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. 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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.


2. Raising a Power to a Power
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 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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


3. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
2(pie)r
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.


4. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
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.
The value that falls in the middle of the set.
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.


5. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
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.
VofaC: (pie)r(2)h


6. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Two relatively prime numbers are integers that have no common factor other than 1.
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.
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.
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.


7. Finding the Missing Number in a Series When You are Given the Average
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
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.


8. Setting Up a Ratio
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


9. Adding and Subtracting Polynomials
Just add or subtract the coefficients in front of the radicals.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Combine like terms.
The value that appears the most often.


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

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11. Properties of the Interior and Exterior Angles of a Triangle
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


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

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13. Definition of an Irrational Number
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
-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.


14. Adding and Subtracting Roots
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
Just add or subtract the coefficients in front of the radicals.
Four equal acute angles and four equal obtuse angles.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


15. PEMDAS
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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 units to keep things straight - Snowfall inches/hours
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


16. Characteristics of a Rectangle
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


17. Quickly Finding the Average of a Series of Evenly Spaced Numbers
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.
-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.
The value that appears the most often.
Average the smallest and largest number


18. Multiplying 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.
Cancel factors common to the numerator and denominator.
Multiply the numerators and multiply the denominators.
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.


19. If 4(x(2)-10x+25) - then what is the value of x?
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.
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.
Average: Sum of the Terms/Number of the Terms


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

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21. Finding the LCM of Two or More Numbers

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22. What are Two Special Pythagorean Triples?

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23. Multiplying Monomials
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


24. 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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
2(pie)r
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds


25. Factoring the Difference of Two Squares
VofaC: (pie)r(2)h
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


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

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27. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
The value that falls in the middle of the set.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Cancel factors common to the numerator and denominator.


28. What value of x is not in the domain of the function f(x)=x-2/x-3?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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
FOIL: First - Outer - Inner - Last... Combine Like Terms
Factor out and cancel all factors the numerator and denominator have in common.


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


30. Finding the y-intercept When Given an Equation of a Line
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


31. Properties of Similar Triangles
Slope=change in y/change in x
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Use the formula distance=rate*time and its variations to help in this question.


32. Finding the Sum of the Interior Angles of a Polygon
Combine like terms.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Do whatever is necessary to both sides to isolate the variable.
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.


33. Finding the Rate of Speed
Use the formula distance=rate*time and its variations to help in this question.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
VofaC: (pie)r(2)h
Part=Percent x Whole


34. 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
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.
A(2)+b(2)=c(2)
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


35. Finding the Area of a Triangle

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36. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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
Do whatever is necessary to both sides to isolate the variable.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


37. Multiply and Divide Positive and Negative Numbers
VofaRS=lwh
Put the equation into y=mx+b-- in which case b is the y-intercept.
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
Switch the numerator and denominator.


38. What types of angles are formed when a transversal cross parallel lines?
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Four equal acute angles and four equal obtuse angles.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


39. Convert From a Fraction to a Decimal - Vice Versa
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


40. Finding the Midpoint Between Two Points
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
(x1+x2)/2 -(y1+y2)/2
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.


41. Prime Factorization of a Number
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


42. Difference Between a Factor and a Multiple
2(pie)r
-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 the smallest and largest number
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4


43. An Important Property of a Line Tangent to a Circle
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
-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.
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.
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. Knowing if an Integer is a Multiple of 5 or 10
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
-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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


45. What Does Solving In Terms of Mean?
Find a common denominator - then add or subtract the numerators.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
Use the formula distance=rate*time and its variations to help in this question.


46. Number of Groups - +1 Each Time
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
The value that falls in the middle of the set.


47. Solving a System of Equations
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
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


48. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
VofaC: (pie)r(2)h
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.
VofaRS=lwh
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


49. Simplifying an Algebraic Equation
The whole number left over after division.
Cancel factors common to the numerator and denominator.
Use the units to keep things straight - Snowfall inches/hours
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


50. 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?
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Two relatively prime numbers are integers that have no common factor other than 1.
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 value that appears the most often.