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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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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. Multiplying Fractions
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Multiply the numerators and multiply the denominators.
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.

2. If 4(x(2)-10x+25) - then what is the value of x?
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Just add or subtract the coefficients in front of the radicals.
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.

3. What is the positive difference between the answers to the equation 35+x(2)=12x?
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

4. Properties of a 30-60-90 Triangle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Slope=change in y/change in x
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 one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

5. What is the Pythagorean Theorem?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
(x1+x2)/2 -(y1+y2)/2
A(2)+b(2)=c(2)

6. Factoring the Difference of Two Squares
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

7. Knowing if an Integer is a Multiple of 2 or 4
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
-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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

8. Counting Consecutive Integers
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Subtract the smallest from the largest and add 1
VofaC: (pie)r(2)h

9. 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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
Sum: Average x Number of Terms

10. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
A(2)+b(2)=c(2)
-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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

11. What value of x is not in the domain of the function f(x)=x-2/x-3?
Average: Sum of the Terms/Number of the Terms
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Use the formula distance=rate*time and its variations to help in this question.
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

12. What is the greatest of three consecutive odd integers where the sum of the third and twice the first is equal to nine more than twice the second?
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.

13. Determining Absolute Value of a Number
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Adjacent angles are supplementary - Vertical angles are equal
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

14. Solving a Problem Involving Rates
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Express them with a common denominator.
Use the units to keep things straight - Snowfall inches/hours
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

15. Solving a Proportion
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
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.
Cross multiply.

16. Scalene - Isosceles - and Equilateral Triangles
Just add or subtract the coefficients in front of the radicals.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
Express them with a common denominator.

17. Dividing Fractions
Multiply the numerators and multiply the denominators.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

18. Comparing the values of two or more Fractions
Express them with a common denominator.
Part=Percent x Whole
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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

19. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

20. If 3(3x)=9(x+2) - what is the value of x?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.

21. Converting from part-to-part ratios to part-to-whole ratios
-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 each number in the original ratio over the sum of the numbers.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

22. What is the Triangle Inequality Theorem?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
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.

23. Average Rate and How Do You Find It
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

24. Finding the Missing Number in a Series When You are Given the Average
Isolate the radical expression and use the standard rules of algebra.
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.
Average: Sum of the Terms/Number of the Terms
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.

25. Finding the Sum of the Interior Angles of a Polygon
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

26. 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.
Two relatively prime numbers are integers that have no common factor other than 1.
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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

27. Simplifying a Fraction to Lowest Terms
Isolate the radical expression and use the standard rules of algebra.
Factor out and cancel all factors the numerator and denominator have in common.
(x1+x2)/2 -(y1+y2)/2
The value that appears the most often.

28. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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

29. Definition of a Rational Number
Combine like terms.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Switch the numerator and denominator.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

30. Finding the Volume of a Rectangular Solid
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 relatively prime numbers are integers that have no common factor other than 1.
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
VofaRS=lwh

31. Multiplying Expressions with Exponents that Have a Common Base
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
-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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

32. Finding the Rate of Speed
Cross multiply.
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
Use the formula distance=rate*time and its variations to help in this question.
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.

33. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
VofaC: (pie)r(2)h
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.

34. Finding the Mode of a Set of Numbers
The value that appears the most often.
Do whatever is necessary to both sides to isolate the variable.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

35. Identifying Which Number of a Fraction is the Part and Which Number is the Whole
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

36. Calculating the Probability that an Event will Take Place
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Use the formula distance=rate*time and its variations to help in this question.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.

37. Definition of an Integer
VofaRS=lwh
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Find a common denominator - then add or subtract the numerators.

38. Finding the Area of a Triangle
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 value that falls in the middle of the set.
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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

39. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Switch the numerator and denominator.
-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.

40. Evaluating an Algebraic Expression
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Plug in the given values for the unknowns and calculate according to PEMDAS.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

41. Converting from an Improper Fraction to a Mixed Number
-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.
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
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.
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.

42. What Does Solving In Terms of Mean?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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
(pie)r(squared)
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

43. If x(2)=7x+18 - what is the positive value of x?
Use the distributive property then combine the like terms.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

44. Characteristics of a Parallelogram
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
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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

45. 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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Plug in the given values for the unknowns and calculate according to PEMDAS.
2(pie)r

46. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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
Multiply the exponents - (x^3)^4=x^3*4=x^12
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.

47. Finding the Distance Between Two Points on a Coordinate Graph
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Change the division sign to a multiplication sign - invert the second fraction - and 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.

48. Finding the Surface Area of a Rectangular Solid
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

49. Adding and Subtracting Polynomials
Combine like terms.
Cross multiply.
Use the formula distance=rate*time and its variations to help in this question.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

50. Finding the Volume of a Cylinder
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Isolate the radical expression and use the standard rules of algebra.
VofaC: (pie)r(2)h

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