SECTION A – MULTIPLE CHOICE QUESTIONS (16 marks)
1.Which one of the following statements is TRUE for the graph with equation:
?
A.It has a y-intercept at the point (0, –7)
B.Its gradient is 3
C.It would be parallel to the line with equation
D.It is a horizontal line
E.The angle it makes with the positive x direction is acute.
2.Which one of these graphs would have a quadratic rule for which the discriminant is zero?
A.B.C.
D.E.
- The angle (to two decimal places) that the line makes with the positive x – axis is
A -0.05oB 108.43oC 71.57oD91.57oE -3
- When is divided by the remainder is 9. The value of m is :
A 25 B C D 1 E
- A point is transformed by reflecting it in the x – axis and dilating it by a factor of 2 from the y – axis.
A matrix that would perform these transformations is
A B C D E
- The maximal domain of the graph with equation is equal to
A R \ {3} B R \ {2} C {x: x 2}D R \ { } E R \ { }
Questions7 and 8 refer to the following diagram
- From the Venn diagram above, is
A B C D E
- From the Venn diagram above, │B) is
A B C D E
- The range of the graph of the relation (x+ 2)2 + y2 = 16 is
A [–4, 4]B[C [16, 16] D(2, ) (, 2) E (4, 4)
- Which one of the following functions is not a one-to-one function?
A y = 3x2 – 3x, x > 3B y =, C y = 2x2, x > 0
D y =E y = 3x
- Which one of the following ordered pairs is not a member of the relation ?
A (1, 4)B C D E (2, 5)
- Two balls are randomly drawn without replacement from a bucket containing 8 yellow balls and 4 green balls. The probability of drawing one yellow ball and one green ball is:
A B C D E
- The range of the graph of the function is
A [2, 52)B[2, 52]C [10, 27]D [10, 52)E [10, 27)
- Given that events A and B are independent, the values of p and q in the probability table below are:
B / B/
A / p
A/ / q / 0.3
0.5 / 1
A p = 0.15, q = 0.85B p = 1.5, q = 1.3 C p = 0.35, q = 0.65
D p = 0.8, q = 0.2E p = 0.35, q = 0.15
- The graph of is reflected in the x axis then translated 3 units in the negative x direction. The resulting graph has a range of:
A.B.C.
D.R–E.R– {0}
- The given graph below is of an hyperbola. It is best described by which equation?
Asymptotes have equations
A.1B.1
C.1D.a
E.a
SECTION B: Extended ResponseQuestions (34 marks)
Question 1
A builder has of wood to make a frame. The shape and dimensions, in metres, of the frame are shown below.
a)Show that an expression for y in terms of x is
b)Hence, show that the area, , in m2, inside the frame is given by
c)State the domain of the function found in part b).
d)On the set of axes below, sketch the graph of A against x. Indicate clearly on thegraph the co-ordinates of anyturning point and endpoints.
Because of a shortage of concrete which will be poured into the frame, the area inside the frame must be less than252m2..
e)Find the possible values of , which will fulfil this requirement.
(2 + 2 + 1 + 3 + 2 = 10 marks)
Question 2
In the South American jungle, a large spider weaves a web from the perfectly horizontal branch of a tree. The bottom strand of the spider web has a shape described by the rule
where x metres is the distance from the vertical tree trunk and y metres is the height of the strand above the branch
a)Sketch a graph showing the shape of this strand on the axes below, showing coordinates of endpoints and the lowest point of the strand to 2 decimal places, where appropriate.
b)Show algebraically that the strand only touches the branch at two places.
c)State the maximum vertical distance the web is below the branch, correct to 2 decimal places.
The branch is 5 metres above the ground.
d)The spider is on the strand of the spider web 1.7 metres above the ground. What are the two distances from the tree trunk that the spider could be, correct to 2 decimal places?
(3+3+1+2=9 marks)
Question 3
Jo has an old car which does not always start when she turns the key.
In winter, the probability of the temperature in the morning being at least 10o C is 0.4.
If the temperature in the morning is 10o C or more, the probability of Jo’s car starting is 0.9.
If the temperature in the morning is less than 10o C, the probability of Jo’s car starting is 0.3.
Using T = {temperature in the morning is at least 10o C} and S = {car starts}
a)Complete the probability tree diagram by adding the probabilities to each branch.
Temperature Car
b)Determine the probability that Jo’s car starts.
c)Given that Jo’s car starts, what is the probability that the temperature was at least 10o C?
(3+2+2 =7 marks)
Question 4
A function, f, is defined below:
a)State the largest value of k that makes function f a one-to-one function
b)On the axes below, sketch the one-to-one function f showing the coordinates of key points.
c)Find the exact value of x such that f (x ) = 10.
d)On the axes above, sketch the graph of the inverse of f, labelling it clearly and showing coordinates of key features.
(1+3+2+2 = 8 marks)
END OF EXAM
Multiple Choice Answer Sheet
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TEACHER : ______
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