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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. If r#t=t(r)-r(t) - then what is 4#3?
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Find a common denominator - then add or subtract the numerators.

2. Finding the Circumference of a Circle
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.
2(pie)r
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.

3. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply the numerators and multiply the denominators.
FOIL: First - Outer - Inner - Last... Combine Like Terms
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

4. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
(x1+x2)/2 -(y1+y2)/2
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 - 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.

5. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
The whole number left over after division.
Find a common denominator - then add or subtract the numerators.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

6. Finding the Rate of Speed
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Four equal acute angles and four equal obtuse angles.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the formula distance=rate*time and its variations to help in this question.

7. 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?
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.
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 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

8. If (Square Root: x-1)+5=12 - what is the value of x/2?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Put each number in the original ratio over the sum of the numbers.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

9. Finding the Slope When Given an Equation of a Line
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.

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

11. Definition of an Integer
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.

12. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

13. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.

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

15. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Switch the numerator and denominator.
(pie)r(squared)

16. Calculating the Probability that an Event will Take Place
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Put each number in the original ratio over the sum of the numbers.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

17. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

18. What types of angles are formed when a transversal cross parallel lines?
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 equal acute angles and four equal obtuse angles.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.

19. Adding and Subtracting Fractions
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Find a common denominator - then add or subtract the numerators.
Put each number in the original ratio over the sum of the numbers.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

20. Multiplying Expressions with Exponents that Have a Common Base
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

21. Finding the Length of an Arc in a Circle

22. Average Rate and How Do You Find It
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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

23. Counting the Total Number of Possibilities for Several Events to Occur
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.

24. Properties of a 45-45-90 Triangle
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Multiply the exponents - (x^3)^4=x^3*4=x^12

25. What is the Triangle Inequality Theorem?
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.
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.
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.
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.

26. If 3(3x)=9(x+2) - what is the value of x?
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.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Multiply the exponents - (x^3)^4=x^3*4=x^12

27. Finding the GCF of Two or More Numbers
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.

28. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
FOIL: First - Outer - Inner - Last... Combine 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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

29. Expressing the Union and Intersection of Sets
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.
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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

30. Adding and Subtracting Monomials
Part=Percent x Whole
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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

31. Adding and Subtracting Roots
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Just add or subtract the coefficients in front of the radicals.
Do whatever is necessary to both sides to isolate the variable.
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.

32. Number of Groups - +1 Each Time
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Subtract the smallest from the largest and add 1
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

33. Direct Variation and Inverse Variation
Put each number in the original ratio over the sum of the numbers.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

34. Factoring the Difference of Two Squares
Multiply the whole number part by the denominator - then add the numerator. Keep the same 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
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.

35. Solving a Proportion
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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

36. Definition of an Irrational 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.
Average the smallest and largest number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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

37. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Sum: Average x Number of Terms
Multiply the numerators and multiply the denominators.

38. How do you know if an integer is a multiple of 3 or 9?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.

39. Characteristics of a Parallelogram
Combine like terms.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
-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.

40. Properties of Similar Triangles
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.

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?
2(pie)r
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Four equal acute angles and four equal obtuse angles.

42. Multiplying and Dividing Roots
(x1+x2)/2 -(y1+y2)/2
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

43. Simplifying Square Roots
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The value that falls in the middle of the set.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

44. Finding the Midpoint Between Two Points
2(pie)r
(x1+x2)/2 -(y1+y2)/2
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

45. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Switch the numerator and denominator.
Use the distributive property then combine the like terms.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

46. Dividing Expressions with Exponents that Have a Common Base
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
VofaRS=lwh
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

47. Solving a System of Equations
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Subtract the smallest from the largest and add 1
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.

48. 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.
Adjacent angles are supplementary - Vertical angles are equal
FOIL: First - Outer - Inner - Last... Combine Like 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

49. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Use the distance formula: d=(square root over) (x2-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.
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.
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

50. Solving a Problem Involving Rates
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
Use the units to keep things straight - Snowfall inches/hours
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)