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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.
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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. Add the exponents and keep the same base
(Least) Common Multiple
Adding/Subtracting Signed Numbers
Multiplying and Dividing Powers
Dividing Fractions
2. Volume of a Cylinder = pr^2h
Solving a Quadratic Equation
Finding the Missing Number
Volume of a Cylinder
Direct and Inverse Variation
3. Surface Area = 2lw + 2wh + 2lh
Area of a Triangle
Surface Area of a Rectangular Solid
Triangle Inequality Theorem
Adding/Subtracting Signed Numbers
4. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Multiplying and Dividing Powers
Raising Powers to Powers
Prime Factorization
Using an Equation to Find the Slope
5. 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
Finding the Original Whole
(Least) Common Multiple
Combined Percent Increase and Decrease
Adding and Subtracting monomials
6. 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
Characteristics of a Square
Adding and Subtraction Polynomials
Comparing Fractions
Rate
7. Part = Percent x Whole
Adding and Subtraction Polynomials
Area of a Triangle
Percent Formula
Multiplying/Dividing Signed Numbers
8. The smallest multiple (other than zero) that two or more numbers have in common.
Isosceles and Equilateral triangles
Rate
(Least) Common Multiple
Repeating Decimal
9. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Prime Factorization
Area of a Sector
Characteristics of a Square
Solving an Inequality
10. 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
Interior and Exterior Angles of a Triangle
Solving a Proportion
Domain and Range of a Function
11. 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
Isosceles and Equilateral triangles
Reducing Fractions
Finding the Missing Number
Evaluating an Expression
12. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Combined Percent Increase and Decrease
Adding/Subtracting Signed Numbers
Determining Absolute Value
Area of a Triangle
13. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Simplifying Square Roots
Probability
Evaluating an Expression
Multiplying and Dividing Powers
14. 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
Negative Exponent and Rational Exponent
Identifying the Parts and the Whole
Isosceles and Equilateral triangles
Area of a Triangle
15. 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.
Average Rate
Multiplying and Dividing Powers
Mixed Numbers and Improper Fractions
Number Categories
16. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Interior Angles of a Polygon
Percent Increase and Decrease
Multiples of 3 and 9
17. 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
Raising Powers to Powers
Isosceles and Equilateral triangles
Adding/Subtracting Signed Numbers
Average Rate
18. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Adding and Subtracting monomials
Pythagorean Theorem
Multiplying and Dividing Roots
(Least) Common Multiple
19. Probability= Favorable Outcomes/Total Possible Outcomes
Volume of a Rectangular Solid
Evaluating an Expression
Probability
Multiplying and Dividing Powers
20. 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
Volume of a Cylinder
Reducing Fractions
Mixed Numbers and Improper Fractions
The 5-12-13 Triangle
21. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Characteristics of a Parallelogram
Part-to-Part Ratios and Part-to-Whole Ratios
Even/Odd
22. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Using an Equation to Find the Slope
Domain and Range of a Function
Multiplying Monomials
23. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Intersecting Lines
Percent Formula
Volume of a Rectangular Solid
Characteristics of a Parallelogram
24. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Multiples of 2 and 4
Counting the Possibilities
Raising Powers to Powers
25. Change in y/ change in x rise/run
Reducing Fractions
Using Two Points to Find the Slope
Volume of a Cylinder
(Least) Common Multiple
26. 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
Multiplying Fractions
Percent Increase and Decrease
Finding the Distance Between Two Points
Relative Primes
27. Combine like terms
Union of Sets
Even/Odd
Adding and Subtraction Polynomials
Combined Percent Increase and Decrease
28. 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
Combined Percent Increase and Decrease
Characteristics of a Rectangle
Even/Odd
Triangle Inequality Theorem
29. 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
Interior and Exterior Angles of a Triangle
Function - Notation - and Evaulation
Factor/Multiple
30. Subtract the smallest from the largest and add 1
Greatest Common Factor
Counting Consecutive Integers
Finding the Original Whole
Negative Exponent and Rational Exponent
31. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Union of Sets
Pythagorean Theorem
Volume of a Cylinder
32. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Multiplying Fractions
Adding and Subtracting monomials
PEMDAS
Similar Triangles
33. 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
Interior and Exterior Angles of a Triangle
Function - Notation - and Evaulation
Using Two Points to Find the Slope
Area of a Triangle
34. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying/Dividing Signed Numbers
Intersection of sets
Multiplying Monomials
Adding/Subtracting Fractions
35. To solve a proportion - cross multiply
Number Categories
Interior and Exterior Angles of a Triangle
Solving a Proportion
Greatest Common Factor
36. (average of the x coordinates - average of the y coordinates)
Area of a Circle
Interior Angles of a Polygon
Finding the midpoint
Similar Triangles
37. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Relative Primes
Multiplying/Dividing Signed Numbers
Finding the Distance Between Two Points
Interior Angles of a Polygon
38. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
PEMDAS
Average Rate
Prime Factorization
Adding/Subtracting Fractions
39. Multiply the exponents
Raising Powers to Powers
Characteristics of a Rectangle
Adding/Subtracting Fractions
Using an Equation to Find the Slope
40. For all right triangles: a^2+b^2=c^2
Adding and Subtracting monomials
Pythagorean Theorem
The 5-12-13 Triangle
Solving a Proportion
41. pr^2
Area of a Circle
Remainders
Using Two Points to Find the Slope
Finding the Original Whole
42. 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
Solving a Proportion
Adding and Subtraction Polynomials
Using an Equation to Find an Intercept
Identifying the Parts and the Whole
43. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Raising Powers to Powers
Multiples of 3 and 9
Solving an Inequality
Finding the Missing Number
44. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Exponential Growth
Adding and Subtraction Polynomials
Reducing Fractions
PEMDAS
45. To find the reciprocal of a fraction switch the numerator and the denominator
Multiplying/Dividing Signed Numbers
Similar Triangles
Domain and Range of a Function
Reciprocal
46. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg
Mixed Numbers and Improper Fractions
Using an Equation to Find the Slope
Characteristics of a Square
Isosceles and Equilateral triangles
47. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Tangency
Using an Equation to Find the Slope
Parallel Lines and Transversals
Characteristics of a Rectangle
48. 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
Dividing Fractions
Using an Equation to Find an Intercept
Average Rate
Multiplying/Dividing Signed Numbers
49. To multiply fractions - multiply the numerators and multiply the denominators
Solving a Quadratic Equation
Multiplying Fractions
Area of a Circle
The 3-4-5 Triangle
50. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Identifying the Parts and the Whole
Even/Odd
Multiplying Fractions
Intersecting Lines
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