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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. What are Two Special Pythagorean Triples?
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
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.
Find a common denominator - then add or subtract the numerators.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

2. Finding the Slope of a Line When Given Two Points on the Line
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Slope=change in y/change in x
Just add or subtract the coefficients in front of the radicals.

3. Finding a Term in a Geometric Sequence
If there are m ways one event can happen and n ways a second event can happen - then there are m*n ways for the 2 events to happen.
Use the units to keep things straight - Snowfall inches/hours
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
Use the formula - a(n)=a(1)r(n-1) - where a(n) is the nth term - a1 is the first term - and r is the ratio between the terms.

4. Multiplying Monomials
Do whatever is necessary to both sides to isolate the variable.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

5. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

6. Finding the Domain and Range of a Function
Cancel factors common to the numerator and denominator.
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
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.

7. Setting Up a Ratio
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
-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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
FOIL: First - Outer - Inner - Last... Combine Like Terms

8. Calculating the Probability that an Event will Take Place
A(2)+b(2)=c(2)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Use simple numbers like 1 and 2 and see what happens.

9. Number of Groups - +1 Each Time
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Use the sum... If the average of 4 numbers is 7 - then the sum of those 4 numbers is 4*7 - or 28. Suppose that 3 of the numbers are 3 -5 - and 9. These 3 numbers add up to 16 of that 28 - 12 is the fourth number.

10. If 4(x(2)-10x+25) - then what is the value of x?
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
2(pie)r
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

11. Convert From a Fraction to a Decimal - Vice Versa
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.
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.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

12. Properties of a 30-60-90 Triangle
(pie)r(squared)
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
-Increasing: Add the percent to 100 percent - convert to a decimal - and multiply - Decrease: Subtract the percent from 100 percent - convert to a decimal - and multiply.

13. Solving a Linear Equation
Average the smallest and largest number
Do whatever is necessary to both sides to isolate the variable.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

14. Finding the Area of a Sector
Get the absolute value equation by itself. Solve.
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
Subtract the smallest from the largest and add 1
If there are m ways one event can happen and n ways a second event can happen - then there are m*n ways for the 2 events to happen.

15. Finding the y-intercept When Given an Equation of a Line
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Slope=change in y/change in x

16. Knowing if an Integer is a Multiple of 2 or 4
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
-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.

17. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

18. Multiply and Divide Positive and Negative Numbers
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
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
VofaC: (pie)r(2)h

19. Difference Between a Factor and a Multiple
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.
Cross multiply.
-Increasing: Add the percent to 100 percent - convert to a decimal - and multiply - Decrease: Subtract the percent from 100 percent - convert to a decimal - and multiply.
-The Factors of integer n are the positive integers that divide into n with no remainder - The Multiples of n are the positive integers that n divides into with no remainder.

20. Comparing the values of two or more Fractions
Express them with a common denominator.
Find a common denominator - then add or subtract the numerators.
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

21. Definition of Remainder
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The whole number left over after division.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

22. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Get the absolute value equation by itself. Solve.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

23. Simplifying an Algebraic Equation
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Cancel factors common to the numerator and denominator.
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.

24. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

25. Simplifying a Fraction to Lowest Terms
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Factor out and cancel all factors the numerator and denominator have in common.

26. What types of angles are formed when a transversal cross parallel lines?
The value that falls in the middle of the set.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Multiplying: Multiply the numbers under the different radicals. The product goes under one radical - Dividing: The quotient of more than one square root is equal to the square root of their total quotient.
Four equal acute angles and four equal obtuse angles.

27. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Slope=change in y/change in x
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

28. Average Rate and How Do You Find It
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Get the absolute value equation by itself. Solve.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

29. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?
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
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
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

30. What types of angles are formed when two lines intersect?
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Adjacent angles are supplementary - Vertical angles are equal
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.
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

31. If r#t=t(r)-r(t) - then what is 4#3?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Put each number in the original ratio over the sum of the numbers.
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.

32. Characteristics of a Square
Use the sum... If the average of 4 numbers is 7 - then the sum of those 4 numbers is 4*7 - or 28. Suppose that 3 of the numbers are 3 -5 - and 9. These 3 numbers add up to 16 of that 28 - 12 is the fourth number.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

33. Finding the Surface Area of a Rectangular Solid
Put the equation into y=mx+b-- in which case b is the y-intercept.
(x1+x2)/2 -(y1+y2)/2
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

34. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
(pie)r(squared)
Do whatever is necessary to both sides to isolate the variable.

35. What is the positive difference between the answers to the equation 35+x(2)=12x?
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
FOIL: First - Outer - Inner - Last... Combine Like Terms
Factor out and cancel all factors the numerator and denominator have in common.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

36. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Average: Sum of the Terms/Number of the Terms
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

37. 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?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Do whatever is necessary to both sides to isolate the variable.
Part=Percent x Whole
Average: Sum of the Terms/Number of the Terms

38. Definition of a Rational Number
Use simple numbers like 1 and 2 and see what happens.
Use the formula - a(n)=a(1)r(n-1) - where a(n) is the nth term - a1 is the first term - and r is the ratio between the terms.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
-Increasing: Add the percent to 100 percent - convert to a decimal - and multiply - Decrease: Subtract the percent from 100 percent - convert to a decimal - and multiply.

39. Numbers that are Relatively Prime
Multiply the numerators and multiply the denominators.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Two relatively prime numbers are integers that have no common factor other than 1.
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.

40. Expressing the Union and Intersection of Sets
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
Plug in the given values for the unknowns and calculate according to PEMDAS.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Part=Percent x Whole

41. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
-Increasing: Add the percent to 100 percent - convert to a decimal - and multiply - Decrease: Subtract the percent from 100 percent - convert to a decimal - and multiply.
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.
Use the units to keep things straight - Snowfall inches/hours

42. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

43. If 3(3x)=9(x+2) - what is the value of x?
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Use the formula distance=rate*time and its variations to help in this question.
Adjacent angles are supplementary - Vertical angles are equal
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

44. Increasing and Decreasing a Number by a Certain Percentage
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.
-Increasing: Add the percent to 100 percent - convert to a decimal - and multiply - Decrease: Subtract the percent from 100 percent - convert to a decimal - and multiply.
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.
Average: Sum of the Terms/Number of the Terms

45. Converting from part-to-part ratios to part-to-whole ratios
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Factor out and cancel all factors the numerator and denominator have in common.
Put each number in the original ratio over the sum of the numbers.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

46. What is a Function and how do you Evaluate one?
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

47. Finding the Volume of a Cylinder
Use simple numbers like 1 and 2 and see what happens.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
VofaC: (pie)r(2)h
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

48. Direct Variation and Inverse Variation
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
Use the distributive property then combine the like terms.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

49. Dividing Fractions
Express them with a common denominator.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

50. Adding and Subtracting Roots
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Just add or subtract the coefficients in front of the radicals.

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