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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.
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. 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
Adding and Subtracting monomials
Area of a Circle
Evaluating an Expression
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
Using an Equation to Find an Intercept
Function - Notation - and Evaulation
Number Categories
Repeating Decimal
3. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Relative Primes
The 5-12-13 Triangle
Multiples of 3 and 9
Number Categories
4. To divide fractions - invert the second one and multiply
Dividing Fractions
Multiplying Fractions
Factor/Multiple
Counting Consecutive Integers
5. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Area of a Sector
Part-to-Part Ratios and Part-to-Whole Ratios
Negative Exponent and Rational Exponent
6. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Counting Consecutive Integers
Counting the Possibilities
Length of an Arc
Average Rate
7. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Mixed Numbers and Improper Fractions
Parallel Lines and Transversals
Volume of a Cylinder
Characteristics of a Square
8. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Characteristics of a Rectangle
Counting Consecutive Integers
Multiples of 2 and 4
Determining Absolute Value
9. 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
Using the Average to Find the Sum
Surface Area of a Rectangular Solid
The 5-12-13 Triangle
Function - Notation - and Evaulation
10. 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)
Function - Notation - and Evaulation
Solving an Inequality
Length of an Arc
Adding and Subtracting Roots
11. Part = Percent x Whole
Using an Equation to Find an Intercept
Percent Formula
Finding the midpoint
(Least) Common Multiple
12. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Finding the Missing Number
Intersecting Lines
Average Formula -
The 5-12-13 Triangle
13. The smallest multiple (other than zero) that two or more numbers have in common.
Median and Mode
Average Formula -
(Least) Common Multiple
Finding the midpoint
14. 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.
Median and Mode
Adding and Subtraction Polynomials
Number Categories
Domain and Range of a Function
15. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Evaluating an Expression
Reducing Fractions
Using an Equation to Find the Slope
Intersection of sets
16. 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
Setting up a Ratio
Adding and Subtracting Roots
Average of Evenly Spaced Numbers
17. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Counting Consecutive Integers
Tangency
Finding the Distance Between Two Points
Evaluating an Expression
18. 2pr
Circumference of a Circle
Counting the Possibilities
Adding/Subtracting Signed Numbers
Length of an Arc
19. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Finding the midpoint
Comparing Fractions
Length of an Arc
Setting up a Ratio
20. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Circumference of a Circle
Function - Notation - and Evaulation
Interior Angles of a Polygon
Median and Mode
21. 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
Combined Percent Increase and Decrease
Area of a Triangle
Mixed Numbers and Improper Fractions
Multiples of 2 and 4
22. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Surface Area of a Rectangular Solid
Adding/Subtracting Fractions
Area of a Sector
23. To solve a proportion - cross multiply
Multiplying/Dividing Signed Numbers
Intersecting Lines
Solving a Proportion
Adding and Subtracting Roots
24. To multiply fractions - multiply the numerators and multiply the denominators
Finding the Original Whole
Multiplying Fractions
Intersecting Lines
Prime Factorization
25. 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
Adding and Subtracting Roots
Isosceles and Equilateral triangles
Percent Increase and Decrease
Counting Consecutive Integers
26. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Solving a Quadratic Equation
Greatest Common Factor
Multiples of 3 and 9
27. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Exponential Growth
Area of a Circle
Interior Angles of a Polygon
Finding the Distance Between Two Points
28. 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
Finding the Missing Number
Percent Formula
Prime Factorization
Multiplying/Dividing Signed Numbers
29. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Finding the Distance Between Two Points
PEMDAS
Adding/Subtracting Fractions
Multiplying and Dividing Powers
30. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Triangle Inequality Theorem
Factor/Multiple
Interior Angles of a Polygon
Mixed Numbers and Improper Fractions
31. 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
Domain and Range of a Function
Relative Primes
The 3-4-5 Triangle
Dividing Fractions
32. 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
Area of a Circle
Finding the midpoint
Part-to-Part Ratios and Part-to-Whole Ratios
Similar Triangles
33. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Multiples of 2 and 4
Counting Consecutive Integers
Percent Formula
Finding the Distance Between Two Points
34. 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
Mixed Numbers and Improper Fractions
Multiplying Fractions
Probability
Percent Formula
35. Factor out the perfect squares
Parallel Lines and Transversals
Exponential Growth
Function - Notation - and Evaulation
Simplifying Square Roots
36. 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
Domain and Range of a Function
Remainders
Interior and Exterior Angles of a Triangle
Area of a Triangle
37. 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
Determining Absolute Value
The 3-4-5 Triangle
Using an Equation to Find an Intercept
Average of Evenly Spaced Numbers
38. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Percent Increase and Decrease
Identifying the Parts and the Whole
Mixed Numbers and Improper Fractions
39. 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
Number Categories
Raising Powers to Powers
Average Formula -
40. The largest factor that two or more numbers have in common.
Finding the midpoint
Greatest Common Factor
Interior Angles of a Polygon
Average Rate
41. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Remainders
Percent Increase and Decrease
Adding/Subtracting Fractions
PEMDAS
42. Sum=(Average) x (Number of Terms)
Intersection of sets
Using the Average to Find the Sum
Using an Equation to Find the Slope
Adding and Subtracting monomials
43. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Solving a Proportion
Union of Sets
Adding/Subtracting Fractions
Finding the Distance Between Two Points
44. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Number Categories
Factor/Multiple
Tangency
Finding the Original Whole
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
Length of an Arc
Solving a Quadratic Equation
Characteristics of a Rectangle
Average of Evenly Spaced Numbers
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
Multiplying Monomials
Identifying the Parts and the Whole
Percent Increase and Decrease
Multiplying and Dividing Powers
47. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Using an Equation to Find the Slope
Multiples of 2 and 4
Union of Sets
Interior and Exterior Angles of a Triangle
48. Change in y/ change in x rise/run
Circumference of a Circle
Using Two Points to Find the Slope
Reducing Fractions
Mixed Numbers and Improper Fractions
49. 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
Identifying the Parts and the Whole
Finding the Missing Number
Greatest Common Factor
50. Combine like terms
PEMDAS
Rate
Function - Notation - and Evaulation
Adding and Subtraction Polynomials