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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.
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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. Counting Consecutive Integers
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Part=Percent x Whole
Subtract the smallest from the largest and add 1
Put the equation into y=mx+b-- in which case b is the y-intercept.

2. 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
Cross multiply.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

3. Number of Groups - +1 Each Time
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

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

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5. Simplifying Square Roots
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.

6. Scalene - Isosceles - and Equilateral Triangles
Cross multiply.
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.
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.
Find a common denominator - then add or subtract the numerators.

7. Solving an Inequality
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Isolate the radical expression and use the standard rules of algebra.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

8. Finding the Area of a Circle
Use the formula distance=rate*time and its variations to help in this question.
(pie)r(squared)
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

9. Characteristics of a Square
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
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.
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.

10. Adding and Subtracting Polynomials
Combine like terms.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

11. Factoring a Polynomial ('FOIL in Reverse')
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.
(x1+x2)/2 -(y1+y2)/2
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
FOIL: First - Outer - Inner - Last... Combine Like Terms

12. Solving a Proportion
Cross multiply.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.

13. Formula Used to Find Percent
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Part=Percent x Whole

14. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Use the distributive property then combine the like terms.
Do whatever is necessary to both sides to isolate the variable.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

15. Finding the LCM of Two or More Numbers

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16. Evaluating an Algebraic Expression
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating 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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

17. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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 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.

18. Direct Variation and Inverse Variation
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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

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

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20. If (Square Root: x-1)+5=12 - what is the value of x/2?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
(pie)r(squared)
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

21. Convert From a Fraction to a Decimal - Vice Versa
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Factor out and cancel all factors the numerator and denominator have in common.
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 formula distance=rate*time and its variations to help in this question.

22. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Combine like terms.
Cross multiply.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

23. Calculating the Probability that an Event will Take Place
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Multiply the numerators and multiply the denominators.

24. Counting the Total Number of Possibilities for Several Events to Occur
-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.
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
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.

25. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Isolate the radical expression and use the standard rules of algebra.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Get the absolute value equation by itself. Solve.

26. If 3(3x)=9(x+2) - what is the value of x?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Sum: Average x Number of Terms

27. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
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.
-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.

28. PEMDAS
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

29. Converting from part-to-part ratios to part-to-whole ratios
-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.
Put each number in the original ratio over the sum of the numbers.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

30. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
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.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

31. 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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Isolate the radical expression and use the standard rules of algebra.
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.

32. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Two relatively prime numbers are integers that have no common factor other than 1.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

33. 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
(x1+x2)/2 -(y1+y2)/2
-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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

34. Finding the Volume of a Cylinder
The value that appears the most often.
VofaC: (pie)r(2)h
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

35. Finding the Circumference of a Circle
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
2(pie)r
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.

36. Simplifying an Algebraic Equation
Adjacent angles are supplementary - Vertical angles are equal
Cancel factors common to the numerator and denominator.
The value that appears the most often.
Plug in the given values for the unknowns and calculate according to PEMDAS.

37. What value of x is not in the domain of the function f(x)=x-2/x-3?
Cross multiply.
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
Isolate the radical expression and use the standard rules of algebra.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

38. 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.
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
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.
2(pie)r

39. Finding the GCF of Two or More Numbers
Put the equation into y=mx+b-- in which case b is the y-intercept.
Switch the numerator and denominator.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

40. What types of angles are formed when a transversal cross parallel lines?
Use the distributive property then combine the like terms.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
Four equal acute angles and four equal obtuse angles.

41. 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?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Put the equation into y=mx+b-- in which case b is the y-intercept.

42. Setting Up a Ratio
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

43. Finding the Distance Between Two Points on a Coordinate Graph
Use the formula distance=rate*time and its variations to help in this question.
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.
-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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

44. 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.
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.
Slope=change in y/change in x

45. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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
Get the absolute value equation by itself. Solve.
Use simple numbers like 1 and 2 and see what happens.

46. Properties of the Interior and Exterior Angles of a Triangle
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.
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 square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

47. Multiply and Divide Positive and Negative Numbers
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
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

48. Factoring the Difference of Two Squares
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Switch the numerator and denominator.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

49. What Does Solving In Terms of Mean?
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.

50. What is the Pythagorean Theorem?
Adjacent angles are supplementary - Vertical angles are equal
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
A(2)+b(2)=c(2)
Part=Percent x Whole