UPCAT MOCK EXAM

• Alice, Bob, and Cathy each have a number of marbles. Alice splits all her marbles equally between Bob and Cathy.
• Concentration


  Ratio of the amount of a substance to the total volume of the solution
• Calculating concentration


  Given initial volume and concentration, add water, calculate new concentration
• Concentration calculation


  • 45%
  • 40%
  • 35%
  • 50%
• Solving for ratio


  Given equation, solve for ratio value
• Trapezoid


  Quadrilateral with two parallel sides
• Finding angle in trapezoid

  Given diagram, determine value of angle x
• Angle values


  • 35°
  • 32°
  • 30°
  • 28°

  
• Limit


  Value that a function approaches as the input approaches a certain point
• Evaluating limit


  Given limit expression, determine limit value
• Equivalent expressions


  Algebraic expressions that have the same value
• Simplifying algebraic expression


  Given expression, simplify to equivalent form
• Solving problem with marbles


  Given information about marbles, determine how many Cathy started with
• Equilateral triangle


  Triangle with all sides of equal length
• Finding altitude of equilateral triangle


  Given side length, calculate altitude
• Altitude values


  • 3√3
  • 3√2
  • 4√2
  • 5√3
• Analyzing logic statement


  Determine which logical equivalence is always true
• Logic statement equivalences


  • ¬p → ¬q
  • ¬q → ¬p
  • ¬q → p
  • Depends on p and q
• Odd and even integers

  Integers that are either divisible by 2 or not divisible by 2
• Determining if expression is odd


  Given a and b as odd/even integers, decide if expression is odd
• Stem and leaf plot


  Data visualization showing distribution of numerical data
• Finding median from stem and leaf plot

  Given stem and leaf plot, determine median value
• Median values


  • 24
  • 25
  • 27
  • 29
• Truthfulness assumption


  Assumption that one student is telling the truth and one student brought the cellphone
• Determining which student brought cellphone

  Given statements by 4 students, identify which student brought the cellphone
• Vertical asymptote


  Vertical line that a function approaches but never touches
• Identifying vertical asymptotes


  Given rational function, determine its vertical asymptotes
• Solving absolute value inequality

  Given absolute value inequality, determine solution set
• Rhombus


  Quadrilateral with all sides of equal length
• Finding angle in rhombus


  Given rhombus diagram, determine measure of angle A

  
• Angle values


  • 105°
  • 110°
  • 145°
  • 95°

  
• Expression results


  • 11.5
  • -4
  • 15.875
  • 4/2
• Sphere


  3D geometric shape with all points on the surface equidistant from the center
• Relating sphere volume and surface area


  Given sphere radius, determine the ratio between volume and surface area
• Volume to surface area ratios

  • 3/r : 4π/3
  • r^3 : 1
  • 4π/3 : r
  • r : 4π
• Quadrant


  One of the four regions formed by the x and y axes in a coordinate plane

  
• Determining which quadrant an equation will never pass through

  Given equation with constraint on R, identify the quadrant it will never pass through
• Discount


  Reduction in the original price of a product
• Comparing discounted prices


  Given multiple discounts, determine which offer is most worth it
• Discounted offers


  • Johnny Apple's offer
  • Craw Caster's offer
  • Shortcake Muffin's offer
  • Johnny Apple and Shortcake Muffin are equally good