Mock Test for Year 11 Maths Methods

Mock Test For Year 11 Maths methods

Question 1

This graph shows a portion of a parabola. It represents a diver’s position (horizontal and vertical distance) from the edge of a pool as he dives from a 5 ft long board 25 ft above the water.

a. Identify points on the graph that represent when the diver leaves the board, when he reaches his maximum height, and when he enters the water.

b. Sketch a graph of the diver’s position if he dives from a 10 ft long board 10 ft above the water. (Assume that he leaves the board at the same angle and with the same force.)

c. In the scenario described in part b, what is the diver’s position when he reaches his maximum height?

Question 2:

A Cricket ball is thrown by a fielder. It leaves his hand at a height of 2 metres above the ground and the wicketkeeper takes the ball 60 metres away again at a height of 2 m. It is known that after the ball has gone 25n it is 15m above the ground the path of the cricket ball is a parabola with equation y = ax2 + bx +c

a)  Find the values of a, b, c

b)  Find the maximum height of the ball above the ground.

c)  Find the height of the ball 5 metres horizontally before it hits the wicketkeeper’s gloves.

Question 3:

As Jake and Arthur travel together from Detroit to Chicago, each makes a graph relating time and distance. Jake, who lives in Detroit and keeps his watch on Detroit times graphs his distance from Detroit. Arthur who lives in Chicago and keeps his watch on Chicago time (1hour earlier than Detroit), graphs his distance from Chicago.

They both use the time shown on their watches as the x-axis. The distance between Detroit and Chicago is 250 miles.

a)  Sketch what you think the graph might look like.

b)  If jakes graph is described by the function y = f(x), what function describes Arthurs graph?

c)  If Arthurs’ graph is described by the function y = g(x), what function describes Jakes graph?

4 For each of the following relations, sketch the graph and state the range:

a y = x2 + 4x + 10

b (x - 3)2 + (y - 3)2 = 4

5 a A quadratic function has rule f (x) = a(x + b)2 + c and f(1) = f(-3) = 6.

i Find b in terms of a and c.

ii If the turning point of the parabola is on the x-axis, find the values of c anda.

iii State the rule for f(x), given that all the properties above hold.

b A quadratic function is defined by f: [-6, 1] ® R and rule f(x) = ax2 + bx + c.
The turning point has coordinates (-1, 10). The minimum value of the function is-10. Find the values of a, b and c.

6 Sketch the graph of each of the following equations showing intercepts. and determine the domain and range for each.

(a) 

(b) 

7 For each of the following state:

i whether they are a function or a relation

ii if they are a function whether they are a many-to-one or a one-to-one function

/
/ (c) 

8

(a) Sketch the graph of showing endpoints and intercepts.

(b) Write the range of f.

9 Rewrite the following sets in interval notation.

(a)  {x: 2 < x 6}

(b)  \{2}

10 State the transformations required to form from f(x) = .