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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. The largest factor that two or more numbers have in common.
Prime Factorization
Reciprocal
Domain and Range of a Function
Greatest Common Factor
2. 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
Similar Triangles
Using an Equation to Find the Slope
Dividing Fractions
Relative Primes
3. Factor out the perfect squares
Characteristics of a Rectangle
Multiples of 3 and 9
Simplifying Square Roots
Similar Triangles
4. Volume of a Cylinder = pr^2h
Remainders
Determining Absolute Value
Characteristics of a Square
Volume of a Cylinder
5. 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
Part-to-Part Ratios and Part-to-Whole Ratios
PEMDAS
Similar Triangles
Evaluating an Expression
6. 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
Dividing Fractions
Solving a Proportion
7. 2pr
Intersecting Lines
Circumference of a Circle
Repeating Decimal
Similar Triangles
8. Probability= Favorable Outcomes/Total Possible Outcomes
Solving a System of Equations
Multiples of 3 and 9
Probability
Finding the midpoint
9. 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
Percent Formula
Function - Notation - and Evaulation
Area of a Triangle
Mixed Numbers and Improper Fractions
10. 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
Characteristics of a Parallelogram
Using the Average to Find the Sum
The 5-12-13 Triangle
Finding the Original Whole
11. To find the reciprocal of a fraction switch the numerator and the denominator
Counting the Possibilities
Circumference of a Circle
Reciprocal
Adding and Subtraction Polynomials
12. Part = Percent x Whole
Area of a Circle
Multiplying and Dividing Powers
Median and Mode
Percent Formula
13. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Remainders
Setting up a Ratio
Length of an Arc
Volume of a Cylinder
14. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Rate
Circumference of a Circle
Surface Area of a Rectangular Solid
Multiplying Monomials
15. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Average Rate
Adding/Subtracting Fractions
Reducing Fractions
Volume of a Rectangular Solid
16. Change in y/ change in x rise/run
Adding/Subtracting Signed Numbers
Using Two Points to Find the Slope
The 5-12-13 Triangle
Counting the Possibilities
17. 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
Solving an Inequality
Rate
Negative Exponent and Rational Exponent
Multiples of 2 and 4
18. 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
Finding the Distance Between Two Points
The 3-4-5 Triangle
Negative Exponent and Rational Exponent
Solving a Quadratic Equation
19. 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
Interior and Exterior Angles of a Triangle
Repeating Decimal
Similar Triangles
Median and Mode
20. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Using the Average to Find the Sum
The 3-4-5 Triangle
Rate
Tangency
21. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Probability
The 5-12-13 Triangle
Determining Absolute Value
Volume of a Rectangular Solid
22. 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
Negative Exponent and Rational Exponent
Direct and Inverse Variation
Adding and Subtraction Polynomials
Intersecting Lines
23. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
The 5-12-13 Triangle
Solving a Proportion
Finding the Distance Between Two Points
Percent Increase and Decrease
24. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Simplifying Square Roots
Solving a Proportion
Number Categories
Multiples of 3 and 9
25. To divide fractions - invert the second one and multiply
Determining Absolute Value
Similar Triangles
Reducing Fractions
Dividing Fractions
26. you can add/subtract when the part under the radical is the same
Adding and Subtracting Roots
Determining Absolute Value
Raising Powers to Powers
Parallel Lines and Transversals
27. 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
The 5-12-13 Triangle
Area of a Triangle
Relative Primes
Interior and Exterior Angles of a Triangle
28. 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 Original Whole
Length of an Arc
Adding/Subtracting Signed Numbers
Area of a Sector
29. 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
Triangle Inequality Theorem
Volume of a Cylinder
Finding the midpoint
30. The smallest multiple (other than zero) that two or more numbers have in common.
Adding and Subtracting Roots
Number Categories
(Least) Common Multiple
Surface Area of a Rectangular Solid
31. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average Formula -
Union of Sets
Direct and Inverse Variation
Dividing Fractions
32. pr^2
Area of a Circle
Circumference of a Circle
Prime Factorization
Repeating Decimal
33. 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
Union of Sets
Multiplying and Dividing Roots
Using the Average to Find the Sum
34. 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
Union of Sets
Negative Exponent and Rational Exponent
Triangle Inequality Theorem
35. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Reciprocal
Union of Sets
Pythagorean Theorem
36. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Adding/Subtracting Fractions
Median and Mode
PEMDAS
Isosceles and Equilateral triangles
37. Sum=(Average) x (Number of Terms)
Median and Mode
Parallel Lines and Transversals
Using the Average to Find the Sum
Area of a Circle
38. 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)
Multiplying/Dividing Signed Numbers
(Least) Common Multiple
Determining Absolute Value
Area of a Sector
39. 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
Adding and Subtracting Roots
Adding/Subtracting Fractions
Comparing Fractions
40. Surface Area = 2lw + 2wh + 2lh
Multiples of 2 and 4
Multiples of 3 and 9
Surface Area of a Rectangular Solid
Multiplying and Dividing Roots
41. 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
Percent Increase and Decrease
Combined Percent Increase and Decrease
Multiplying Fractions
Setting up a Ratio
42. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Intersecting Lines
Length of an Arc
Average of Evenly Spaced Numbers
Part-to-Part Ratios and Part-to-Whole Ratios
43. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Multiplying and Dividing Powers
Repeating Decimal
Union of Sets
Setting up a Ratio
44. Multiply the exponents
Area of a Triangle
Percent Formula
Raising Powers to Powers
Part-to-Part Ratios and Part-to-Whole Ratios
45. 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
Number Categories
Average of Evenly Spaced Numbers
Solving a Quadratic Equation
46. 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
Using an Equation to Find an Intercept
Average Formula -
Characteristics of a Rectangle
Multiplying/Dividing Signed Numbers
47. 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
Finding the midpoint
Part-to-Part Ratios and Part-to-Whole Ratios
Repeating Decimal
Mixed Numbers and Improper Fractions
48. A square is a rectangle with four equal sides; Area of Square = side*side
Percent Increase and Decrease
Characteristics of a Square
Volume of a Rectangular Solid
Similar Triangles
49. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Average Rate
Using Two Points to Find the Slope
Finding the Original Whole
Evaluating an Expression
50. Combine like terms
Average Rate
Adding and Subtraction Polynomials
Multiplying and Dividing Powers
Finding the Original Whole