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SAT Math

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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. If (Square Root: x-1)+5=12 - what is the value of x/2?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
A(2)+b(2)=c(2)
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.

2. Multiplying Fractions
Multiply the numerators and multiply the denominators.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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

3. Definition of Remainder
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.
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
The whole number left over after division.

4. Multiplying Binomials
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
-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.
FOIL: First - Outer - Inner - Last... Combine Like Terms

5. Finding the Mode of a Set of Numbers
The value that appears the most often.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.

6. Finding the Slope of a Line When Given Two Points on the Line
Cross multiply.
Slope=change in y/change in x
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Probability: Number of Favorable Outcomes/Total Possible Outcomes

7. Finding the Sum of the Interior Angles of a Polygon
Average the smallest and largest number
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

8. Solving a Radical Equation
Multiply the numerators and multiply the denominators.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Isolate the radical expression and use the standard rules of algebra.

9. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Use simple numbers like 1 and 2 and see what happens.
FOIL: First - Outer - Inner - Last... Combine Like Terms

10. 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?
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.
Part=Percent x Whole
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.

11. What are Two Special Pythagorean Triples?
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.
Switch the numerator and denominator.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

12. Multiply and Divide Positive and Negative Numbers
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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

13. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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 whole number part by the denominator - then add the numerator. Keep the same denominator.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

14. What is a Function and how do you Evaluate one?
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Average: Sum of the Terms/Number of the Terms
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.

15. Average Rate and How Do You Find It
Express them with a common denominator.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
-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.

16. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Combine like terms.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

17. 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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.

18. What types of angles are formed when two lines intersect?
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Use the formula distance=rate*time and its variations to help in this question.
Adjacent angles are supplementary - Vertical angles are equal

19. Finding the Domain and Range of a Function
The value that appears the most often.
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.
2(pie)r
Get the absolute value equation by itself. Solve.

20. Finding a Term in a Geometric Sequence
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Just add or subtract the coefficients in front of the radicals.
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.

21. If 4(x(2)-10x+25) - then what is the value of x?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Switch the numerator and denominator.
-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.

22. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Subtract the smallest from the largest and add 1
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 whole number part by the denominator - then add the numerator. Keep the same denominator.

23. Knowing if an Integer is a Multiple of 2 or 4
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
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.

24. Number of Groups - +1 Each Time
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Subtract the smallest from the largest and add 1
Sum: Average x Number of Terms
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

25. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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

26. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
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.
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.
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.

27. Adding and Subtracting Polynomials
Combine like terms.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
(pie)r(squared)
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

28. Scalene - Isosceles - and Equilateral Triangles
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.
Average: Sum of the Terms/Number of the Terms
Use the units to keep things straight - Snowfall inches/hours
Factor out and cancel all factors the numerator and denominator have in common.

29. How do you know if an integer is a multiple of 3 or 9?
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Plug in the given values for the unknowns and calculate according to PEMDAS.

30. Calculating the Probability that an Event will Take Place
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
Adjacent angles are supplementary - Vertical angles are equal
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Average the smallest and largest number

31. Characteristics of a Rectangle
Two relatively prime numbers are integers that have no common factor other than 1.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

32. Solving a Problem Involving Rates
Average: Sum of the Terms/Number of the Terms
Use the units to keep things straight - Snowfall inches/hours
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
FOIL: First - Outer - Inner - Last... Combine Like Terms

33. Finding the Volume of a Rectangular Solid
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
The value that falls in the middle of the set.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
VofaRS=lwh

34. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

35. Properties of the Interior and Exterior Angles of a Triangle
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

36. Dividing Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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 value that appears the most often.

37. Finding the Area of a Sector
2(pie)r
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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
Do whatever is necessary to both sides to isolate the variable.

38. Solving a System of Equations
Get the absolute value equation by itself. Solve.
Use the units to keep things straight - Snowfall inches/hours
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

39. What types of angles are formed when a transversal cross parallel lines?
-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.
Use the units to keep things straight - Snowfall inches/hours
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Four equal acute angles and four equal obtuse angles.

40. Converting from part-to-part ratios to part-to-whole ratios
Slope=change in y/change in x
Put each number in the original ratio over the sum of the numbers.
Use the units to keep things straight - Snowfall inches/hours
The whole number left over after division.

41. What is the positive difference between the answers to the equation 35+x(2)=12x?
The value that falls in the middle of the set.
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
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
2(pie)r

42. Finding the Surface Area of a Rectangular Solid
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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 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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

43. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.

44. Adding and Subtracting Roots
Just add or subtract the coefficients in front of the radicals.
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.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

45. 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.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

46. Solving an Inequality
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

47. If the average of a - b - and 48 is 48 - what is the value of a + b?
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
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

48. Finding the Volume of a Cylinder
FOIL: First - Outer - Inner - Last... Combine Like Terms
VofaC: (pie)r(2)h
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

49. 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.
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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

50. PEMDAS
Combine like terms.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

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