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SAT Math

Subjects : sat, math

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. Multiplying Expressions with Exponents that Have a Common Base
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Find a common denominator - then add or subtract the numerators.
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.
Factor out and cancel all factors the numerator and denominator have in common.

2. Prime Factorization of a Number
Combine like terms.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
The value that falls in the middle of the set.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

3. Properties of the Interior and Exterior Angles of a Triangle
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: 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.
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.

4. Simplifying a Fraction to Lowest Terms
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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 out and cancel all factors the numerator and denominator have in common.
Put the equation into y=mx+b-- in which case b is the y-intercept.

5. If the average of a - b - and 48 is 48 - what is the value of a + b?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Use the units to keep things straight - Snowfall inches/hours

6. 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?
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Cross multiply.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

7. Solving an Inequality
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

8. Finding the Slope When Given an Equation of a Line
-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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.

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
Do whatever is necessary to both sides to isolate the variable.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Get the absolute value equation by itself. Solve.

10. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Average: Sum of the Terms/Number of the Terms
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
VofaRS=lwh
Get the absolute value equation by itself. Solve.

11. Solving a System of Equations
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Fraction to a Decimal: Divide the Denominator into the numerator - Decimal to a Fraction: Set the decimal over 1 and multiply the numerator and denominator by 10 raised to the number of digits to the right of the decimal point.
Combine 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.

12. Definition of a Rational Number
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Sum: Average x Number of Terms
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

13. Finding the Distance Between Two Points on a Coordinate Graph
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
VofaRS=lwh
Two relatively prime numbers are integers that have no common factor other than 1.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

14. Finding the Surface Area of a Rectangular Solid
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)
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

15. Calculating Negative Exponents and Radical Exponents
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Multiply the exponents - (x^3)^4=x^3*4=x^12
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

16. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
Express them with a common denominator.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

17. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
(pie)r(squared)
The whole number left over after division.

18. Finding the Reciprocal of a Fraction
-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.
Switch the numerator and denominator.
Use the units to keep things straight - Snowfall inches/hours
Slope=change in y/change in x

19. Solving a Problem Involving Rates
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)
Use the units to keep things straight - Snowfall inches/hours
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.

20. If (Square Root: x-1)+5=12 - what is the value of x/2?
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Plug in the given values for the unknowns and calculate according to PEMDAS.

21. Raising a Power to a Power
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Multiply the exponents - (x^3)^4=x^3*4=x^12
Isolate the radical expression and use the standard rules of algebra.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

22. What types of angles are formed when two lines intersect?
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Adjacent angles are supplementary - Vertical angles are equal
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.

23. Convert From a Fraction to a Decimal - Vice Versa
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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

24. Numbers that are Relatively Prime
Combine like terms.
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.
Two relatively prime numbers are integers that have no common factor other than 1.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

25. Simplifying an Algebraic Equation
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Average the smallest and largest number
Cancel factors common to the numerator and denominator.

26. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
Set the quadratic equation equal to zero with the terms in order of decreasing exponents - and solve for the roots by factoring. Don't forget to then find the difference in the roots by subtracting them. Ans: 2
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Use simple numbers like 1 and 2 and see what happens.

27. Adding and Subtracting Monomials
Sum: Average x Number of Terms
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
The whole number left over after division.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

28. Characteristics of a Square
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Switch the numerator and denominator.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

29. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
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 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.
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.

30. Characteristics of a Parallelogram
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Do whatever is necessary to both sides to isolate the variable.

31. Factoring the Difference of Two Squares
The whole number left over after division.
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.

32. Dividing Expressions with Exponents that Have a Common Base
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
A(2)+b(2)=c(2)
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Probability: Number of Favorable Outcomes/Total Possible Outcomes

33. Finding the Area of a Triangle

34. Finding the Mode of a Set of Numbers
VofaRS=lwh
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.
The value that appears the most often.

35. Multiplying Fractions
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
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Multiply the numerators and multiply the denominators.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

36. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

37. Solving a Linear Equation
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Do whatever is necessary to both sides to isolate the variable.

38. Finding the Slope of a Line When Given Two Points on the Line
Factor out and cancel all factors the numerator and denominator have in common.
Find a common denominator - then add or subtract the numerators.
Slope=change in y/change in x
-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.

39. Direct Variation and Inverse Variation
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.
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
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

40. Scalene - Isosceles - and Equilateral Triangles
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Four equal acute angles and four equal obtuse angles.
Scalene- No sides or angles are equal - Isosceles- Have two equal sides. The angles opposite the equal sides are also equal - Equilateral- All three sides and angles are equal.
Average: Sum of the Terms/Number of the Terms

41. General Procedure for Multiplying Polynomials
Cross multiply.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
The value that falls in the middle of the set.
Use the distributive property then combine the like terms.

42. Adding and Subtracting Fractions
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Find a common denominator - then add or subtract the numerators.
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

43. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Switch the numerator and denominator.
Use simple numbers like 1 and 2 and see what happens.
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
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

44. Finding the Circumference of a Circle
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
2(pie)r
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.

45. Calculating the Probability that an Event will Take Place
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.
Express them with a common denominator.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

46. Finding the Length of an Arc in a Circle

47. Comparing the values of two or more Fractions
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.
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.
Express them with a common denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

48. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
2(pie)r
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Put the equation into y=mx+b-- in which case b is the y-intercept.

49. Expressing the Union and Intersection of Sets
The union of Set A and Set B is the set of elements that are in either or both Set A and Set B - The intersection of Set A and Set B is the set of elements common to both Set A and Set B
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.
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.

50. Finding the Area of a Sector