SAT Math

Instructions:

• Answer 50 questions in 15 minutes.
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• Match each statement with the correct term.
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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. Finding the Domain and Range of a Function
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


2. Characteristics of a Parallelogram
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
FOIL: First - Outer - Inner - Last... Combine Like Terms
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


3. Finding the y-intercept When Given an Equation of a Line
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.


4. PEMDAS
A(2)+b(2)=c(2)
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Cancel factors common to the numerator and denominator.


5. Converting From a Mixed Number to an Improper Fraction
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Four equal acute angles and four equal obtuse angles.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


6. Solving a Linear Equation
Use the formula distance=rate*time and its variations to help in this question.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Do whatever is necessary to both sides to isolate the variable.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


7. Sale Price of a Jacket Marked Down 30% Each Week for 3 Weeks - What % of the Original Price is the Cost of the Jacket After the 3 Week Sale Period
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


8. Formula Used to Find Percent
Isolate the radical expression and use the standard rules of algebra.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Part=Percent x Whole
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


9. What are Two Special Pythagorean Triples?

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10. If 4(x(2)-10x+25) - then what is the value of x?
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.
Part=Percent x Whole
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


11. Scalene - Isosceles - and Equilateral Triangles
-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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Slope=change in y/change in x
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. 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?
The value that falls in the middle of the set.
Use the formula distance=rate*time and its variations to help in this question.
Average: Sum of the Terms/Number of the Terms
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


13. Adding a Positive Number to a Negative Number
The value that falls in the middle of the set.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Do whatever is necessary to both sides to isolate the variable.


14. Definition of an Integer
Factor out and cancel all factors the numerator and denominator have in common.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


15. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Consecutive odd integers are odd integers in order in a row - such as 1 - 3 - and 5. The difference between any two consecutive odd integers is 2. Translate the question into an equation that expresses the relationship between the integers.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


16. Finding the Length of an Arc in a Circle

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17. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Combine like terms.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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


18. Multiplying Fractions
Multiply the numerators and multiply the denominators.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


19. Properties of the Interior and Exterior Angles of a Triangle
Consecutive odd integers are odd integers in order in a row - such as 1 - 3 - and 5. The difference between any two consecutive odd integers is 2. Translate the question into an equation that expresses the relationship between the integers.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
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.


20. What is a Function and how do you Evaluate one?

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21. Solving a Radical Equation
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Isolate the radical expression and use the standard rules of algebra.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.


22. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
-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.
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.
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.


23. Finding the LCM of Two or More Numbers

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24. How do you know if an integer is a multiple of 3 or 9?
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


25. Finding the Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


26. Dividing Expressions with Exponents that Have a Common Base
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Factor out and cancel all factors the numerator and denominator have in common.


27. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Average: Sum of the Terms/Number of the Terms
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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Do whatever is necessary to both sides to isolate the variable.


28. Solving an Inequality
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Do whatever is necessary to both sides to isolate the variable.


29. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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.
Switch the numerator and denominator.
Factor out and cancel all factors the numerator and denominator have in common.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


30. Finding the Distance Between Two Points on a Coordinate Graph
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
VofaC: (pie)r(2)h
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


31. Knowing if an Integer is a Multiple of 2 or 4
Multiply the numerators and multiply the denominators.
VofaC: (pie)r(2)h
-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.
Sum: Average x Number of Terms


32. Solving a Proportion
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Cross multiply.
Two relatively prime numbers are integers that have no common factor other than 1.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


33. Adding and Subtracting Polynomials
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.
Combine like terms.
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


34. Formula to Find Average
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.
Average: Sum of the Terms/Number of the Terms
The value that falls in the middle of the set.
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.


35. What is the Pythagorean Theorem?
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
A(2)+b(2)=c(2)


36. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
VofaC: (pie)r(2)h
Do whatever is necessary to both sides to isolate the variable.
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.


37. Prime Factorization of a Number
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.
2(pie)r
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


38. Number of Groups - +1 Each Time
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
Use the units to keep things straight - Snowfall inches/hours
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


39. Multiplying Monomials
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Part=Percent x Whole


40. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Sum: Average x Number of Terms
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.


41. 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.
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.
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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.


42. Finding the Area of a Triangle

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43. 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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Adjacent angles are supplementary - Vertical angles are equal
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


44. 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
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


45. Evaluating an Algebraic Expression
Adjacent angles are supplementary - Vertical angles are equal
Plug in the given values for the unknowns and calculate according to PEMDAS.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


46. Solving a Problem Involving Rates
Cancel factors common to the numerator and denominator.
Use the units to keep things straight - Snowfall inches/hours
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
VofaRS=lwh


47. Finding the Circumference of a Circle
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
2(pie)r
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


48. Properties of Similar Triangles
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
Cross multiply.


49. Factoring the Difference of Two Squares
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


50. What is the Triangle Inequality Theorem?
Four equal acute angles and four equal obtuse angles.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
Find a common denominator - then add or subtract the numerators.