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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
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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. 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 and Dividing Powers
Triangle Inequality Theorem
Multiplying/Dividing Signed Numbers
Greatest Common Factor
2. 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
Characteristics of a Rectangle
Surface Area of a Rectangular Solid
Part-to-Part Ratios and Part-to-Whole Ratios
Setting up a Ratio
3. pr^2
Evaluating an Expression
Length of an Arc
The 3-4-5 Triangle
Area of a Circle
4. 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
Area of a Triangle
Adding and Subtraction Polynomials
The 3-4-5 Triangle
5. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Adding/Subtracting Signed Numbers
Multiples of 3 and 9
Tangency
Setting up a Ratio
6. 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
Simplifying Square Roots
Tangency
Using an Equation to Find an Intercept
The 3-4-5 Triangle
7. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Reducing Fractions
Probability
Finding the Distance Between Two Points
Factor/Multiple
8. For all right triangles: a^2+b^2=c^2
Solving an Inequality
Pythagorean Theorem
Using Two Points to Find the Slope
Solving a System of Equations
9. 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
Isosceles and Equilateral triangles
Greatest Common Factor
Area of a Sector
Triangle Inequality Theorem
10. 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
Isosceles and Equilateral triangles
Adding and Subtracting monomials
Circumference of a Circle
11. Combine like terms
Finding the midpoint
Adding and Subtraction Polynomials
Pythagorean Theorem
The 5-12-13 Triangle
12. you can add/subtract when the part under the radical is the same
Similar Triangles
Adding and Subtracting Roots
Multiplying and Dividing Roots
(Least) Common Multiple
13. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Adding/Subtracting Fractions
Remainders
Characteristics of a Parallelogram
Average Formula -
14. 2pr
Multiples of 3 and 9
Circumference of a Circle
Mixed Numbers and Improper Fractions
Setting up a Ratio
15. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Domain and Range of a Function
Solving an Inequality
Relative Primes
16. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Similar Triangles
Finding the midpoint
Probability
Average Rate
17. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Circumference of a Circle
Parallel Lines and Transversals
Reducing Fractions
Length of an Arc
18. The smallest multiple (other than zero) that two or more numbers have in common.
Volume of a Cylinder
(Least) Common Multiple
Setting up a Ratio
Comparing Fractions
19. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Average Formula -
Adding/Subtracting Signed Numbers
Even/Odd
Average of Evenly Spaced Numbers
20. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Area of a Sector
Multiplying/Dividing Signed Numbers
Area of a Circle
Intersection of sets
21. 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)
Relative Primes
Counting the Possibilities
Area of a Circle
Area of a Sector
22. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them
Domain and Range of a Function
Even/Odd
Multiplying and Dividing Roots
Intersecting Lines
23. Subtract the smallest from the largest and add 1
Using the Average to Find the Sum
Counting Consecutive Integers
Adding and Subtraction Polynomials
Interior and Exterior Angles of a Triangle
24. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Negative Exponent and Rational Exponent
Solving a Proportion
Solving a Quadratic Equation
Multiplying and Dividing Powers
25. 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
Direct and Inverse Variation
Triangle Inequality Theorem
Surface Area of a Rectangular Solid
The 3-4-5 Triangle
26. To multiply fractions - multiply the numerators and multiply the denominators
Union of Sets
Multiplying Monomials
Multiplying Fractions
Adding and Subtraction Polynomials
27. 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
Average Formula -
Isosceles and Equilateral triangles
Repeating Decimal
Area of a Triangle
28. Multiply the exponents
Raising Powers to Powers
Even/Odd
Solving a Quadratic Equation
PEMDAS
29. 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 System of Equations
Multiplying/Dividing Signed Numbers
Repeating Decimal
Identifying the Parts and the Whole
30. 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
Interior and Exterior Angles of a Triangle
Using an Equation to Find an Intercept
Parallel Lines and Transversals
Adding and Subtracting Roots
31. 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
Average Rate
The 3-4-5 Triangle
The 5-12-13 Triangle
32. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Solving a System of Equations
(Least) Common Multiple
Characteristics of a Parallelogram
Using an Equation to Find the Slope
33. 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
Greatest Common Factor
Repeating Decimal
Multiplying and Dividing Powers
Multiples of 3 and 9
34. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Greatest Common Factor
Characteristics of a Parallelogram
Adding/Subtracting Fractions
Using Two Points to Find the Slope
35. To divide fractions - invert the second one and multiply
Domain and Range of a Function
Identifying the Parts and the Whole
Dividing Fractions
Tangency
36. 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
Even/Odd
Solving a Proportion
Relative Primes
Average of Evenly Spaced Numbers
37. 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
Number Categories
Raising Powers to Powers
Reducing Fractions
Rate
38. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Solving a System of Equations
Pythagorean Theorem
Average Rate
Intersecting Lines
39. 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 Missing Number
Adding/Subtracting Fractions
Multiplying and Dividing Roots
Pythagorean Theorem
40. Factor out the perfect squares
Multiplying and Dividing Powers
Simplifying Square Roots
Volume of a Rectangular Solid
Area of a Sector
41. 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
Dividing Fractions
Relative Primes
The 3-4-5 Triangle
Finding the Missing Number
42. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Remainders
Similar Triangles
Using the Average to Find the Sum
43. 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
Median and Mode
Percent Increase and Decrease
Area of a Triangle
Adding and Subtracting Roots
44. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Function - Notation - and Evaulation
Similar Triangles
Characteristics of a Square
Characteristics of a Rectangle
45. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Interior and Exterior Angles of a Triangle
Setting up a Ratio
Number Categories
Surface Area of a Rectangular Solid
46. Part = Percent x Whole
Part-to-Part Ratios and Part-to-Whole Ratios
Prime Factorization
Percent Formula
Determining Absolute Value
47. 1. Re-express them with common denominators 2. Convert them to decimals
Circumference of a Circle
Comparing Fractions
Domain and Range of a Function
The 3-4-5 Triangle
48. The whole # left over after division
Median and Mode
Remainders
Pythagorean Theorem
Length of an Arc
49. 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
Multiples of 3 and 9
Combined Percent Increase and Decrease
Intersecting Lines
Relative Primes
50. Sum=(Average) x (Number of Terms)
Simplifying Square Roots
Dividing Fractions
Using the Average to Find the Sum
Reducing Fractions