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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 find the reciprocal of a fraction switch the numerator and the denominator
Counting the Possibilities
Reciprocal
Factor/Multiple
Relative Primes
2. 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
Reciprocal
Using Two Points to Find the Slope
Solving a System of Equations
3. 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.
Number Categories
Average Formula -
Determining Absolute Value
Isosceles and Equilateral triangles
4. Multiply the exponents
Part-to-Part Ratios and Part-to-Whole Ratios
Adding and Subtraction Polynomials
Raising Powers to Powers
Identifying the Parts and the Whole
5. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Volume of a Rectangular Solid
Dividing Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
6. The largest factor that two or more numbers have in common.
Greatest Common Factor
Number Categories
Counting Consecutive Integers
Adding/Subtracting Fractions
7. 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
Interior and Exterior Angles of a Triangle
Mixed Numbers and Improper Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
Median and Mode
8. 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
Isosceles and Equilateral triangles
Using the Average to Find the Sum
PEMDAS
Volume of a Rectangular Solid
9. Subtract the smallest from the largest and add 1
Finding the Missing Number
Simplifying Square Roots
Counting Consecutive Integers
Using an Equation to Find an Intercept
10. 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
Multiples of 3 and 9
Using an Equation to Find an Intercept
Finding the Missing Number
Interior and Exterior Angles of a Triangle
11. 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
Mixed Numbers and Improper Fractions
Exponential Growth
Union of Sets
Isosceles and Equilateral triangles
12. 2pr
Raising Powers to Powers
Pythagorean Theorem
Circumference of a Circle
(Least) Common Multiple
13. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Volume of a Cylinder
Relative Primes
Multiples of 3 and 9
Number Categories
14. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Adding/Subtracting Fractions
Mixed Numbers and Improper Fractions
Average Formula -
Surface Area of a Rectangular Solid
15. 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
Mixed Numbers and Improper Fractions
Combined Percent Increase and Decrease
Finding the Missing Number
Finding the midpoint
16. 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
Function - Notation - and Evaulation
Triangle Inequality Theorem
Isosceles and Equilateral triangles
Percent Increase and Decrease
17. Volume of a Cylinder = pr^2h
Reciprocal
Average Rate
Similar Triangles
Volume of a Cylinder
18. 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
Reducing Fractions
Identifying the Parts and the Whole
Exponential Growth
Circumference of a Circle
19. 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
Volume of a Cylinder
Remainders
Finding the Original Whole
Using an Equation to Find an Intercept
20. Factor out the perfect squares
Adding/Subtracting Signed Numbers
Reciprocal
Multiplying and Dividing Roots
Simplifying Square Roots
21. 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
Multiplying and Dividing Roots
Adding/Subtracting Signed Numbers
Union of Sets
Identifying the Parts and the Whole
22. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Relative Primes
Using an Equation to Find the Slope
Average Rate
Circumference of a Circle
23. The whole # left over after division
Remainders
The 3-4-5 Triangle
Similar Triangles
Combined Percent Increase and Decrease
24. Combine like terms
Rate
Adding and Subtraction Polynomials
Reducing Fractions
Using an Equation to Find an Intercept
25. 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
Area of a Triangle
Pythagorean Theorem
Finding the Original Whole
Interior Angles of a Polygon
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
Characteristics of a Rectangle
Direct and Inverse Variation
Solving an Inequality
27. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Setting up a Ratio
Mixed Numbers and Improper Fractions
(Least) Common Multiple
28. 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)
Multiplying and Dividing Powers
Adding/Subtracting Signed Numbers
Reducing Fractions
Length of an Arc
29. 1. Re-express them with common denominators 2. Convert them to decimals
Characteristics of a Rectangle
Comparing Fractions
Number Categories
Percent Increase and Decrease
30. A square is a rectangle with four equal sides; Area of Square = side*side
Area of a Triangle
Characteristics of a Square
Finding the Distance Between Two Points
Repeating Decimal
31. 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
Surface Area of a Rectangular Solid
Adding/Subtracting Signed Numbers
Relative Primes
Volume of a Rectangular Solid
32. To solve a proportion - cross multiply
Multiplying Fractions
Solving a Proportion
The 5-12-13 Triangle
PEMDAS
33. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Comparing Fractions
Solving an Inequality
Solving a Quadratic Equation
Solving a Proportion
34. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Identifying the Parts and the Whole
Comparing Fractions
Solving an Inequality
Union of Sets
35. 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
Adding and Subtracting Roots
Solving an Inequality
Interior Angles of a Polygon
Dividing Fractions
36. The smallest multiple (other than zero) that two or more numbers have in common.
Greatest Common Factor
Multiplying and Dividing Roots
Finding the Missing Number
(Least) Common Multiple
37. 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
Volume of a Rectangular Solid
Adding and Subtracting Roots
Characteristics of a Square
Repeating Decimal
38. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Adding/Subtracting Fractions
Multiplying Monomials
Adding and Subtraction Polynomials
Negative Exponent and Rational Exponent
39. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Median and Mode
Adding and Subtracting Roots
Union of Sets
40. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Area of a Triangle
Solving a Proportion
Parallel Lines and Transversals
41. 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
Factor/Multiple
Using an Equation to Find an Intercept
Finding the Missing Number
Using an Equation to Find the Slope
42. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Rate
Solving an Inequality
Tangency
Interior and Exterior Angles of a Triangle
43. Combine equations in such a way that one of the variables cancel out
Multiplying/Dividing Signed Numbers
Adding/Subtracting Fractions
Solving a System of Equations
Solving a Quadratic Equation
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
Union of Sets
Direct and Inverse Variation
Surface Area of a Rectangular Solid
Multiplying and Dividing Powers
45. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Simplifying Square Roots
Characteristics of a Rectangle
Length of an Arc
Evaluating an Expression
46. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Finding the Missing Number
PEMDAS
Intersection of sets
Multiplying/Dividing Signed Numbers
47. 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
Circumference of a Circle
Domain and Range of a Function
Average of Evenly Spaced Numbers
Rate
48. Change in y/ change in x rise/run
Interior Angles of a Polygon
Using Two Points to Find the Slope
Repeating Decimal
Pythagorean Theorem
49. 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
Finding the midpoint
Triangle Inequality Theorem
50. To divide fractions - invert the second one and multiply
Union of Sets
Relative Primes
(Least) Common Multiple
Dividing Fractions