math

• Sections of the exam

  • Multiple choice
  • Short answer on algebra
  • Short answer on linear relations
  • Short answer on geometry
• Question 1: 87 to the power of zero

  Anything to the power of zero, except for zero to the power of zero, is equal to 1
• Question 2: a to the power of 10 times a to the power of 5

  When multiplying powers with the same base, you keep the base and add the exponents
• Question 3: Power of a power where the base of a power is a product of two things

  Put the outside exponent on both factors of the base
• For questions involving variables, you can check your answer by substituting a test value for the variable and verifying the two expressions are equal
• Question 4: 7 to the power of 5 times 7 to the power of 1 divided by 7 to the power of 3

  When multiplying powers with the same base, add the exponents. When dividing powers with the same base, subtract the exponents.
• Question 5: Simplifying a quotient of two expressions

  Divide the coefficients, and subtract the exponents for any common variables in the numerator and denominator
• Question 6: Power where the base is a fraction


  The exponent applies to both the numerator and denominator
• Question 7: Identifying which pair of terms are not like terms

  Like terms have the exact same variables with the exact same exponents
• Question 8: Classifying a polynomial expression by name

  A polynomial with 3 terms is called a trinomial
• Question 9: Finding the degree of a polynomial expression

  The degree is equal to the degree of the highest degree term
• Question 10: 5 to the power of negative 2

  Negative exponents mean the reciprocal of the positive exponent
• Question 11: Solving for m in the equation 6/2 * a^(m-3) = 3a^5

  To make the equation true, m-3 must equal 5, so m=8
• Question 12: Solving the equation x-2=-4


  Isolate the variable by adding 2 to both sides, giving the solution x=-2
• Question 13: Rearranging the formula a=bh/2 to isolate h

  Multiply both sides by 2 to get rid of the fraction, then divide both sides by b to isolate h
• Question 14: Solving the equation 4(4x-1)=6(3x+2)


  Cross-multiply, distribute, collect like terms, and solve for x
• Question 15: Expanding and simplifying the expression x(x-2)-4(x-1)

  Distribute the x and -4 into the binomials, then collect like terms
• Question 16: Determining if the relation y=66x represents a direct, partial, or neither variation

  Direct variation has no constant term, partial variation has a constant term
• Question 17: Identifying primary vs secondary data sources

  Primary data is collected directly by the researcher, secondary data is collected by others
• Question 19: Distinguishing between extrapolation and interpolation

  Extrapolation is estimating values beyond the known data, interpolation is estimating within the known data
• Question 20: Determining the fastest moving section on a distance-time graph

  The steepest slope represents the fastest speed
• Question 21: Identifying the graph showing acceleration away from home

  The graph with an increasing positive slope shows acceleration away from home
• Question 23: Finding the constant of variation for earnings varying directly with rap battles won

  The constant of variation is the earnings per battle, calculated by dividing the total earnings by the number of battles
• Question 24: Calculating the slope of a line segment on a graph


  Slope is the rise over the run, or (y2-y1)/(x2-x1)
• Question 25: Identifying the slope and y-intercept in the equation y=-3x+4

  The slope is -3, the y-intercept is 4
• Calculating slope from point E to point F

  1. Go down 4 units (rise is -4)

  2. Go right 5 units (run is 5)

  3. Slope is -4/5
• Calculating slope from point F to point E gives the same result as -4/5
• Slope formula


  Change in y / change in x
• Equation of a line

  y = mx + b, where m is the slope and b is the y-intercept
• The slope is -3 and the y-intercept is 4
• Calculating slope between two points

  Second y - first y / second x - first x
• The slope of the line passing through the given points is 14/5
• Parallel lines


  • Have the same slope
• Perpendicular lines


  • Have slopes that are negative reciprocals of each other
• The slope of a vertical line is undefined
• Equation of a horizontal line

  y = constant
• The table with y-values increasing by a constant amount represents a linear relationship
• Calculating perimeter


  Add up all the side lengths
• Calculating area


  Area of full rectangle - area of cut-out rectangle
• Angle ABC is not 40 degrees