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. Multiplying Fractions
Multiply the numerators and multiply the denominators.
Adjacent angles are supplementary - Vertical angles are equal
Put the equation into y=mx+b-- in which case b is the y-intercept.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


2. What are Two Special Pythagorean Triples?

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3. Finding the Area of a Sector

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4. Finding the Volume of a Cylinder
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
VofaC: (pie)r(2)h
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


5. Definition of an Irrational Number
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


6. Knowing if an Integer is a Multiple of 2 or 4
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Change the division sign to a multiplication sign - invert the second fraction - and 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.
Plug in the given values for the unknowns and calculate according to PEMDAS.


7. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.


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

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9. Finding the Length of an Arc in a Circle

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10. Knowing if an Integer is a Multiple of 5 or 10
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.
VofaC: (pie)r(2)h
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


11. Evaluating an Algebraic Expression
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Use the units to keep things straight - Snowfall inches/hours
Plug in the given values for the unknowns and calculate according to PEMDAS.


12. Expressing the Union and Intersection of Sets
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
VofaRS=lwh
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


13. Properties of the Interior and Exterior Angles of a Triangle
Switch the numerator and denominator.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


14. Finding the Sum of the Interior Angles of a Polygon
Cross multiply.
VofaC: (pie)r(2)h
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


15. Converting From a Mixed Number to an Improper Fraction
Put each number in the original ratio over the sum of the numbers.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
The whole number left over after division.
VofaRS=lwh


16. Number of Groups - +1 Each Time
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Use the formula distance=rate*time and its variations to help in this question.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


17. Definition of Remainder
-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.
The whole number left over after division.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Combine like terms.


18. Finding the Volume of a Rectangular Solid
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
VofaRS=lwh


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


20. Finding the Distance Between Two Points on a Coordinate Graph
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
The value that falls in the middle of the set.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


21. Converting from part-to-part ratios to part-to-whole ratios
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Put each number in the original ratio over the sum of the numbers.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


22. Characteristics of a Parallelogram
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Four equal acute angles and four equal obtuse angles.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
2(pie)r


23. Convert From a Fraction to a Decimal - Vice Versa
Express them with a common denominator.
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
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.
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.


24. How do you know if an integer is a multiple of 3 or 9?
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
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use simple numbers like 1 and 2 and see what happens.
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. Formula to Find Average
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.
Average: Sum of the Terms/Number of the Terms
Sum: Average x Number of Terms
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


26. What is the Triangle Inequality Theorem?
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.


27. Determining Absolute Value of a Number
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.
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
Do whatever is necessary to both sides to isolate the variable.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


28. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.


29. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Switch the numerator and denominator.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


30. Adding and Subtracting Polynomials
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
Combine like terms.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.


31. Finding the Area of a Triangle

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32. Solving a Linear Equation
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Combine like terms.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Do whatever is necessary to both sides to isolate the variable.


33. Setting Up a Ratio
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use the units to keep things straight - Snowfall inches/hours
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


34. Finding the Missing Number in a Series When You are Given the Average
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 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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


35. Finding a Term in a Geometric Sequence
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.
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
Switch the numerator and denominator.
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.


36. Finding the Area 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.
(pie)r(squared)
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
Combine like terms.


37. Numbers that are Relatively Prime
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
(pie)r(squared)
Two relatively prime numbers are integers that have no common factor other than 1.


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

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39. Scalene - Isosceles - and Equilateral Triangles
-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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.


40. 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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Combine like terms.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


41. Finding the GCF of Two or More Numbers
Use the distributive property then combine the like terms.
Break down the integers into their prime factorizations - and multiply all prime factors they 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.
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.


42. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 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.
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
Use simple numbers like 1 and 2 and see what happens.


43. Calculating Negative Exponents and Radical Exponents
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


44. Properties of Similar Triangles
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Combine like terms.


45. Direct Variation and Inverse Variation
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
The whole number left over after division.
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
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


46. Multiply and Divide Positive and Negative Numbers
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
(x1+x2)/2 -(y1+y2)/2
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
Get the absolute value equation by itself. Solve.


47. Solving a System of Equations
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Multiply the numerators and multiply the denominators.
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.
Get the absolute value equation by itself. Solve.


48. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
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
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.


49. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
-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.
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.


50. Simplifying an Algebraic Equation
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Cancel factors common to the numerator and denominator.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%