Hi Math studies Classes: Problem set 27. Is due at the ...mysticva.entest.org/Math - Grade 12 Math Studies - Week of March 30.pdfMatryoshka dolls, or Russian dolls, are similarly designed

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Hi Math studies Classes: Problem set 27. Is due at the time stated below: Monday March 30, 2020: pages 1-7 Are due no later than 10:00 pm Tuesday March 31, 2020: pages 8-5 are due no later than 10:00 pm Wednesday April 1st, 2020 : pages 16-23 are due no later than 10:00 pm Thursday April 2nd, 2020: Pages 24-31 are due no later than 10:00 pm Friday April 3rd, 2020: pages 32-38 are due no later than 10:00 pm

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The assignment for the week of March 30th- April 3rd will be graded as follows: Monday: 20 pts Class participation Tuesday: 20 pts Class participation Wednesday: 20 pts Class participation Thursday : 20 pts Class participation Friday: 20 pts Class participation You are to turn in the assignment via email. My suggestion is to scan the document or take a picture of your work and email it to me at the following email: [email protected]. Please make sure you get a conformation email back from me. Look back at the appropriate chapters in the Math Studies text book or email me at [email protected] if you are struggling to get an answer.

Maximum marks will be given for correct answers. Where an answer is incorrect, some marks may be given for a correct method, provided this is shown by written working. Answers must be written within the answer boxes provided. Solutions found from a graphic display calculator should be supported by suitable working, for example, if graphs are used to find a solution, you should sketch these as part of your answer.

1. Each year the soccer team, Peterson United, plays 25 games at their home stadium. The owner of Peterson United claimed that last year the mean attendance per game at their home stadium was 24 500.

(a) Based on the owner’s claim, calculate the total attendance for the games at Peterson United’s home stadium last year. [2]

The actual total attendance last year was 617 700.

(b) Calculate the percentage error in the owner’s claim. [2]

(c) Write down your answer to part (b) in the form a × 10k where 1 ≤ a < 10 , k∈ . [2]

Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28EP03

– 3 –

Turn over

M18/5/MATSD/SP1/ENG/TZ1/XX

2. Each month the number of days of rain in Cardiff is recorded. The following data was collected over a period of 10 months.

11 13 8 11 8 7 8 14 x 15

For these data the median number of days of rain per month is 10.

(a) Find the value of x . [2]

(b) Find

(i) the standard deviation;

(ii) the interquartile range. [4]

Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) (i) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28EP04

– 4 – M18/5/MATSD/SP1/ENG/TZ1/XX

3. Consider the following propositions.

p: my Mathematical Studies homework is due tomorrowq: today is Wednesday

(a) Write down in words the compound proposition ¬ p ⇒ q . [2]

(b) Complete the truth table. [3]

p q ¬ p ¬ p ⇒ q ¬ p ∧ q (¬ p ⇒ q) ∨ (¬ p ∧ q)

T T F

T F F

F T T

F F T

(c) State whether the compound proposition (¬ p ⇒ q) ∨ (¬ p ∧ q) is a tautology, contradiction or neither. [1]

Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28EP05

– 5 –

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4. A scientist measures the concentration of dissolved oxygen, in milligrams per litre ( y) , in a river. She takes 10 readings at different temperatures, measured in degrees Celsius (x) .

The results are shown in the table.

Temperature, C (x) 20 24 25 28 29 32 27 25 23 21

Dissolved Oxygen, mg l-1 ( y) 10.9 9.7 9.2 7.6 7.3 6.4 7.9 8.4 9.4 9.9

It is believed that the concentration of dissolved oxygen in the river varies linearly with the temperature.

(a) For these data, find

(i) Pearson’s product-moment correlation coefficient, r ;

(ii) the equation of the regression line y on x . [4]

(b) Using the equation of the regression line, estimate the concentration of dissolved oxygen in the river when the temperature is 18 C . [2]

Working:

Answers:

(a) (i) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28EP06


5. The point A has coordinates (4 , -8) and the point B has coordinates (-2 , 4) .

(a) Write down the coordinates of C, the midpoint of line segment AB. [2]

The point D has coordinates (-3 , 1) .

(b) Find the gradient of the line DC. [2]

(c) Find the equation of the line DC. Write your answer in the form ax + by + d = 0 where a , b and d are integers. [2]

Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28EP07

– 7 –

Turn over


6. In a high school, 160 students completed a questionnaire which asked for the number of people they are following on a social media website. The results were recorded in the following box-and-whisker diagram.

0 50 100 150 200 250 300Number of people they are following

(a) Write down the median. [1]

The following incomplete table shows the distribution of the responses from these 160 students.

Number of people they are following (x) Number of high school students

0 ≤ x ≤ 50 4

50 < x ≤ 100

100 < x ≤ 150 34

150 < x ≤ 200 46

200 < x ≤ 250

250 < x ≤ 300 16

(b) Complete the table. [2]

(c) (i) Write down the mid-interval value for the 100 < x ≤ 150 group.

(ii) Using the table, calculate an estimate for the mean number of people being followed on the social media website by these 160 students. [3]

(This question continues on the following page)

28EP08


(Question 6 continued)

Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) (i) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28EP09

– 9 –

Turn over


Please do not write on this page.

Answers written on this page will not be marked.

28EP10


7. Sergei is training to be a weightlifter. Each day he trains at the local gym by lifting a metal bar that has heavy weights attached. He carries out successive lifts. After each lift, the same amount of weight is added to the bar to increase the weight to be lifted.

The weights of each of Sergei’s lifts form an arithmetic sequence.

Sergei’s friend, Yuri, records the weight of each lift. Unfortunately, last Monday, Yuri misplaced all but two of the recordings of Sergei’s lifts.

On that day, Sergei lifted 21 kg on the third lift and 46 kg on the eighth lift.

(a) For that day

(i) find how much weight was added after each lift;

(ii) find the weight of Sergei’s first lift. [4]

On that day, Sergei made 12 successive lifts.

(b) Find the total combined weight of these lifts. [2]

Working:

Answers:

(a) (i) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28EP11

– 11 –

Turn over


8. Two fixed points, A and B, are 40 m apart on horizontal ground. Two straight ropes, AP and BP, are attached to the same point, P, on the base of a hot air balloon which is vertically above the line AB. The length of BP is 30 m and angle BAP is 48 .

diagram not to scale

48˚

40

30

BA

P

(a) On the diagram, draw and label with an x the angle of depression of B from P. [1]

Angle APB is acute.

(b) Find the size of angle APB. [3]

(c) Find the size of the angle of depression of B from P. [2]


28EP12



Working:

Answers:

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28EP13

– 13 –

Turn over




28EP14


9. In an experiment, a number of fruit flies are placed in a container. The population of fruit flies, P , increases and can be modelled by the function

P (t) = 12 × 30.498t , t ≥ 0 ,

where t is the number of days since the fruit flies were placed in the container.

(a) Find the number of fruit flies

(i) which were placed in the container;

(ii) that are in the container after 6 days. [4]

The maximum capacity of the container is 8000 fruit flies.

(b) Find the number of days until the container reaches its maximum capacity. [2]

Working:

Answers:

(a) (i) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28EP15

– 15 –

Turn over


10. A group of 60 sports enthusiasts visited the PyeongChang 2018 Winter Olympic games to watch a variety of sporting events.

The most popular sports were snowboarding (S), figure skating (F) and ice hockey (H).

For this group of 60 people:

4 did not watch any of the most popular sports, x watched all three of the most popular sports, 9 watched snowboarding only, 11 watched figure skating only, 15 watched ice hockey only, 7 watched snowboarding and figure skating, 13 watched figure skating and ice hockey, 11 watched snowboarding and ice hockey.

(a) Complete the Venn diagram using the given information. [3]

U

FS

H

x

(b) Find the value of x . [2]

(c) Write down the value of ( )( )n F H S′∪ ∩ . [1]


28EP16



Working:

Answers:

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28EP17

– 17 –

Turn over


11. Matryoshka dolls, or Russian dolls, are similarly designed dolls which open up and fit inside each other.

The largest set of these type of dolls is a 51 piece set which was completed in 2003. The height of the largest piece in this set is 54 cm. The heights of successive smaller dolls are 94 % of the preceding larger doll, as shown.

h 0.94h

(a) Find the height of the smallest doll in this set. [3]

(b) Find the total height if all 51 dolls were placed one on top of another. [3]

Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28EP18


12. Consider the quadratic function f (x) = ax2 + bx + 22 . The equation of the line of symmetry of the graph y = f (x) is x = 1.75 .

(a) Using only this information, write down an equation in terms of a and b . [1]

The graph intersects the x-axis at the point (-2 , 0) .

(b) Using this information, write down a second equation in terms of a and b . [1]

(c) Hence find the value of a and of b . [2]

The graph intersects the x-axis at a second point, P.

(d) Find the x-coordinate of P. [2]

Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28EP19

– 19 –

Turn over




28EP20


13. Malthouse school opens at 08:00 every morning.

The daily arrival times of the 500 students at Malthouse school follow a normal distribution. The mean arrival time is 52 minutes after the school opens and the standard deviation is 5 minutes.

(a) Find the probability that a student, chosen at random

(i) arrives at least 60 minutes after the school opens;

(ii) arrives between 45 minutes and 55 minutes after the school opens. [4]

A second school, Mulberry Park, also opens at 08:00 every morning. The arrival times of the students at this school follows exactly the same distribution as Malthouse school.

(b) Given that, on one morning, 15 students arrive at least 60 minutes after the school opens, estimate the number of students at Mulberry Park school. [2]

Working:

Answers:

(a) (i) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28EP21

– 21 –

Turn over


14. A solid right circular cone has a base radius of 21 cm and a slant height of 35 cm. A smaller right circular cone has a height of 12 cm and a slant height of 15 cm, and is

removed from the top of the larger cone, as shown in the diagram.


15

12

21

35

(a) Calculate the radius of the base of the cone which has been removed. [2]

(b) Calculate the curved surface area of the cone which has been removed. [2]

(c) Calculate the curved surface area of the remaining solid. [2]


28EP22



Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28EP23

– 23 –

Turn over


15. Consider the functions f (x) = x4 - 2 and g (x) = x3 - 4x2 + 2x + 6 .

The functions intersect at points P and Q. Part of the graph of y = f (x) and part of the graph of y = g (x) are shown on the diagram.

y

xP

Q

f

g

(a) Find the range of f . [2]

(b) Write down the x-coordinate of P and the x-coordinate of Q. [2]

(c) Write down the values of x for which f (x) > g (x) . [2]


28EP24



Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28EP25


24EP01

Candidate session number

Mathematical studiesStandard levelPaper 1

21 pages

Wednesday 2 May 2018 (afternoon)

1 hour 30 minutes

Instructions to candidates

y Write your session number in the boxes above. y Do not open this examination paper until instructed to do so. y A graphic display calculator is required for this paper. y A clean copy of the mathematical studies SL formula booklet is required for this paper. y Answer all questions. y Answers must be written within the answer boxes provided. y Unless otherwise stated in the question, all numerical answers should be given exactly or

correct to three significant figures. y The maximum mark for this examination paper is [90 marks].

© International Baccalaureate Organization 2018


2218 – 7405

Maximum marks will be given for correct answers. Where an answer is incorrect, some marks may be given for a correct method, provided this is shown by written working. Answers must be written within the answer boxes provided. Solutions found from a graphic display calculator should be supported by suitable working, for example, if graphs are used to find a solution, you should sketch these as part of your answer.

1. The following scatter diagram shows the scores obtained by seven students in their mathematics test, m , and their physics test, p .

0 10 20 30 40 50 60 70 80

5

10

15

20

25

30

Scores in mathematics test (m)

Scor

es in

phy

sics

test

( p)

The mean point, M, for these data is (40 , 16).

(a) Plot and label the point M( , )m p on the scatter diagram. [2]

(b) Draw the line of best fit, by eye, on the scatter diagram. [2]

(c) Using your line of best fit, estimate the physics test score for a student with a score of 20 in their mathematics test. [2]

Working:

Answer:

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24EP03

Turn over


2. Consider the following propositions.

p : the baby criesq : the baby is happyr : the baby wants to play

(a) Write down, in words, ( )q r p∧ ⇒¬ . [3]

(b) Complete the following truth table. [2]

p q r ¬ p ( )q r∧ ( )q r p∧ ⇒¬

T T T F

T T F F

T F T F

T F F F

F T T T

F T F T

F F T T

F F F T

(c) State whether ( )q r p∧ ⇒¬ is a tautology, contradiction or neither. [1]

Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24EP04


3. Last year a South American candy factory sold 4.8 × 108 spherical sweets. Each sweet has a diameter of 2.5 cm.

The factory is producing an advertisement showing all of these sweets placed in a straight line.

2.5 cm 2.5 cm 2.5 cm 2.5 cm… …

(a) Find the length, in cm, of this line. Give your answer in the form a × 10k , where 1 ≤ a < 10 and k ∈ . [3]

The advertisement claims that the length of this line is x times the length of the Amazon River. The length of the Amazon River is 6400 km.

(b) (i) Write down the length of the Amazon River in cm.

(ii) Find the value of x . [3]

Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) (i) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24EP05

Turn over


4. The following table shows four different sets of numbers: , , and .

Set Example of a number in the set

(a) Complete the second column of the table by giving one example of a number from each set. [4]

Josh states: “Every integer is a natural number”.

(b) Write down whether Josh’s statement is correct. Justify your answer. [2]

Working:

Answer:

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24EP06


5. In this question, give all answers to two decimal places.

Karl invests 1000 US dollars (USD) in an account that pays a nominal annual interest of 3.5 % , compounded quarterly. He leaves the money in the account for 5 years.

(a) (i) Calculate the amount of money he has in the account after 5 years;

(ii) Write down the amount of interest he earned after 5 years. [4]

Karl decides to donate this interest to a charity in France. The charity receives 170 euros (EUR) . The exchange rate is 1 USD = t EUR .

(b) Calculate the value of t . [2]

Working:

Answers:

(a) (i) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24EP07

Turn over


6. Consider the straight lines L1 and L2 . R is the point of intersection of these lines.

0 2

1

−2−1

−2

−4−6−8 4

2

6

3

8

4

5

6

7

8

10 12

L1

L2

y

x

R

The equation of line L1 is y = ax + 5 .

(a) Find the value of a . [2]

The equation of line L2 is y = -2x + 3 .

(b) Find the coordinates of R . [2]

Line L3 is parallel to line L2 and passes through the point (2 , 3) .

(c) Find the equation of line L3 . Give your answer in the form y = mx + c . [2]


24EP08



Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24EP09

Turn over


7. In an international competition, participants can answer questions in only one of the three following languages: Portuguese, Mandarin or Hindi. 80 participants took part in the competition. The number of participants answering in Portuguese, Mandarin or Hindi is shown in the table.

Languages

Portuguese Mandarin Hindi Total

ParticipantsBoys 20 18 5 43

Girls 18 7 12 37

Total 38 25 17 80

(a) State the number of boys who answered questions in Portuguese. [1]

A boy is chosen at random.

(b) Find the probability that the boy answered questions in Hindi. [2]

Two girls are selected at random.

(c) Calculate the probability that one girl answered questions in Mandarin and the other answered questions in Hindi. [3]

Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24EP10


8. A park in the form of a triangle, ABC, is shown in the following diagram. AB is 79 km and BC is 62 km . Angle AB̂C is 52 .


52°

62

79

A

C

B

(a) Calculate the length of side AC in km. [3]

(b) Calculate the area of the park. [3]

Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24EP11

Turn over


9. Consider the following Venn diagrams.

UBA

U

D

CU FE

G

Diagram 1 Diagram 2 Diagram 3

(a) Write down an expression, in set notation, for the shaded region represented by

(i) Diagram 1;

(ii) Diagram 2;

(iii) Diagram 3. [4]

(b) Shade, on the Venn diagram, the region represented by the set

(i) (H ∪ I )′ ;

UIH

(ii) J ∩ K . [2]

U

K

J


24EP12



Working:

Answers:

(a) (i) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(iii) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24EP13

Turn over


10. The following function models the growth of a bacteria population in an experiment,

P (t) = A × 2t , t ≥ 0

where A is a constant and t is the time, in hours, since the experiment began.

Four hours after the experiment began, the bacteria population is 6400.

(a) Find the value of A . [2]

(b) Interpret what A represents in this context. [1]

(c) Find the time since the experiment began for the bacteria population to be equal to 40A . [3]

Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24EP14


11. Consider the graph of the function f xx

( ) = −32 , x ≠ 0 .

(a) Write down the equation of the vertical asymptote. [2]

(b) Write down the equation of the horizontal asymptote. [2]

(c) Calculate the value of x for which f (x) = 0 . [2]

Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24EP15

Turn over


12. The histogram shows the time, t , in minutes, that it takes the customers of a restaurant to eat their lunch on one particular day. Each customer took less than 25 minutes.

The histogram is incomplete, and only shows data for 0 ≤ t < 20 .

0 5 10 15 20 25

2

4

6

8

10

time (minutes)

num

ber o

f cus

tom

ers

(a) Write down the mid-interval value for 10 ≤ t < 15 . [1]

The mean time it took all customers to eat their lunch was estimated to be 12 minutes.

It was found that k customers took between 20 and 25 minutes to eat their lunch.

(b) (i) Write down the total number of customers in terms of k .

(ii) Calculate the value of k . [4]

(c) Hence, complete the histogram. [1]


24EP16



Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) (i) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24EP17

Turn over


13. A factory produces shirts. The cost, C , in Fijian dollars (FJD), of producing x shirts can be modelled by

C (x) = (x - 75)2 + 100 .

(a) Find the cost of producing 70 shirts. [2]

The cost of production should not exceed 500 FJD. To do this the factory needs to produce at least 55 shirts and at most s shirts.

(b) Find the value of s . [2]

(c) Find the number of shirts produced when the cost of production is lowest. [2]

Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24EP18


14. Consider the function f x x( ) =

4

4.

(a) Find f ′ (x) . [1]

(b) Find the gradient of the graph of f at x = − 12

. [2]

(c) Find the x-coordinate of the point at which the normal to the graph of f has gradient -1

8. [3]

Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24EP19

Turn over


15. Julio is making a wooden pencil case in the shape of a large pencil. The pencil case consists of a cylinder attached to a cone, as shown.

The cylinder has a radius of r cm and a height of 12 cm.

The cone has a base radius of r cm and a height of 10 cm.


10

12

r

(a) Find an expression for the slant height of the cone in terms of r . [2]

The total external surface area of the pencil case rounded to 3 significant figures is 570 cm2.

(b) Using your graphic display calculator, calculate the value of r . [4]


24EP20



Working:

Answers:

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24EP21


Documents

Hi Math studies Classes: Problem set 27. Is due at the ...mysticva.entest.org/Math - Grade 12 Math Studies - Week of March 30.pdfMatryoshka dolls, or Russian dolls, are similarly designed