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Practice IB EXAM #2 Name: ________________________________

Paper 1 – NON CALCULATOR #1-10

1. [2 marks] In a group of 20 girls, 13 take history and 8 take economics. Three girls take both history and economics,

as shown in the following Venn diagram. The values and represent numbers of girls.

a. Find the value of ;

b. [2 marks] Find the value of .

c. [2 marks] A girl is selected at random. Find the

probability that she takes economics but not history.

2. [2 marks] Let and , for .

a. Find .

b. [3 marks] Find .

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3. [6 marks] The following diagram shows triangle PQR.

Find PR.

4. [1 mark] Jim heated a liquid until it boiled. He measured the temperature of the liquid as it cooled. The following

table shows its temperature, degrees Celsius, minutes after it boiled.

a. Write down the independent variable.

b. [1 mark] Write down the boiling temperature of the liquid.

c. [2 marks] Jim believes that the relationship between and can be modelled by a linear regression equation.

Jim describes the correlation as very strong. Circle the value below which best represents the correlation coefficient.

d. [2 marks] Jim’s model is , for . Use his model to predict the decrease in temperature

for any 2 minute interval.

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5a. [4 marks] Find .

5b. [3 marks] Find , given that and .

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6a. [1 mark] The following diagram shows the graph of , the derivative of .

The graph of has a local minimum at A, a local maximum at B and passes through .

The point lies on the graph of the function, .

Write down the gradient of the curve of at P.

6b. [3 marks] Find the equation of the normal to the curve of at P.

6c. [2 marks] Determine the concavity of the graph of when and justify your answer.

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7. [3 marks] The first three terms of a geometric sequence are , , , for .

a. Find the common ratio.

b. [5 marks] Solve .

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*Note you may need an extra sheet of paper for #8-10 (may take more room)!

8a. [2 marks] A line passes through the points and .

Find .

b. [2 marks] Hence, write down a vector equation for .

c. [3 marks] A second line , has equation r = .Given that and are perpendicular, show

that .

d. [5 marks] Given that and are perpendicular, show that . The lines and intersect at .

Find .

e. [2 marks] Find a unit vector in the direction of .

f. [3 marks] Hence or otherwise, find one point on which is units from C.

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9a. [3 marks] A quadratic function can be written in the form . The graph of has axis of

symmetry and -intercept at

Find the value of .

b. [3 marks] Find the value of .

c. [8 marks] The line is a tangent to the curve of . Find the values of .

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10a. [6 marks] The following table shows the probability distribution of a discrete random variable , in terms of an

angle .

Show that .

b. [3 marks] Given that , find .

c. [6 marks] Let , for . The graph of between and is rotated 360° about the -axis.

Find the volume of the solid formed.

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Paper 2 –CALCULATOR #11-20 11. Consider the following frequency table.

a. [1 mark] Write down the mode.

b. [2 marks] Find the value of the range.

c. [2 marks] Find the mean.

d. [2 marks] Find the variance.

12.

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13. Consider the graph of , for .

a. [2 marks] Find the -intercept.

b. [2 marks] Find the equation of the vertical asymptote.

c. [2 marks] Find the minimum value of for .

14. In a large university the probability that a student is left handed is 0.08. A sample of 150 students is randomly

selected from the university. Let be the expected number of left-handed students in this sample.

a. [2 marks] Find .

b. [2 marks] Hence, find the probability that exactly students are left handed;

c. [2 marks] Hence, find the probability that fewer than students are left handed.

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15. [7 marks] The following diagram shows the chord [AB] in a circle of radius 8 cm, where .

Find the area of the shaded segment.

16. [7 marks] Let . Find the term in in the expansion of the derivative, .

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17. A particle P moves along a straight line. Its velocity after seconds is given by , for

. The following diagram shows the graph of .

a. [1 mark] Write down the first value of at which P changes direction.

b. [2 marks] Find the total distance travelled by P, for .

c. [4 marks] A second particle Q also moves along a straight line. Its velocity, after seconds is given

by for . After seconds Q has travelled the same total distance as P.

Find .

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For questions #18-20, you MUST show work on a SEPARATE SHEET OF PAPER!

DO NOT squeeze your solutions and approaches on these pages. THERE IS NOT ENOUGH ROOM WE PROMISE!

18. At Grande Anse Beach the height of the water in metres is modelled by the function ,

where is the number of hours after 21:00 hours on 10 December 2017. The following diagram shows the graph of ,

for .

The point represents the first low tide and represents the next high tide.

a. [2 marks] How much time is there between the first low tide and the next high tide?

b. [2 marks] Find the difference in height between low tide and high tide.

c. [2 marks] Find the value of ;

d. [3 marks] Find the value of ;

e. [2 marks] Find the value of .

f. [3 marks] There are two high tides on 12 December 2017. At what time does the second high tide occur?

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19. A random variable is normally distributed with mean, . In the following diagram, the shaded region

between 9 and represents 30% of the distribution.

a. [2 marks] Find .

b. [3 marks] The standard deviation of is 2.1.

Find the value of .

c. [5 marks] The random variable is normally distributed with mean and standard deviation 3.5. The events

and are independent, and .

Find .

d. [5 marks] Given that , find .

Separate page

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20. [1 mark] Let and , for .

The graph of can be obtained from the graph of by two transformations:

a. Write down the value of ;

b. [1 mark] Write down the value of ;

c. [1 mark] Write down the value of .

d. [2 marks] Let , for . The following diagram shows the graph of and

the line .

The graph of intersects the graph of at two points. These points have coordinates 0.111 and 3.31 correct

to three significant figures.

Find .

e. [3 marks] Hence, find the area of the region enclosed by the graphs of and .

f. [7 marks] Let be the vertical distance from a point on the graph of to the line . There is a point on

the graph of where is a maximum.

Find the coordinates of P, where .