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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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1. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
-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 distributive property then combine the like terms.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

2. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 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.
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.
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.
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.

3. Multiply and Divide Positive and Negative Numbers
Use the units to keep things straight - Snowfall inches/hours
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

4. Difference Between a Factor and a Multiple
-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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use the formula distance=rate*time and its variations to help in this question.
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

5. Finding the Slope of a Line When Given Two Points on the Line
Get the absolute value equation by itself. Solve.
Average the smallest and largest number
Slope=change in y/change in x
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

6. Factoring the Difference of Two Squares
Express them with a common denominator.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Do whatever is necessary to both sides to isolate the variable.
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.

7. Scalene - Isosceles - and Equilateral Triangles
The value that falls in the middle of the set.
Cross multiply.
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.
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.

8. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

9. Solving a System of Equations
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
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

10. Prime Factorization of a Number
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
-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.
Multiply the exponents - (x^3)^4=x^3*4=x^12

11. What is a Function and how do you Evaluate one?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Use the distributive property then combine the like terms.

12. Finding the Sum of the Interior Angles of a Polygon
Two relatively prime numbers are integers that have no common factor other than 1.
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.
Find a common denominator - then add or subtract the numerators.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

13. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
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
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Average the smallest and largest number

14. 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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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

15. Finding the Area of a Sector
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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
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

16. Solving an Inequality
Probability: Number of Favorable Outcomes/Total Possible Outcomes
-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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
The whole number left over after division.

17. 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
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.
Adjacent angles are supplementary - Vertical angles are equal
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Four equal acute angles and four equal obtuse angles.

18. Finding the Midpoint Between Two Points
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.
(x1+x2)/2 -(y1+y2)/2
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

19. 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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.

20. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Use the units to keep things straight - Snowfall inches/hours

21. Properties of Similar Triangles
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

22. Converting from part-to-part ratios to part-to-whole ratios
Put each number in the original ratio over the sum of the numbers.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/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.

23. 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.
Slope=change in y/change in x
Isolate the radical expression and use the standard rules of algebra.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

24. General Procedure for Multiplying Polynomials
Average: Sum of the Terms/Number of the 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.
Use the distributive property then combine the like terms.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

25. Calculating Negative Exponents and Radical Exponents
Express them with a common denominator.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.

26. Finding the Length of an Arc in a Circle
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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 pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Get the absolute value equation by itself. Solve.

27. What is the Triangle Inequality Theorem?
(x1+x2)/2 -(y1+y2)/2
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.
Average the smallest and largest number

28. What value of x is not in the domain of the function f(x)=x-2/x-3?
Get the absolute value equation by itself. Solve.
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.

29. If (Square Root: x-1)+5=12 - what is the value of x/2?
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Find a common denominator - then add or subtract the numerators.

30. Finding the GCF of Two or More Numbers
(x1+x2)/2 -(y1+y2)/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.
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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

31. What types of angles are formed when a transversal cross parallel lines?
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
Four equal acute angles and four equal obtuse angles.

32. Finding a Term in a Geometric Sequence
Sum: Average x Number of Terms
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

33. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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 value that falls in the middle of the set.

34. 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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.

35. Counting Consecutive Integers
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Subtract the smallest from the largest and add 1
-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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

36. Converting from an Improper Fraction to a Mixed Number
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of 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.
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
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. Characteristics of a Rectangle
Use the formula distance=rate*time and its variations to help in this question.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
A(2)+b(2)=c(2)

38. Simplifying Square Roots
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.
VofaRS=lwh
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Isolate the radical expression and use the standard rules of algebra.

39. Characteristics of a Square
Use the units to keep things straight - Snowfall inches/hours
Put the equation into y=mx+b-- in which case b is the y-intercept.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
A(2)+b(2)=c(2)

40. Counting the Total Number of Possibilities for Several Events to Occur
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

41. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Average the smallest and largest number
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

42. 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?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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 variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

43. Convert From a Fraction to a Decimal - Vice Versa
VofaC: (pie)r(2)h
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
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.

44. Formula Used to Find Percent
Multiply the numerators and multiply the denominators.
-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.
Part=Percent x Whole
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

45. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Do whatever is necessary to both sides to isolate the variable.
Get the absolute value equation by itself. Solve.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.

46. What is the Pythagorean Theorem?
Average the smallest and largest number
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.
A(2)+b(2)=c(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.

47. What types of angles are formed when two lines intersect?
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Adjacent angles are supplementary - Vertical angles are equal

48. If x(2)=7x+18 - what is the positive value of x?
Find a common denominator - then add or subtract the numerators.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

49. If the average of a - b - and 48 is 48 - what is the value of a + b?
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
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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. An Important Property of a Line Tangent to a Circle
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.
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 group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

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