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SAT Math

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Answer 50 questions in 15 minutes.
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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 Reciprocal of a Fraction
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Switch the numerator and denominator.
Use the units to keep things straight - Snowfall inches/hours

2. Difference Between a Factor and a Multiple
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
-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 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.

3. Finding the GCF of Two or More Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Just add or subtract the coefficients in front of the radicals.
Four equal acute angles and four equal obtuse angles.

4. 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.
-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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Switch the numerator and denominator.

5. Comparing the values of two or more Fractions
Express them with a common 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.
Slope=change in y/change in 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.

6. Dividing Fractions
Slope=change in y/change in x
(x1+x2)/2 -(y1+y2)/2
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Cancel factors common to the numerator and denominator.

7. What types of angles are formed when a transversal cross parallel lines?
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
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Four equal acute angles and four equal obtuse angles.
Plug in the given values for the unknowns and calculate according to PEMDAS.

8. Multiplying Monomials
'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
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

9. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
-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.
Part=Percent x Whole
-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.

10. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.

11. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Get the absolute value equation by itself. Solve.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

12. Definition of a Rational Number
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.
Part=Percent x Whole
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.

13. Convert From a Fraction to a Decimal - Vice Versa
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
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 whole number left over after division.
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.

14. If r#t=t(r)-r(t) - then what is 4#3?
(x1+x2)/2 -(y1+y2)/2
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.

15. Properties of a 45-45-90 Triangle
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

16. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
-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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

17. Scalene - Isosceles - and Equilateral Triangles
Put the equation into y=mx+b-- in which case b is the y-intercept.
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 of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

18. If (Square Root: x-1)+5=12 - what is the value of x/2?
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.
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.

19. Adding and Subtracting Fractions
Two relatively prime numbers are integers that have no common factor other than 1.
Sum: Average x Number of Terms
Find a common denominator - then add or subtract the numerators.
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

20. Finding the Sum of the Average of a Series of Numbers
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The value that falls in the middle of the set.
Sum: Average x Number of Terms
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

21. Finding the y-intercept When Given an Equation of a Line
Find a common denominator - then add or subtract the numerators.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Put the equation into y=mx+b-- in which case b is the y-intercept.
(x1+x2)/2 -(y1+y2)/2

22. Numbers that are Relatively Prime
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 up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Two relatively prime numbers are integers that have no common factor other than 1.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

23. Converting from part-to-part ratios to part-to-whole ratios
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.
Put each number in the original ratio over the sum of the numbers.
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.
Four equal acute angles and four equal obtuse angles.

24. Finding the Slope of a Line When Given Two Points on the Line
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Slope=change in y/change in x
-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.

25. Definition of an Irrational Number
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Multiply the numerators and multiply the denominators.

26. General Procedure for Multiplying Polynomials
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Use the distributive property then combine the like terms.
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.

27. An Important Property of a Line Tangent to a Circle
(pie)r(squared)
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.
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

28. Finding the Length of an Arc in a Circle

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29. Raising a Power to a Power
FOIL: First - Outer - Inner - Last... Combine Like Terms
Slope=change in y/change in x
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12

30. Definition of Remainder
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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 whole number left over after division.

31. Counting the Total Number of Possibilities for Several Events to Occur
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.
Find a common denominator - then add or subtract the numerators.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Use simple numbers like 1 and 2 and see what happens.

32. 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.
-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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
A(2)+b(2)=c(2)

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

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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?
Use simple numbers like 1 and 2 and see what happens.
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
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 coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

35. Finding the Surface Area of a Rectangular Solid
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

36. If the average of a - b - and 48 is 48 - what is the value of a + b?
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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Average the smallest and largest number

37. Solving a Proportion
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Put each number in the original ratio over the sum of the numbers.
Cross multiply.

38. If 4(x(2)-10x+25) - then what is the value of x?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
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.

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

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40. If 3(3x)=9(x+2) - what is the value of x?
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.
Average: Sum of the Terms/Number of the Terms
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

41. Multiplying Expressions with Exponents that Have a Common Base
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

42. 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
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 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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

43. Finding a Term in a Geometric Sequence
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

44. 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
Sum: Average x Number of 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.
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.

45. PEMDAS
Adjacent angles are supplementary - Vertical angles are equal
Average: Sum of the Terms/Number of the Terms
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Probability: Number of Favorable Outcomes/Total Possible Outcomes

46. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
Multiply the numerators and multiply the denominators.
Average: Sum of the Terms/Number of the Terms
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.

47. Definition of an Integer
Subtract the smallest from the largest and add 1
Plug in the given values for the unknowns and calculate according to PEMDAS.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

48. Knowing if an Integer is a Multiple of 2 or 4
-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.
VofaC: (pie)r(2)h
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

49. 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
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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Cancel factors common to the numerator and denominator.
Four equal acute angles and four equal obtuse angles.

50. Prime Factorization of a Number
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 find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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
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.

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