SAT Math

Instructions:

• Answer 50 questions in 15 minutes.
• If you are not ready to take this test, you can study here.
• Match each statement with the correct term.
• Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Identifying Which Number of a Fraction is the Part and Which Number is the Whole

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2. Convert From a Fraction to a Decimal - Vice Versa
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
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)
The value that appears the most often.


3. General Procedure for Multiplying Polynomials
(pie)r(squared)
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Use the distributive property then combine the like terms.


4. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Express them with a common denominator.


5. Properties of the Interior and Exterior Angles of a Triangle
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


6. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

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7. Finding the Area of a Sector

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8. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Two relatively prime numbers are integers that have no common factor other than 1.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


9. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
Use the distributive property then combine the like terms.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.


10. 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.
Factor out and cancel all factors the numerator and denominator have in common.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.


11. Adding a Positive Number to a Negative Number
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Average: Sum of the Terms/Number of the Terms
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


12. What is the Pythagorean Theorem?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Express them with a common denominator.
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.
A(2)+b(2)=c(2)


13. 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
-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 simple numbers like 1 and 2 and see what happens.
Use the units to keep things straight - Snowfall inches/hours


14. Finding a Term in a Geometric Sequence
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc'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.


15. Counting Consecutive Integers
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
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Subtract the smallest from the largest and add 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.


16. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
2(pie)r
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
Use the formula distance=rate*time and its variations to help in this question.


17. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
VofaC: (pie)r(2)h
Use simple numbers like 1 and 2 and see what happens.


18. Finding the Volume of a Rectangular Solid
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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
VofaRS=lwh


19. Knowing if an Integer is a Multiple of 2 or 4
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 group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
-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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


20. Counting the Total Number of Possibilities for Several Events to Occur
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Multiply the numerators and multiply the denominators.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.


21. Definition of an Irrational Number
-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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


22. What are Two Special Pythagorean Triples?

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

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24. Prime Factorization of a Number
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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


25. Solving an Inequality
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.


26. Finding the Rate of Speed
Find a common denominator - then add or subtract the numerators.
Do whatever is necessary to both sides to isolate the variable.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Use the formula distance=rate*time and its variations to help in this question.


27. Let N represent the smallest positive integer that is a multiple of 6 and 8 - but leaves a remainder of 2 when divided by 7. What is the value of N?
2(pie)r
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
VofaC: (pie)r(2)h


28. 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.
-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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


29. Formula Used to Find Percent
Part=Percent x Whole
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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


30. Definition of a Rational Number
Adjacent angles are supplementary - Vertical angles are equal
-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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


31. Increasing and Decreasing a Number by a Certain Percentage
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
-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.


32. Finding the Area of a Triangle

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33. Finding the Length of an Arc in a Circle

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34. Finding the Circumference of a Circle
2(pie)r
Switch the numerator and denominator.
Use simple numbers like 1 and 2 and see what happens.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


35. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Find a common denominator - then add or subtract the numerators.
Multiply the numerators and multiply the denominators.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


36. What value of x is not in the domain of the function f(x)=x-2/x-3?
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Part=Percent x Whole
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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


37. What types of angles are formed when two lines intersect?
Get the absolute value equation by itself. Solve.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Adjacent angles are supplementary - Vertical angles are equal
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


38. Solving a Problem Involving Rates
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Use the units to keep things straight - Snowfall inches/hours
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


39. Simplifying Square Roots
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
The whole number left over after division.
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 the perfect squares under the radical - take their square roots - and put the result in front.


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
-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.
Four equal acute angles and four equal obtuse angles.
-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.


41. Properties of a 45-45-90 Triangle
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


42. Adding and Subtracting Roots
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.
Cross multiply.
-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.
Just add or subtract the coefficients in front of the radicals.


43. 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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
VofaC: (pie)r(2)h
Just add or subtract the coefficients in front of the radicals.


44. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
Multiply the numerators and multiply the denominators.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


45. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


46. Knowing if an Integer is a Multiple of 5 or 10
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.
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.
Sum: Average x Number of Terms
-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.


47. Adding and Subtracting Monomials
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Factor out and cancel all factors the numerator and denominator have in common.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


48. Multiplying Fractions
-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.
Put each number in the original ratio over the sum of the numbers.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Multiply the numerators and multiply the denominators.


49. PEMDAS
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
2(pie)r
Express them with a common denominator.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


50. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)