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SAT Math

Subjects : sat, 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. Finding the y-intercept When Given an Equation of a Line
Just add or subtract the coefficients in front of the radicals.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Use the units to keep things straight - Snowfall inches/hours

2. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
Four equal acute angles and four equal obtuse angles.
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.

3. If the average of a - b - and 48 is 48 - what is the value of a + b?
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
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

4. Finding the Surface Area of a Rectangular Solid
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

5. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Put each number in the original ratio over the sum of the numbers.
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Use simple numbers like 1 and 2 and see what happens.

6. If (Square Root: x-1)+5=12 - what is the value of x/2?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

7. Increasing and Decreasing a Number by a Certain Percentage
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Cancel factors common to the numerator and denominator.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
-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.

8. If 4(x(2)-10x+25) - then what is the value of x?
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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
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.

9. What is the Pythagorean Theorem?
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
Average: Sum of the Terms/Number of the Terms
A(2)+b(2)=c(2)
The value that appears the most often.

10. Finding the Slope of a Line When Given Two Points on the Line
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
Slope=change in y/change in x
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

11. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Average the smallest and largest number

12. Adding a Positive Number to a Negative Number
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Cancel factors common to the numerator and denominator.
Adjacent angles are supplementary - Vertical angles are equal
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

13. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
VofaRS=lwh
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

14. Setting Up a Ratio
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
VofaC: (pie)r(2)h
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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 length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Get the absolute value equation by itself. Solve.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

16. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Adjacent angles are supplementary - Vertical angles are equal
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
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

17. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.

18. Solving an Inequality
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Just add or subtract the coefficients in front of the radicals.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

19. Converting From a Mixed Number to an Improper Fraction
Use the distributive property then combine the like terms.
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

20. Finding the Reciprocal of a Fraction
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Switch the numerator and 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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

21. How do you know if an integer is a multiple of 3 or 9?
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

22. Adding and Subtracting Polynomials
Sum: Average x Number of Terms
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Factor out and cancel all factors the numerator and denominator have in common.
Combine like terms.

23. Finding the LCM of Two or More Numbers

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24. Simplifying a Fraction to Lowest Terms
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Factor out and cancel all factors the numerator and denominator have in common.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Use simple numbers like 1 and 2 and see what happens.

25. Converting from part-to-part ratios to part-to-whole ratios
Put the equation into y=mx+b-- in which case b is the y-intercept.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Put each number in the original ratio over the sum of the numbers.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

26. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
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 two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

27. Simplifying an Algebraic Equation
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.
Cancel factors common to the numerator and denominator.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
A(2)+b(2)=c(2)

28. Finding the Sum of the Interior Angles of a Polygon
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.

29. Counting the Total Number of Possibilities for Several Events to Occur
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

30. Definition of a Rational Number
Use the units to keep things straight - Snowfall inches/hours
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

31. Finding the Circumference of a Circle
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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
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
2(pie)r

32. 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 - substitute for the variable. Then evaluate the expression using the correct order of operations.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

33. Difference Between a Factor and a Multiple
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Probability: Number of Favorable Outcomes/Total Possible Outcomes
-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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

34. Characteristics of a Parallelogram
The value that appears the most often.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

35. What is the Triangle Inequality Theorem?
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

36. Solving a Linear Equation
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Do whatever is necessary to both sides to isolate the variable.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Use simple numbers like 1 and 2 and see what happens.

37. Definition of Remainder
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
The whole number left over after division.
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.

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

39. Solving a System of Equations
Combine like terms.
(pie)r(squared)
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 the formula distance=rate*time and its variations to help in this question.

40. 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.
Use simple numbers like 1 and 2 and see what happens.
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
Just add or subtract the coefficients in front of the radicals.

41. Multiply and Divide Positive and Negative Numbers
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
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

42. PEMDAS
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.
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
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

43. Properties of a 45-45-90 Triangle
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

44. Formula to Find Average
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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

45. Multiplying Fractions
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Express them with a common denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Multiply the numerators and multiply the denominators.

46. If r#t=t(r)-r(t) - then what is 4#3?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

47. 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?
Switch the numerator and denominator.
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.
Cancel factors common to the numerator and denominator.

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

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49. Average Rate and How Do You Find It
Multiply the numerators and multiply the denominators.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
-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.
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. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

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