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. Convert From a Fraction to a Decimal - Vice Versa
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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 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.
Cross multiply.


2. Finding the Slope of a Line When Given Two Points on the Line
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.
Multiply the numerators and multiply the denominators.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Slope=change in y/change in x


3. Solving a Linear Equation
-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.
Do whatever is necessary to both sides to isolate the variable.
Switch the numerator and denominator.
The whole number left over after division.


4. Properties of the Interior and Exterior Angles of a Triangle
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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 simple numbers like 1 and 2 and see what happens.
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.


5. What are Two Special Pythagorean Triples?

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6. Finding the LCM of Two or More Numbers

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7. Finding the Volume of a Cylinder
Just add or subtract the coefficients in front of the radicals.
(x1+x2)/2 -(y1+y2)/2
VofaC: (pie)r(2)h
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


8. Knowing if an Integer is a Multiple of 5 or 10
-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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Put each number in the original ratio over the sum of the numbers.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds


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

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10. 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
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


11. Multiply and Divide Positive and Negative Numbers
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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


12. Multiplying and Dividing Roots
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.


13. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Multiply the numerators and multiply the denominators.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


14. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Four equal acute angles and four equal obtuse angles.
Subtract the smallest from the largest and add 1
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. What is the Triangle Inequality Theorem?
The value that appears the most often.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


16. 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 value that appears the most often.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


17. Converting from an Improper Fraction to a Mixed Number
The value that falls in the middle of the set.
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.
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.
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


18. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
VofaRS=lwh
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
-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.


19. What value of x is not in the domain of the function f(x)=x-2/x-3?
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


20. Raising a Power to a Power
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.
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


21. Determining Absolute Value of a Number
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


22. Multiplying Binomials
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
FOIL: First - Outer - Inner - Last... Combine Like Terms
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


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

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24. 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?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
VofaC: (pie)r(2)h
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Average the smallest and largest number


25. What types of angles are formed when a transversal cross parallel lines?
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Four equal acute angles and four equal obtuse angles.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


26. Prime Factorization of a Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Find a common denominator - then add or subtract the numerators.
Factor out and cancel all factors the numerator and denominator have in common.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


27. Simplifying an Algebraic Equation
(pie)r(squared)
Cancel factors common to the numerator and denominator.
Do whatever is necessary to both sides to isolate the variable.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


28. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
Find a common denominator - then add or subtract the numerators.
Cancel factors common to the numerator and denominator.
Use the formula distance=rate*time and its variations to help in this question.


29. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.


30. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Part=Percent x Whole
-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.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


31. Simplifying Square Roots
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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
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.


32. Formula Used to Find Percent
A(2)+b(2)=c(2)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Part=Percent x Whole
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. If (Square Root: x-1)+5=12 - what is the value of x/2?
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.
VofaC: (pie)r(2)h
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


34. If 4(x(2)-10x+25) - then what is the value of x?
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
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.


35. Characteristics of a Square
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.
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.
Cross multiply.


36. Finding the Slope When Given an Equation of a Line
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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


37. Finding the Length of an Arc in a Circle

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38. Finding the Area of a Triangle

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39. Definition of Remainder
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.
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 whole number left over after division.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


40. Increasing and Decreasing a Number by a Certain Percentage
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
-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.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4


41. 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?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Express them with a common denominator.
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.
The value that falls in the middle of the set.


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


43. Setting Up a Ratio
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
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


44. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
-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 units to keep things straight - Snowfall inches/hours


45. Finding the GCF of Two or More Numbers
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Average the smallest and largest number
The whole number left over after division.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


46. Finding the Area of a Sector

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47. If r#t=t(r)-r(t) - then what is 4#3?
Isolate the radical expression and use the standard rules of algebra.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Four equal acute angles and four equal obtuse angles.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


48. 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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


49. What Does Solving In Terms of Mean?
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.
Use simple numbers like 1 and 2 and see what happens.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


50. Finding the Midpoint Between Two Points
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
(x1+x2)/2 -(y1+y2)/2
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.