SAT 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.
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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. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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.
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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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


2. Definition of Remainder
Cross multiply.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
-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.
The whole number left over after division.


3. Convert From a Fraction to a Decimal - Vice Versa
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.
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.
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.


4. What is the Triangle Inequality Theorem?
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.


5. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.


6. Solving a Problem Involving Rates
Part=Percent x Whole
Plug in the given values for the unknowns and calculate according to PEMDAS.
Use the units to keep things straight - Snowfall inches/hours
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


7. Number of Groups - +1 Each Time
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Factor out and cancel all factors the numerator and denominator have in common.
Use the distributive property then combine the like terms.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


8. Counting the Total Number of Possibilities for Several Events to Occur
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
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.
Adjacent angles are supplementary - Vertical angles are equal


9. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
Cancel factors common to the numerator and denominator.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


10. If the average of a - b - and 48 is 48 - what is the value of a + b?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Two relatively prime numbers are integers that have no common factor other than 1.
Isolate the radical expression and use the standard rules of algebra.


11. Calculating the Probability that an Event will Take Place
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Just add or subtract the coefficients in front of the radicals.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Probability: Number of Favorable Outcomes/Total Possible Outcomes


12. Characteristics of a Square
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Average the smallest and largest number


13. Adding and Subtracting Monomials
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


14. Finding the GCF of Two or More Numbers
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


15. Solving a System of Equations
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
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.
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms


16. 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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Average the smallest and largest number


17. Simplifying a Fraction to Lowest Terms
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Factor out and cancel all factors the numerator and denominator have in common.


18. Properties of Similar Triangles
-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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Find a common denominator - then add or subtract the numerators.


19. Difference Between a Factor and a Multiple
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
-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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


20. 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.
Isolate the radical expression and use the standard rules of algebra.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


21. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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
Two relatively prime numbers are integers that have no common factor other than 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.


22. An Important Property of a Line Tangent to a Circle
Express them with a common 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.
-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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


23. Finding the Domain and Range of a Function
Cross multiply.
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.
The whole number left over after division.
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.


24. Finding the Volume of a Rectangular Solid
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Cancel factors common to the numerator and denominator.
VofaRS=lwh


25. If r#t=t(r)-r(t) - then what is 4#3?
-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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


26. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

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27. Multiplying Expressions with Exponents that Have a Common Base
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


28. Finding the LCM of Two or More Numbers

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29. Comparing the values of two or more Fractions
Express them with a common denominator.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
-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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


30. Finding the Circumference of a Circle
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
2(pie)r
-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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


31. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Sum: Average x Number of Terms
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The whole number left over after division.


32. Converting from an Improper Fraction to a Mixed Number
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
Use the units to keep things straight - Snowfall inches/hours
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.


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

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34. Formula Used to Find Percent
Part=Percent x Whole
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
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


35. Knowing if an Integer is a Multiple of 5 or 10
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
-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.
VofaRS=lwh
Cancel factors common to the numerator and denominator.


36. Adding and Subtracting Roots
Just add or subtract the coefficients in front of the radicals.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


37. Identifying Which Number of a Fraction is the Part and Which Number is the Whole

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38. Simplifying Square Roots
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


39. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.


40. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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


41. Finding a Term in a Geometric Sequence
Use the formula distance=rate*time and its variations to help in this question.
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.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


42. Finding the Volume of a Cylinder
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
(x1+x2)/2 -(y1+y2)/2
VofaC: (pie)r(2)h
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


43. Multiplying Monomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Slope=change in y/change in x
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.


44. Dividing Fractions
Slope=change in y/change in x
Just add or subtract the coefficients in front of the radicals.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


45. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


46. Properties of the Interior and Exterior Angles of a Triangle
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
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.
Sum: Average x Number of Terms


47. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
The whole number left over after division.
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.


48. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Isolate the radical expression and use the standard rules of algebra.
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.
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.


49. Multiplying Fractions
(x1+x2)/2 -(y1+y2)/2
Multiply the numerators and multiply the denominators.
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
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.


50. What is the positive difference between the answers to the equation 35+x(2)=12x?

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