024 Upward Bound Mathematics Test Two solutions

  1. Multiply: (x + 3)(x² − 5x + 7) = x³ − 2x² − 8x + 21
  2. Parabola What is the name of the shape a marble makes when rolled on a sloped surface?
  3. On the graph, draw lines connecting the vocabulary words (vertex, y-intercept, roots, origin) on the graph with the correct location on the graph.

Arc of a marble y = − ( k r2 ) x2 + k Marble Marble text layers x y (−20, 0) (0, 0) (20, 0) (0, 40) marble r r k vertex y-intercept roots origin

  1. k = 40 Using the graph and the equation on the graph, write down the value of k for the above curve on the graph.
  2. r = 20 Using the graph and the equation on the graph, write down the value of r for the above curve on the graph.
  3. Write the equation for the ball path shown above using the equation above by substituting in the values for k and r. y = − 0.1 x² + 40
  4. y = 30 Use the above equation to calculate the value for y when x = 10.
  5. 5050 What is the sum of the first 100 numbers?
  6. The sum of the first "n" even numbers is sum = n(n + 1). Write this out as an equation using y for the sum and x for the number of even numbers n: y = 1 x² + 1 x + 0
  7. Fill in the table below with y values for the equation y = x² + 2x − 8.

SVG blank graph (-5,-10) to (5,10) background rectangle major grid lines minor grid lines axes a path data points as rectangles text layers Graph 2 x y y-axis labels −10 −8 −6 −4 −2 0 2 4 6 8 10 x-axis labels −5 −4 −3 −2 −1 0 1 2 3 4 5

xy
−57
−40
−3−5
−2−8
−1−9
0−8
1−5
20
37
  1. Use the table values to plot the equation y = x² + 2x − 8 on the graph.