and the Whole
9. 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
Characteristics of a Square
Length of an Arc
Repeating Decimal
Evaluating an Expression
10. 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
Circumference of a Circle
Solving a Quadratic Equation
Solving an Inequality
11. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Intersecting Lines
Function - Notation - and Evaulation
Even/Odd
(Least) Common Multiple
12. The largest factor that two or more numbers have in common.
Dividing Fractions
Greatest Common Factor
Using an Equation to Find an Intercept
Median and Mode
13. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Finding the Distance Between Two Points
Probability
Multiplying and Dividing Roots
Isosceles and Equilateral triangles
14. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Domain and Range of a Function
Greatest Common Factor
Similar Triangles
Rate
15. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Solving an Inequality
Pythagorean Theorem
Multiplying Monomials
Length of an Arc
16. 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
Adding and Subtraction Polynomials
Area of a Circle
Using an Equation to Find the Slope
17. Multiply the exponents
Relative Primes
Domain and Range of a Function
Counting the Possibilities
Raising Powers to Powers
18. 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
Union of Sets
Solving a System of Equations
The 5-12-13 Triangle
Finding the Original Whole
19. 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
Rate
Function - Notation - and Evaulation
Adding/Subtracting Fractions
Circumference of a Circle
20. 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
Average Formula -
Percent Formula
Repeating Decimal
Part-to-Part Ratios and Part-to-Whole Ratios
21. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Intersection of sets
Determining Absolute Value
Finding the Original Whole
Multiples of 2 and 4
22. Factor out the perfect squares
Circumference of a Circle
Exponential Growth
Simplifying Square Roots
Relative Primes
23. The smallest multiple (other than zero) that two or more numbers have in common.
Combined Percent Increase and Decrease
Identifying the Parts and the Whole
Union of Sets
(Least) Common Multiple
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
Comparing Fractions
Circumference of a Circle
Direct and Inverse Variation
Setting up a Ratio
25. Combine equations in such a way that one of the variables cancel out
Multiples of 2 and 4
Solving a Quadratic Equation
Using the Average to Find the Sum
Solving a System of Equations
26. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Direct and Inverse Variation
Solving a System of Equations
Parallel Lines and Transversals
27. 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
Using an Equation to Find the Slope
Function - Notation - and Evaulation
Multiplying Monomials
28. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Exponential Growth
Solving a Proportion
Evaluating an Expression
29. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Rate
Solving a Proportion
Prime Factorization
Median and Mode
30. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Area of a Circle
Greatest Common Factor
The 5-12-13 Triangle
31. 2pr
Counting the Possibilities
Characteristics of a Square
Factor/Multiple
Circumference of a Circle
32. 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
Counting Consecutive Integers
Factor/Multiple
Percent Increase and Decrease
Isosceles and Equilateral triangles
33. 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
Tangency
Prime Factorization
Multiplying/Dividing Signed Numbers
Solving a Quadratic Equation
34. To divide fractions - invert the second one and multiply
Intersection of sets
Characteristics of a Rectangle
Length of an Arc
Dividing Fractions
35. 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
Adding and Subtracting Roots
Negative Exponent and Rational Exponent
Counting the Possibilities
Multiples of 3 and 9
36. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Using an Equation to Find an Intercept
Finding the Original Whole
Adding and Subtracting monomials
Evaluating an Expression
37. 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
Average Formula -
Adding/Subtracting Signed Numbers
Function - Notation - and Evaulation
Relative Primes
38. 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
The 5-12-13 Triangle
Finding the midpoint
Counting the Possibilities
Relative Primes
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
Triangle Inequality Theorem
Combined Percent Increase and Decrease
Multiples of 3 and 9
Area of a Sector
40. 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
Setting up a Ratio
Intersecting Lines
Mixed Numbers and Improper Fractions
Using Two Points to Find the Slope
41. 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
Average Formula -
Negative Exponent and Rational Exponent
Number Categories
Rate
42. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Intersection of sets
Identifying the Parts and the Whole
Tangency
Characteristics of a Rectangle
43. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Triangle Inequality Theorem
Multiplying/Dividing Signed Numbers
Solving an Inequality
44. Change in y/ change in x rise/run
Multiplying and Dividing Powers
Determining Absolute Value
Using Two Points to Find the Slope
Finding the Missing Number
45. For all right triangles: a^2+b^2=c^2
Solving a Proportion
Pythagorean Theorem
Union of Sets
Counting the Possibilities
46. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Multiples of 3 and 9
Setting up a Ratio
Median and Mode
Average of Evenly Spaced Numbers
47. Add the exponents and keep the same base
Simplifying Square Roots
Counting the Possibilities
Multiplying and Dividing Powers
Median and Mode
48. 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
Domain and Range of a Function
Adding and Subtracting Roots
Mixed Numbers and Improper Fractions
Finding the Missing Number
49. To multiply fractions - multiply the numerators and multiply the denominators
Average of Evenly Spaced Numbers
Circumference of a Circle
Multiplying Fractions
Reciprocal
50. 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
Relative Primes
Counting the Possibilities
Multiplying/Dividing Signed Numbers
Pythagorean Theorem