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SAT Math

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Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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1. Properties of Similar Triangles
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Cross multiply.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

2. Adding and Subtracting Polynomials
Variables that have an inverse relationship will always have the same product. As one value gets larger - the other gets smaller. Set up and solve the equation 310=6x. Answer: 5
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
An integer is divisible by 3 if the sum of its digits is divisible by 3 - - An integer is divisible by 9 is the sum of its digits is divisible by 9.
Combine like terms.

3. Multiplying Monomials
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Adjacent angles are supplementary - Vertical angles are equal

4. If 3(3x)=9(x+2) - what is the value of x?
The length of one side of a triangle must be greater than the difference and less of the sum of the lengths of the other two sides.
FOIL: First - Outer - Inner - Last... Combine Like Terms
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Direct Variation- y=kx - where k is constant. As x gets larger - y gets larger. If the number of units of B were to double - the number of units of A would double - Inverse Variation- xy=k - where k is a constant. As x gets larger - y gets smaller. A

5. Characteristics of a Parallelogram
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Variables that have an inverse relationship will always have the same product. As one value gets larger - the other gets smaller. Set up and solve the equation 310=6x. Answer: 5
Adjacent angles are supplementary - Vertical angles are equal
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

6. Definition of Remainder
The whole number left over after division.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
VofaC: (pie)r(2)h
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

7. Finding the Length of an Arc in a Circle
Find a common denominator - then add or subtract the numerators.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
2(pie)r
Divide the denominator into the numerator to get a whole number quotient with a remainder. The quotient becomes the whole number of the mixed number. Remainder becomes the numerator.

8. Finding the Rate of Speed
Use the formula distance=rate*time and its variations to help in this question.
-An integer is divisible by 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

9. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
Combine the equations so that one of the variables cancels out. 4x+3y=8 and x+y=3. Multiply equation 2 by -3... then add the two equations.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

10. What Does Solving In Terms of Mean?
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Values of x the take the denominator of a faction equal to zero - thereby dividing by zero which is not possible - are not in the domain of a function. Set the denominator equal to zero and solve for x. Ans: 3
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

11. Properties of a 45-45-90 Triangle
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Set the quadratic equation equal to zero with the terms in order of decreasing exponents - and solve for the roots by factoring. Don't forget to then find the difference in the roots by subtracting them. Ans: 2
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Scalene- No sides or angles are equal - Isosceles- Have two equal sides. The angles opposite the equal sides are also equal - Equilateral- All three sides and angles are equal.

12. Finding the Sum of the Average of a Series of Numbers
Standard function notation is written f(x) and read 'f of x.' To evaluate the function f(x)=2x+3 for f(4) - replace every x with 4 and simplify. f(4)=2(4)+3=11.
The value that falls in the middle of the set.
Sum: Average x Number of Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.

13. Solving a System of Equations
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Subtract the smallest from the largest and add 1
Combine the equations so that one of the variables cancels out. 4x+3y=8 and x+y=3. Multiply equation 2 by -3... then add the two equations.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

14. Prime Factorization of a Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Adjacent angles are supplementary - Vertical angles are equal
Sum: Average x Number of Terms
-An integer is divisible by 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.

15. Solving a Proportion
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Cross multiply.
Do whatever is necessary to both sides to isolate the variable.
Variables that have an inverse relationship will always have the same product. As one value gets larger - the other gets smaller. Set up and solve the equation 310=6x. Answer: 5

16. Determining Absolute Value of a Number
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

17. If r#t=t(r)-r(t) - then what is 4#3?
Multiply the exponents - (x^3)^4=x^3*4=x^12
Domain- The domain of a a function is the set of values for which the function is defined - Range- The range of a function is the set of outputs or results of the function.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

18. Finding the Area of a Triangle
Isolate the radical expression and use the standard rules of algebra.
Standard function notation is written f(x) and read 'f of x.' To evaluate the function f(x)=2x+3 for f(4) - replace every x with 4 and simplify. f(4)=2(4)+3=11.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Area of a Triangle=1/29(base)(height) - The height is the perpendicular distance between the side that's chosen as the base and the opposite vertex.

19. Converting from an Improper Fraction to a Mixed Number
-An integer is divisible by 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.
Divide the denominator into the numerator to get a whole number quotient with a remainder. The quotient becomes the whole number of the mixed number. Remainder becomes the numerator.
Sector is a piece of the area of a circle. Area of a Sector: (n/360)((pie)r2) - n is the degree measure of the sector's central angle
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

20. Simplifying a Fraction to Lowest Terms
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Factor out and cancel all factors the numerator and denominator have in common.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

21. Multiplying Binomials
A(2)+b(2)=c(2)
FOIL: First - Outer - Inner - Last... Combine Like Terms
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

22. Finding the Reciprocal of a Fraction
Put the equation into y=mx+b-- in which case b is the y-intercept.
The 3 interior angles of a any triangle add up to 180 degrees. An exterior angle of a triangle is equal to the sum of the remote - that is - non-adjacent - interior angles.
Switch the numerator and denominator.
When a line is tangent to a circle - or touches the circle at just one point - the radius of the circle is perpendicular to the line at the point of contact.

23. Knowing if an Integer is a Multiple of 2 or 4
VofaRS=lwh
-An integer is divisible by 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Average the smallest and largest number

24. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Get the absolute value equation by itself. Solve.
Average: Sum of the Terms/Number of the Terms
Sum: Average x Number of Terms

25. An Important Property of a Line Tangent to a Circle
Use the units to keep things straight - Snowfall inches/hours
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
The union of Set A and Set B is the set of elements that are in either or both Set A and Set B - The intersection of Set A and Set B is the set of elements common to both Set A and Set B
When a line is tangent to a circle - or touches the circle at just one point - the radius of the circle is perpendicular to the line at the point of contact.

26. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Average the smallest and largest number

27. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Variables that have an inverse relationship will always have the same product. As one value gets larger - the other gets smaller. Set up and solve the equation 310=6x. Answer: 5
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

28. What is a Function and how do you Evaluate one?
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
VofaC: (pie)r(2)h
Standard function notation is written f(x) and read 'f of x.' To evaluate the function f(x)=2x+3 for f(4) - replace every x with 4 and simplify. f(4)=2(4)+3=11.
Four equal acute angles and four equal obtuse angles.

29. Solving a Radical Equation
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Isolate the radical expression and use the standard rules of algebra.
Slope=change in y/change in x

30. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Standard function notation is written f(x) and read 'f of x.' To evaluate the function f(x)=2x+3 for f(4) - replace every x with 4 and simplify. f(4)=2(4)+3=11.
-An integer is divisible by 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.
Switch the numerator and denominator.

31. Adding a Positive Number to a Negative Number
Find a common denominator - then add or subtract the numerators.
Two relatively prime numbers are integers that have no common factor other than 1.
Subtract the smallest from the largest and add 1
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

32. What types of angles are formed when two lines intersect?
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Average the smallest and largest number
Adjacent angles are supplementary - Vertical angles are equal
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

33. Simplifying an Algebraic Equation
Average: Sum of the Terms/Number of the Terms
FOIL: First - Outer - Inner - Last... Combine Like Terms
The value that appears the most often.
Cancel factors common to the numerator and denominator.

34. Counting Consecutive Integers
Two relatively prime numbers are integers that have no common factor other than 1.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Subtract the smallest from the largest and add 1
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

35. If x varies directly with y - and the value of x is 12 when y is 11 - what is the value of y when x is 66?
Just add or subtract the coefficients in front of the radicals.
Scalene- No sides or angles are equal - Isosceles- Have two equal sides. The angles opposite the equal sides are also equal - Equilateral- All three sides and angles are equal.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

36. Characteristics of a Square
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
In a 30-60-90 triangle - the measure of the longer leg is 7(square root: 3) - then the length of the shorter side or shorter leg must be 7.

37. Multiplying Expressions with Exponents that Have a Common Base
In a 30-60-90 triangle - the measure of the longer leg is 7(square root: 3) - then the length of the shorter side or shorter leg must be 7.
The length of one side of a triangle must be greater than the difference and less of the sum of the lengths of the other two sides.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Scalene- No sides or angles are equal - Isosceles- Have two equal sides. The angles opposite the equal sides are also equal - Equilateral- All three sides and angles are equal.

38. Solving an Inequality
Fraction to a Decimal: Divide the Denominator into the numerator - Decimal to a Fraction: Set the decimal over 1 and multiply the numerator and denominator by 10 raised to the number of digits to the right of the decimal point.
Remember that any non-zero base to the power of zero is equal to one. Set the exponent equal to zero and solve for x.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

39. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Area of a Triangle=1/29(base)(height) - The height is the perpendicular distance between the side that's chosen as the base and the opposite vertex.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
2(pie)r

40. Finding the Domain and Range of a Function
Just add or subtract the coefficients in front of the radicals.
Use the distributive property then combine the like terms.
An integer is divisible by 3 if the sum of its digits is divisible by 3 - - An integer is divisible by 9 is the sum of its digits is divisible by 9.
Domain- The domain of a a function is the set of values for which the function is defined - Range- The range of a function is the set of outputs or results of the function.

41. Setting Up a Ratio
The whole number left over after division.
Direct Variation- y=kx - where k is constant. As x gets larger - y gets larger. If the number of units of B were to double - the number of units of A would double - Inverse Variation- xy=k - where k is a constant. As x gets larger - y gets smaller. A
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

42. Number of Groups - +1 Each Time
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Area of a Triangle=1/29(base)(height) - The height is the perpendicular distance between the side that's chosen as the base and the opposite vertex.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

43. Solving a Problem Involving Rates
Multiply and/or divide positives and negatives treat the number parts as usual - and attach a negative sign if there is an odd number of negatives
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the units to keep things straight - Snowfall inches/hours
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

44. Let N represent the smallest positive integer that is a multiple of 6 and 8 - but leaves a remainder of 2 when divided by 7. What is the value of N?
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Four equal acute angles and four equal obtuse angles.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

45. Finding the Sum of the Interior Angles of a Polygon
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Express them with a common denominator.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

46. Dividing Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Just add or subtract the coefficients in front of the radicals.
Don't be confused by all the variables. Recall that (x-y)(x+y)=x(2)-y(2). Then - x(2)-y(2)=5*7=35. x(2)+1-y(2)=x(2)-y(2)+1=35+1=36.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

47. If the average of a - b - and 48 is 48 - what is the value of a + b?
Average the smallest and largest number
Ue the formula y=mx+b - and remember that the value of m is the slope of the line. The slopes of two perpendicular lines are negative reciprocals of one another.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

48. Finding the Slope of a Line When Given Two Points on the Line
Isolate the radical expression and use the standard rules of algebra.
Plug in the given values for the unknowns and calculate according to PEMDAS.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Slope=change in y/change in x

49. Adding and Subtracting Monomials
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Cancel factors common to the numerator and denominator.

50. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
Adjacent angles are supplementary - Vertical angles are equal
Combine the equations so that one of the variables cancels out. 4x+3y=8 and x+y=3. Multiply equation 2 by -3... then add the two equations.
Scalene- No sides or angles are equal - Isosceles- Have two equal sides. The angles opposite the equal sides are also equal - Equilateral- All three sides and angles are equal.

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