COLEGIO SAN PATRICIO

9th Grade Math Period III Review

School Year 2014 - 2015

Name______9th _____List # _____ Date ______

  1. Direct and Inverse Variation

Find the Missing Variable:

1)y varies directly with x. If y = -4 when x = 2, find y when x = -6.

2)y varies inversely with x. If y = 40 when x = 16, find x when y = -5.

3)y varies inversely with x. If y = 7 when x = -4, find y when x = 5.

4)y varies directly with x. If y = 15 when x = -18, find y when x = 1.6.

Classify the following as: a) Directb) Inverse c) Neither

5) m = -5p6) c = 7) c = 3v

8) r = 9) n = ½ f10) u =

11) d = 4t12) z =

What is the constant of variation for the following?

13) d = 4t 14) z = 15) n = ½ f 16) r =

Answer the following questions.

17) If x and y vary directly, as x decreases, what happens to the value of y?

18) If x and y vary inversely, as y increases, what happens to the value of x?

19) If x and y vary directly, as y increases, what happens to the value of x?

20) If x and y vary inversely, as x decreases, what happens to the value of y?

Classify the following graphs as a) Direct b) Inverse c) Neither

21) 22) 23)24)

25)Determine the equation that relates x to y in the following table of values:

a) Is the relation a direct proportion? ______

b) Write the Equation: ______

26) The number of kilograms of water in a person’s body varies directly as the person’s mass. A person with a mass of 90 kg contains 60 kg of water. How many kilograms of water are in a person with a mass of 50 kg?

27) On a map, distance in km and distance in cm varies directly, and 25 km are represented by 2cm. If two cities are 7cm apart on the map, what is the actual distance between them?

28) The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane. If the trip takes 6 hours at 900 km/h, how long would it take at 800 km/h?

  1. Quadratic Formula

Find the discriminant to determine number and nature of the solutions.

29) 30) 31)

30) Solve the following quadratic equations using quadratic formula.

a)4x2 = 8x – 4b) 4x2 – x + 5= 0c) 3x2 -18x = -9

31) The square of a number minus the same number is -72. Find the number.

32) If the measure of one side of a square is increased by 2 centimeters and the measure of the other side is decreased by 2 centimeters, the area of the resulting rectangle is 32 square centimeters. Find the measure of one side of the square.

  1. Thales Theorem

33a) In the figure line L1 is parallel to L2 ( L1//L2). Find the missing value.

a)PC = 12 cm., PB = 6cm., BD = 2 cm., AC = ?

33b) A girl 160 cm tall, stands 360 cm from a lamp post at night. Her shadow from the light is 90 cm long. How high is the lamp post?

  1. Homothecy

34) Draw an homothetic image of the rhombus using ratio of 2/5 and trapeze -3/2

35) Find the homothetic ratio of the following figures.(Remember you need to find the homothecy center)

  1. Quadratic Functions

36) Graph the following equations.

37) Fill in the following table:

Direction of opening / Max or Min point / Coordinate of the Vertex
y = (x+2)² –3
y = x2 -5
y = (x - 2)² - 3
y = (x-2)2
y = –(x–1)² + 1
y=3x2+4

38) Find the vertex of the parabola

Vertex ______Vertex ______