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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. Finding the Distance Between Two Points on a Coordinate Graph
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

2. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Average: Sum of the Terms/Number of the Terms
Use the formula distance=rate*time and its variations to help in this question.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

3. Simplifying Square Roots
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Multiply the numerators and multiply the denominators.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

4. Converting from part-to-part ratios to part-to-whole ratios
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.
Put each number in the original ratio over the sum of the numbers.
Get the absolute value equation by itself. Solve.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

5. 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
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

6. Finding the Sum of the Average of a Series of Numbers
Plug in the given values for the unknowns and calculate according to PEMDAS.
Sum: Average x Number of Terms
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

7. Multiplying Monomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Factor out and cancel all factors the numerator and denominator have in common.

8. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

9. Multiplying Expressions with Exponents that Have a Common Base
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.
-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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.

10. Properties of the Interior and Exterior Angles of a Triangle
Use simple numbers like 1 and 2 and see what happens.
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
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.

11. Adding a Positive Number to a Negative Number
Sum: Average x Number of Terms
VofaC: (pie)r(2)h
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

12. Definition of an Integer
Use the distributive property then combine the like terms.
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.
Find a common denominator - then add or subtract the numerators.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

13. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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 the perfect squares under the radical - take their square roots - and put the result in front.

14. Evaluating an Algebraic Expression
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Express them with a common denominator.
Plug in the given values for the unknowns and calculate according to PEMDAS.

15. Dividing Fractions
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
(x1+x2)/2 -(y1+y2)/2
Multiply the numerators and multiply the denominators.

16. Converting From a Mixed Number to an Improper Fraction
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Use the units to keep things straight - Snowfall inches/hours

17. Dividing Expressions with Exponents that Have a Common Base
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
The whole number left over after division.

18. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.

19. If 4(x(2)-10x+25) - then what is the value of x?
Use the formula distance=rate*time and its variations to help in this question.
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
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.
(x1+x2)/2 -(y1+y2)/2

20. Multiplying Fractions
Adjacent angles are supplementary - Vertical angles are equal
Use the formula distance=rate*time and its variations to help in this question.
Multiply the numerators and multiply the denominators.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

21. Adding and Subtracting Polynomials
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Combine like terms.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

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

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23. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Cross multiply.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
-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.

24. Finding the Volume of a Cylinder
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Switch the numerator and denominator.
VofaC: (pie)r(2)h

25. Formula Used to Find Percent
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Part=Percent x Whole

26. 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.
(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
A(2)+b(2)=c(2)

27. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Switch the numerator and denominator.

28. Scalene - Isosceles - and Equilateral Triangles
Slope=change in y/change in x
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.
Average: Sum of the Terms/Number of the Terms
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

29. Finding the Reciprocal of a Fraction
Slope=change in y/change in x
Switch the numerator and denominator.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
-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.

30. Adding and Subtracting Fractions
Sum: Average x Number of Terms
Find a common denominator - then add or subtract the numerators.
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.
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.

31. Comparing the values of two or more Fractions
A(2)+b(2)=c(2)
Use simple numbers like 1 and 2 and see what happens.
Use the units to keep things straight - Snowfall inches/hours
Express them with a common denominator.

32. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Use the formula distance=rate*time and its variations to help in this question.
Two relatively prime numbers are integers that have no common factor other than 1.
Combine like terms.

33. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
The value that falls in the middle of the set.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.

34. Adding and Subtracting Monomials
-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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Switch the numerator and denominator.
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.

35. 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?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Isolate the radical expression and use the standard rules of algebra.
Use the formula distance=rate*time and its variations to help in this question.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

36. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Isolate the radical expression and use the standard rules of algebra.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Use simple numbers like 1 and 2 and see what happens.
Plug in the given values for the unknowns and calculate according to PEMDAS.

37. What is the Pythagorean Theorem?
VofaRS=lwh
A(2)+b(2)=c(2)
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

38. Increasing and Decreasing a Number by a Certain Percentage
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.
Slope=change in y/change in x
-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.
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.

39. Converting from an Improper Fraction to a Mixed Number
Adjacent angles are supplementary - Vertical angles are equal
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.
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 value that falls in the middle of the set.

40. Solving a Radical Equation
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Isolate the radical expression and use the standard rules of algebra.

41. Finding the Slope of a Line When Given Two Points on the Line
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Slope=change in y/change in x
The value that appears the most often.

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

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43. Finding a Term in a Geometric Sequence
Subtract the smallest from the largest and add 1
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.
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

44. Calculating Negative Exponents and Radical Exponents
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.

45. Finding the Rate of Speed
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Do whatever is necessary to both sides to isolate the variable.
Use the formula distance=rate*time and its variations to help in this question.
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.

46. Finding the Volume of a Rectangular Solid
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Multiply the numerators and multiply the denominators.
VofaRS=lwh
A(2)+b(2)=c(2)

47. Finding the Length of an Arc in a Circle

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48. Finding the Area of a Circle
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Multiply the numerators and multiply the denominators.
Multiply the exponents - (x^3)^4=x^3*4=x^12
(pie)r(squared)

49. Characteristics of a Parallelogram
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.
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.
Adjacent angles are supplementary - Vertical angles are equal
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

50. If the average of a - b - and 48 is 48 - what is the value of a + b?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

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