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SAT Math
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sat
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math
Instructions:
Answer 50 questions in 15 minutes.
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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. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
-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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Average the smallest and largest number
2. 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?
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.
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 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.
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. Properties of the Interior and Exterior Angles of a Triangle
Put each number in the original ratio over the sum of the numbers.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Four equal acute angles and four equal obtuse angles.
4. Converting from an Improper Fraction to a Mixed Number
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
(x1+x2)/2 -(y1+y2)/2
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.
5. Solving a Problem Involving Rates
Four equal acute angles and four equal obtuse angles.
(pie)r(squared)
Use the units to keep things straight - Snowfall inches/hours
Use simple numbers like 1 and 2 and see what happens.
6. Definition of Remainder
The whole number left over after division.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
VofaRS=lwh
7. Multiplying and Dividing Roots
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
VofaRS=lwh
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
8. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
9. Finding the Area of a Triangle
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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 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.
Use simple numbers like 1 and 2 and see what happens.
10. 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
Factor out and cancel all factors the numerator and denominator have in common.
-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.
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
11. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
12. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Average the smallest and largest number
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
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
13. Counting the Total Number of Possibilities for Several Events to Occur
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.
Find a common denominator - then add or subtract the numerators.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Express them with a common denominator.
14. What is the positive difference between the answers to the equation 35+x(2)=12x?
-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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
2(pie)r
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
15. Finding the Area of a Sector
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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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
16. What are Two Special Pythagorean Triples?
Put each number in the original ratio over the sum of the numbers.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
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.
17. An Important Property of a Line Tangent to a Circle
Average the smallest and largest number
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Sum: Average x Number of Terms
18. What is a Function and how do you Evaluate one?
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.
Average the smallest and largest number
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
The whole number left over after division.
19. Determining Absolute Value of a Number
Adjacent angles are supplementary - Vertical angles are equal
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Multiply the numerators and multiply the denominators.
20. Numbers that are Relatively Prime
-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.
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.
Two relatively prime numbers are integers that have no common factor other than 1.
Use the units to keep things straight - Snowfall inches/hours
21. Properties of a 30-60-90 Triangle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Adjacent angles are supplementary - Vertical angles are equal
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 out and cancel all factors the numerator and denominator have in common.
22. Direct Variation and Inverse Variation
-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.
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
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
23. If 4(x(2)-10x+25) - then what is the value of x?
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
-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.
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.
24. Knowing if an Integer is a Multiple of 2 or 4
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 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.
-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.
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.
25. What is the Pythagorean Theorem?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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
Slope=change in y/change in x
A(2)+b(2)=c(2)
26. Finding the Missing Number in a Series When You are Given the Average
Use the formula distance=rate*time and its variations to help in this question.
Slope=change in y/change in x
Factor out and cancel all factors the numerator and denominator have in common.
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.
27. Finding the Volume of a Rectangular Solid
(x1+x2)/2 -(y1+y2)/2
Average: Sum of the Terms/Number of the Terms
VofaRS=lwh
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.
28. Properties of Similar Triangles
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Switch the numerator and denominator.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
29. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
The whole number left over after division.
Cross multiply.
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
30. Factoring the Difference of Two Squares
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
31. How do you know if an integer is a multiple of 3 or 9?
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.
Combine like terms.
Use the distributive property then combine the like terms.
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.
32. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
33. Multiplying Monomials
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
(pie)r(squared)
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
34. Characteristics of a Square
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Use the units to keep things straight - Snowfall inches/hours
-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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
35. 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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Use the formula distance=rate*time and its variations to help in this question.
36. Characteristics of a Parallelogram
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
37. If the average of a - b - and 48 is 48 - what is the value of 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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
-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.
38. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
A(2)+b(2)=c(2)
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
39. Adding a Positive Number to a Negative Number
2(pie)r
Use the formula distance=rate*time and its variations to help in this question.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
-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.
40. Convert From a Fraction to a Decimal - Vice Versa
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Cancel factors common to the numerator and denominator.
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
42. Number of Groups - +1 Each Time
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Average the smallest and largest number
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
43. Average Rate and How Do You Find It
Cancel factors common to the numerator and denominator.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
44. Formula Used to Find Percent
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Part=Percent x Whole
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
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.
45. 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?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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 two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Find a common denominator - then add or subtract the numerators.
46. Comparing the values of two or more Fractions
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Express them with a common denominator.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
47. Converting From a Mixed Number to an Improper Fraction
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
VofaRS=lwh
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
48. Identifying Which Number of a Fraction is the Part and Which Number is the Whole
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
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
49. Finding the Domain and Range of a Function
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.
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 distributive property then combine the like terms.
Express them with a common denominator.
50. Adding and Subtracting Fractions
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Find a common denominator - then add or subtract the numerators.
VofaRS=lwh
Express them with a common denominator.
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