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SAT Math

Subjects : 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.
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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. An Important Property of a Line Tangent to a Circle
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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. Finding the Area of a Triangle

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3. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in 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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

4. Comparing the values of two or more Fractions
Use simple numbers like 1 and 2 and see what happens.
Express them with a common denominator.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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

5. Finding the Distance Between Two Points on a Coordinate Graph
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Four equal acute angles and four equal obtuse angles.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Subtract the smallest from the largest and add 1

6. Solving a Linear Equation
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Do whatever is necessary to both sides to isolate the variable.

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

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8. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
FOIL: First - Outer - Inner - Last... Combine Like Terms
Put each number in the original ratio over the sum of the numbers.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

9. 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
-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.
Slope=change in y/change in x
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.

10. Solving a Proportion
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
Cross multiply.
Do whatever is necessary to both sides to isolate the variable.

11. Raising a Power to a Power
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.
Slope=change in y/change in x
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12

12. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Get the absolute value equation by itself. Solve.
Slope=change in y/change in x

13. Finding the GCF of Two or More Numbers
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Combine like terms.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

14. Multiplying and Dividing Roots
Sum: Average x Number of Terms
2(pie)r
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

15. Multiplying Monomials
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

16. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
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.

17. Converting from part-to-part ratios to part-to-whole ratios
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Put each number in the original ratio over the sum of the numbers.
Multiply the numerators and multiply the denominators.
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.

18. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Multiply the exponents - (x^3)^4=x^3*4=x^12

19. What types of angles are formed when a transversal cross parallel lines?
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.
Four equal acute angles and four equal obtuse angles.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
VofaC: (pie)r(2)h

20. Finding the Area of a Circle
(pie)r(squared)
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Slope=change in y/change in x
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

21. Adding a Positive Number to a Negative Number
Cross multiply.
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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

22. Setting Up a Ratio
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Factor out and cancel all factors the numerator and denominator have in common.

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

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24. Properties of Similar Triangles
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Find a common denominator - then add or subtract the numerators.
VofaC: (pie)r(2)h

25. Definition of an Irrational Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes

26. Multiply and Divide Positive and Negative Numbers
VofaRS=lwh
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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
Find a common denominator - then add or subtract the numerators.

27. Finding the Circumference of a Circle
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
2(pie)r
-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.

28. Increasing and Decreasing a Number by a Certain Percentage
-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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

29. If the average of a - b - and 48 is 48 - what is the value of a + b?
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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

30. Scalene - Isosceles - and Equilateral Triangles
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
(pie)r(squared)

31. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
Do whatever is necessary to both sides to isolate the variable.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Use the distributive property then combine the like terms.

32. 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.
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

33. Finding the Sum of the Interior Angles of a Polygon
Factor out and cancel all factors the numerator and denominator have in common.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.

34. Solving a System of Equations
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.
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.
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.
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

35. What Does Solving In Terms of Mean?
Just add or subtract the coefficients in front of the radicals.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
VofaRS=lwh

36. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
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.
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.
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.

37. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

38. Properties of the Interior and Exterior Angles of a Triangle
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 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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Adjacent angles are supplementary - Vertical angles are equal

39. Convert From a Fraction to a Decimal - Vice Versa
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.
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms

40. 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?
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Cancel factors common to the numerator and denominator.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

41. Finding the Length of an Arc in a Circle

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42. Finding the Domain and Range of a Function
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

43. Determining Absolute Value of a Number
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Put each number in the original ratio over the sum of the numbers.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

44. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

45. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

46. Characteristics of a Parallelogram
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

47. Number of Groups - +1 Each Time
Average the smallest and largest number
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
FOIL: First - Outer - Inner - Last... Combine Like Terms
(pie)r(squared)

48. Finding the Midpoint Between Two Points
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
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.
(x1+x2)/2 -(y1+y2)/2

49. Multiplying Fractions
Multiply the numerators and multiply the denominators.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

50. General Procedure for Multiplying Polynomials
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
The whole number left over after division.
Use the distributive property then combine the like terms.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4