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ANNUAL NATIONAL ASSESSMENT 2013

GRADE 9

MATHEMATICS

EXEMPLAR QUESTIONS

This booklet consists of 32 pages, excluding the cover page.

GUIDELINES FOR THE USE OF ANA EXEMPLARS 1. How to use the exemplars While the exemplars for a grade and a subject have been compiled into one comprehensive set, the learner does not have to respond to the whole set in one sitting. The teacher should select exemplar questions that are relevant to the planned lesson at any given time. Carefully selected individual exemplar test questions, or a manageable group of questions, can be used at different stages of the teaching and learning process as follows: 1.1 At the beginning of a lesson as a diagnostic test to identify learner strengths and weaknesses. The diagnosis must lead to prompt feedback to learners and the development of appropriate lessons that address the identified weaknesses and consolidate the strengths. The diagnostic test could be given as homework to save instructional time in class. 1.2 1.3 During the lesson as short formative tests to assess whether learners are developing the intended knowledge and skills as the lesson progresses and ensure that no learner is left behind. At the completion of a lesson or series of lessons as a summative test to assess if the learners have gained adequate understanding and can apply the knowledge and skills acquired in the completed lesson(s). Feedback to learners must be given promptly while the teacher decides on whether there are areas of the lesson(s) that need to be revisited to consolidate particular knowledge and skills. At all stages to expose learners to different techniques of assessing or questioning, e.g. how to answer multiple-choice (MC) questions, open-ended (OE) or free-response (FR) questions, shortanswer questions, etc.

1.4

While diagnostic and formative tests may be shorter in terms of the number of questions included, the summative test will include relatively more questions, depending on the work that has been covered at a particular point in time. It is important to ensure that learners eventually get sufficient practice in responding to the exemplar. 2. Memoranda or marking guidelines A typical example of the expected responses (marking guidelines) has been given for each exemplar test question and for the ANA model test. Teachers must bear in mind that the marking guidelines can in no way be exhaustive. They can only provide broad principles of expected responses and teachers must interrogate and reward acceptable options and variations of the acceptable response(s) given by learners. 3. Curriculum coverage It is extremely critical that the curriculum must be covered in full in every class. The exemplars for each grade and subject do not represent the entire curriculum. They merely sample important knowledge and skills and covers work relating to terms 1, 2 and 3 of the school year.

2 Grade 9 Mathematics ANA Exemplar

1. MULTIPLE CHOICE QUESTIONS Unless otherwise stated, in multiple choice questions you must circle the letter of the correct answer. A practice exercise is provided below.

3 Grade 9 Mathematics ANA Exemplar

1.1

Which of the following numbers is a rational number?

A B C D

√3 √16 √−9 √13

1.2

The next number in the sequence 3 ; 6 ; 11 ; 18; … is A B C D 25 24 26 27

1.3

Which of the following trinomial expressions is a polynomial? A B C D 4 1 − −7 +1 √ +1 1 − −7 4 +1 − −7 4 +1 −√ −7 4

1.4

In the adjacent quadrilateral A B C D ∆ ∆ ∆ ∆ ⫼∆ ⫼∆ ≡∆ ≡∆

=

A

=

, therefore:
D

E

B

C

4 Grade 9 Mathematics ANA Exemplar

1.5

What is the size of each angle in a regular pentagon? A B C D 90° 120° 100° 108°

1.6

Complete: √17 − 15 = A B C D 2 4 8 64

1.7

Complete: 2 A B C D +3 = 5 5 1 6 5 6 = −6 then 9 4 −9 −4 =

1.8

If A B C D

5 Grade 9 Mathematics ANA Exemplar

1.9

If the length of the side of a square is 0,12 cm then the area = A B C D
0,24 0,144 1,44 0,0144

1.10

A married couple decided to have two children. The tree diagram below shows all the different combinations of boys and girls that the couple could have. B represents a boy and G a girl.

B B G B G
What is the probability that both children will be girls? A B C D 0,25 0,5 1 0,75 [10]

G

6 Grade 9 Mathematics ANA Exemplar

2. NUMBERS, OPERATIONS AND RELATIONS 2.1.1 2.1.2 Write 6,7 × 10 in standard form. ________________________________ in scientific notation.__________________________ (1) (1)

Write 0, 00000356

2.2

Simplify: 7,125 ÷ √25 ____________________________________________________ ____________________________________________________ (2)

2.3 There are 96 boys and 120 girls in Grade 9. Write down the ratio of the number of boys to the number of girls in the class. _____________________________________________________________ _____________________________________________________________ (2)

2.4 A bus driver covers a certain distance in 3 hours at an average speed of 80 /ℎ. How long will the journey take at an average speed of 50 /ℎ?

_____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ (5)

7 Grade 9 Mathematics ANA Exemplar

2.5 Calculate the compound interest on an investment of R6 500 at 7,5% per annum invested for 3 years. _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ (5)

2.6

Nomsi’s father wants to buy a new car. He can afford to pay R35 000 as a deposit.

2.6.1 If all the cars are sold at 20% deposit, what is the price of a car he can afford to buy? ____________________________________________________ ____________________________________________________ 2.6.2 After paying the 20% deposit, calculate the total amount that he must still pay. (2)

____________________________________________________ ____________________________________________________ 2.6.3 If the interest rate is 10% per annum simple interest, calculate the monthly instalment if he signs a hire-purchase agreement to pay the balance in 48 equal monthly instalments. ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ (6) (1)

8 Grade 9 Mathematics ANA Exemplar

2.7

Write the ratio 1 : 2

in the simplest form.

_________________________________________________________ _________________________________________________________ 2.8 Six boys each contribute R155,50 towards the purchase of a tent. Calculate how much each would contribute if there were 10 boys in the group. _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ 2.9 How long will it take for an investment of R3000 at 8% per annum simple interest to earn R960 interest? _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ 2.10 Calculate what R10 000 will amount to if it is invested at 10 % per annum compound interest for 3 years. _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ (3) (3) (3)
(2)

9 Grade 9 Mathematics ANA Exemplar

3. PATTERNS, FUNCTIONS AND ALGEBRA 3.1 Simplify: 3.1.1 (2 ) + 3 ____________________________________________________ ____________________________________________________ (2)

3.1.2

2

×

____________________________________________________ ____________________________________________________ 4 (4 ) ____________________________________________________ ____________________________________________________ (3) (2)

3.1.3

3.2

Multiply and simplify if necessary. 3.2.1 3 ² ² (3 ² − 4 − )

____________________________________________________ ____________________________________________________ 3.2.2 ( 2 − 3 ) ( + 1 ) ____________________________________________________ ____________________________________________________ (2) (3)

10 Grade 9 Mathematics ANA Exemplar

3.2.3

(

) . (2)

____________________________________________________ ____________________________________________________ 3.3 Factorise fully: 3.3.1 10 ² − 5 ____________________________________________________ ____________________________________________________

(2)

3.3.2

81 − 100 ____________________________________________________ ____________________________________________________ (2)

3.4

Solve for : 3.4.1 2 − 5 = 5 + 16 ____________________________________________________ ____________________________________________________ ____________________________________________________ −2 2 +1 5 + = 4 3 3 ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ (5) (3)

3.4.2

11 Grade 9 Mathematics ANA Exemplar

3.5

Calculate the value of 2

−3

+ 9 + 2 = −2.

_________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ 3.6 Multiply 5 ² ²+ 2 −3 by 4 (4)

_________________________________________________________ 3.7 Simplify: 3.7.1 ( ) .

(3)

__________________________________________________ __________________________________________________ 3.7.2 (2)

x  y  x  y  yx x y _________________________________________________
_________________________________________________ _________________________________________________ 3.7.3 ×

2

(2)

_________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ (3)

12 Grade 9 Mathematics ANA Exemplar

3.7.4

−

__________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ (5)

3.7.5

÷

__________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ 3.7.6 __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ 3.8 Factorise fully: 3.8.1 (2) (2)

3

− 9

−6

__________________________________________________ __________________________________________________ (2)

13 Grade 9 Mathematics ANA Exemplar

3.8.2

4( + ) −

( + )

__________________________________________________ __________________________________________________ __________________________________________________ 3.9 Solve for : 3.9.1 8 + 3 = 3 − 22 (4)

__________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ 3.9.2 (2)

−

=3

__________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ (3) 3.9.3 3 = 81

_______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ (3)

14 Grade 9 Mathematics ANA Exemplar

3.10

FIGURE 1 3.10.1

FIGURE 2

FIGURE 3

Study the above diagram pattern and complete the table.

Figure

1

2

3

4

Number of sides

5

9 (2)

3.10.2

Describe the pattern in your own words. __________________________________________________________ (1)

3.10.3

Write down the general term of the pattern in the form, Answer the following questions.

= __________

(2)

3.11

Matchsticks are arranged as shown in the following figures.

Figure 1 3.11.1

Figure 2

Figure 3

Determine the number of matchsticks in the next figure if the pattern is continued. _________________________________________________________
15

(2)

Grade 9 Mathematics ANA Exemplar

3.11.2

Write down the general term of the given sequence of the matchsticks in the form.

3.11.3

Tn =___________________. Determine the number of matchsticks in the 20th figure.
_________________________________________________________

(2)

(2)

3.12

If

= −1, calculate the value of if

=2

− 3 + 5. (2)

______________________________________________________

3.13

Study the straight line graphs below and answer the questions that follow.
B

C

D

E

A

Complete: 3.13.1 3.13.2 3.13.3 The equation of the line CD is ___________________________ The equation of the line AB is ____________________________ If = 2, the co-ordinates of E are _______________________ (1) (2) (2)

16 Grade 9 Mathematics ANA Exemplar

3.14.1

On the given grid draw the graphs defined by on the same set of axes.

= 3 − 2 and

=3 +1

Label each graph and clearly mark the points where the graphs cut the axes.

(6) 3.14.2 What is the relationship between the lines that you have drawn? ___________________________________________________________ (1)

17 Grade 9 Mathematics ANA Exemplar

3.15

Determine the co-ordinates of P in the graph below.

Y 3 P

0 y=x

X

______________________________________________________ 3.16.1

(1)

Write down the defining equation of each of the following straight line graphs.

_________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ (4)
18 Grade 9 Mathematics ANA Exemplar

3.16.2

What can you deduce about lines AD and BC? Give a reason for your answer.

_______________________________________________ _______________________________________________ (2)

19 Grade 9 Mathematics ANA Exemplar

4. SPACE AND SHAPE

4.1

A C 95 1

B

30 E D

In the above figure

||

, and .

= 95° and

= 30°.

Determine the sizes of

_____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ (4)

20 Grade 9 Mathematics ANA Exemplar

4.2

In the figure below A D =

= 90° and

=

.

B

C

A

D

Prove that ∆

≡∆

.

______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ (4)

21 Grade 9 Mathematics ANA Exemplar

4.3

A
2 1

B

T
2 3 1 1

2

D

P

C

The bisectors of

and

of parallelogram

intersect at . Points , such that = 90°.

and

do not lie on a straight line. is a point on

4.3.1

Prove that

= 90°.

_______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ Which triangle is similar to ΔBCT? _______________________________________________________ 4.3.3 If BC = 2TC and TP = 4 cm, calculate the length of BT. _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ (3) (2) (5)

4.3.2

22 Grade 9 Mathematics ANA Exemplar

4.4 Study the diagram of trapezium ABCD and answer the questions that follow.

A

B

D

C

4.4.1

Write down the co-ordinates of

and . ___________________________ , (2) . (2) (2)

____________________________ 4.4.2

On the above grid draw trapezium ′ ′ ′ ′, the image of after reflecting ABCD about the Y-axis.

4.4.3

Write down the co-ordinates of

and

____________________________

___________________________

23 Grade 9 Mathematics ANA Exemplar

4.5

Complete the table below. 3-D object Number of faces Number of vertices Number of edges

(3)

C

A 70°

S

H

1 2 E

1 W

2

N

4.6

In the above figure, CS || HN, = 70°, = and = . Determine the value of . _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ (3)

24 Grade 9 Mathematics ANA Exemplar

4.7

In the above figure, AB = AC and BD = CD. 4.7.1 Prove that ∆ ≡∆ ______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________ 4.7.2 Prove that DA bisects . (4)

_______________________________________________ _______________________________________________ _______________________________________________ (2)

25 Grade 9 Mathematics ANA Exemplar

4.8

ABCD is a parallelogram .Calculate the size of

.

A
+ 50°

B

2 − 20° C D

____________________________________________________

____________________________________________________

____________________________________________________

____________________________________________________

____________________________________________________

(4)

26 Grade 9 Mathematics ANA Exemplar

5. MEASUREMENT 5.1 The side length of the cube below is 6 of the cube. . Calculate the total surface area

___________________________________________________________ ___________________________________________________________ (2)

5.2

A solid gold object which is cylindrical in shape has a diameter of 18 its height is 100

and

. The gold object must be re-cast into rectangular prisms × 14 × 8 .

with dimensions 30 5.2.1

Calculate the volume of the cylinder. _____________________________________________________ _____________________________________________________ _____________________________________________________ (3)

5.2.2

Calculate the volume of the rectangular prism. _____________________________________________________ _____________________________________________________ _____________________________________________________ (3)

5.2.3

How many rectangular prisms can be made from the gold cylinder? ____________________________________________________ ____________________________________________________ ____________________________________________________
27

(3)

Grade 9 Mathematics ANA Exemplar

5.3

A ladder is standing against the wall. If the ladder reaches a height of 12 up the wall and has its foot 5 away from it, calculate the length of the ladder. _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ What is the height, correct to the nearest , of a 5 cylindrical oil container with a radius of 20 ? (1 ≈ 1000 ) _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _________________________________________________________ (3) (3)

5.4

28 Grade 9 Mathematics ANA Exemplar

6. DATA HANDLING 6.1 The data below shows the ages of passengers in a bus travelling from Durban to Johannesburg. 3 45 70 6.1.1 2 30 15 15 2 34 27 37 31 35 42 2 4 53 1 5 33 32 14 50 59

How many passengers were in the bus? ______________________________________________________________ (1)

6.1.2

Determine the range of the ages. ______________________________________________________________ (1)

6.1.3

Calculate the mean age of the passengers on the bus to the nearest whole number. ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ (3)

29 Grade 9 Mathematics ANA Exemplar

6.2 Government expenditure in 2003 Protection service 17%

Other 14%

Housing 2%

Transport and communication 4%

Health 11% Welfare 14%

Education 19% Debts 15%

The above pie chart shows how the R105 billion budget was shared amongst the various services in 2003.

6.2.1

How much money was budgeted for education? _____________________________________________________________ _____________________________________________________________ (2)

6.2.2

What percentage was budgeted for protection services and welfare combined? _____________________________________________________________ (1)

6.2.3

What amount was allocated for education and health combined? _____________________________________________________________ (2) [5]

30 Grade 9 Mathematics ANA Exemplar

6.3 The marks obtained by the grade 9 learners for a Maths test out of 30 were listed as follows: 3 11 11 22 5 10 21 13 6 13 15 20 7 11 17 23 9 14 23 26

6.3.1

Complete the stem - and - leaf display in ascending order.

Stem 0 1 2 6.3.2 What was the range of the marks?

Leaves (3)

______________________________________________________________ 6.3.3 What was the median mark? ______________________________________________________________ 6.3.4 What was the modal mark? ______________________________________________________________

(1)

(1)

(1)

31 Grade 9 Mathematics ANA Exemplar

6.4 6.4.1

The three possible outcomes of a soccer game are win, draw or lose. Bafana-Bafana played two games at Soccer City. Complete a two-way table to list all the possible outcomes: Win (W) Win (W) Draw (D) Lose (L) (3) Draw (D ) Lose (L )

6.4.2

What is the probability of 6.4.2.1 winning both games? _______________________________________________________ 6.4.2.2 winning 1 game and losing 1 game ? _______________________________________________________ 6.4.2.3 winning at least 1 game ? _______________________________________________________ (1) (1) (1)

32 Grade 9 Mathematics ANA Exemplar

6.5

The data set contains the heights of a class of grade 9 learners. 140 149 152 159 153 158 154 160 148 166 144 160 159 163 170 153 6.5.1 Complete the table. Class-interval 140---144 145---149 150---154 155---159 160---164 165---169 170---174
6.5.2

153 164 150 172

143 165 155 158

161 165 141 174

152 155 162 166

145 167 161 164

162 153 151 163

Tally marks

Frequency

(14) What is the range of the heights? __________________________________________________ __________________________________________________ (2) What is the modal class-interval? __________________________________________________ (2) __________________________________________________
6.5.4 6.5.3

In which class-interval lies the median?

__________________________________________________ __________________________________________________ (2) 7. PROBLEM SOLVING Share R48 amongst A, B and C so that for every R4 given to A, B receives R3 and for every R4 given to B, C receives R3. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________
END 33 Grade 9 Mathematics ANA Exemplar

(3)

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...Math is used everyday – adding the cost of the groceries before checkout, totaling up the monthly bills, estimating the distance and time a car ride is to a place a person has not been. The problems worked this week have showed how math works in the real world. This paper will show how two math problems from chapter five real world applications numbers 35 and 37 worked out. Number 35 A person hired a firm to build a CB radio tower. The firm charges $100 for labor for the first 10 feet. After that, the cost of labor for each succeeding 10 feet is $25 more than the preceding 10 feet. That is, the nest 10 feet will cost $125; the next 10 feet will cost $150, etc. How much will it cost to build a 90-foot tower? Solving this problem involves the arithmetic sequence. The arithmetic sequence is a sequence of numbers in which each succeeding term differs from the preceding term by the same amount (Bluman, 2011). n = number of terms altogether n = 9 d = the common differences d = 25 ª1 = first term ª1 = 100 ªn = last term ª2 = ª9 The formula used to solve this problem came from the book page 222. ªn = ª1 + (n -1)d ª9 = 100 + (9-1)25 ª9 = 100 + (8)25 ...

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...A | Course Title & Number | Calculus II: MTH104 | B | Pre/Co-requisite(s) | Pre-requisite: MTH103 (Calculus I) | C | Number of credits | 3 | D | Faculty Name | Dr. Ghada Alobaidi | E | Term/ Year | Fall 2014 | F | Sections | Course | Days | Time | Location | MTH104.02 MTH104.04MTH104.06 | UTR UTRMW | 9:00-9:50 10:00-10:50 8:00-9:15 | PHY 113NAB 007NAB010 | | | | | | G | Instructor Information | Instructor | Office | Telephone | Email | Ghada Alobaidi | NAB 249 | 06 515 2754 | galobaidi@aus.edu | Office Hours: UT: 11:00 – 12:30 , R: 11:00 – 12:00 or by appointment. | H | Course Description from Catalog | Covers techniques of integration, improper integrals, sequences, infinite series, power series, parameterized curves, polar coordinates, integration in polar coordinates and complex numbers. | I | Course Learning Outcomes | Upon completion of the course, students will be able to: * Read, analyze, and apply to problems, written material related to the study of calculus. * Use the appropriate technique(s) – including integration by parts, trigonometric substitutions, partial fractions, etc. to integrate algebraic, logarithmic, exponential, trigonometric, and composite functions. * Evaluate improper integrals and test them for convergence. * Compute arc length and surface area of revolution of graphs and parametric curves. * Graph polar curves and find enclosed area and arc length. * Apply theorems about limits of...

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...you come to geometry, your opinion may vary. This class introduces a lot of new topics, which can be challenging, and take lots of practice outside of school if you do not pay attention or do your math homework. I strongly advise you to do your math homework everyday, not for just a grade, but it also helps you when it comes time for quizzes and tests. She rarely checks homework, but when she does, she will not tell you. It is also a great review for tests and quizzes. Ms.Hull’s tests and quizzes are not the easiest things you will take. The quizzes take new concepts and apply to the quiz. Also, her tests are usually always hard. It is a good idea to practice new concepts and review old ones from previous units, so you can get a good grade on the tests. I also advise you to be organized throughout the year. Organization is the key to success especially in math class. Tool kits are an extremely helpful resource to use. There are going to be a lot of conjectures and theorems that will be new, and it would be hard to just memorize them. My overall geometry year was not exactly the way I hoped it would turn out. It was extremely had, and it moves at a very quick pace, so keeping up was hard for me personally. If I could have done something differently, it would have been practicing math more often. Each concept was hard, and I did not have anytime to review it, because I have a lot of honors classes which require a lot of work too. The key to being successful in this course...

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...|7|SURVEY OF MATHEMATICS FALL 2015 | |8| | |8| | |8| | |8| | | |  | | |Instructor  | | |Gary F. Melendy | | | | | |Title  | | |Instructor ...

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...Math 1P05 Assignment #1 Due: September 26 Questions 3, 4, 6, 7, 11 and 12 require some Maple work. 1. Solve the following inequalities: a) b) c) 2. Appendix D #72 3. Consider the functions and . a) Use a Maple graph to estimate the largest value of at which the graphs intersect. Hand in a graph that clearly shows this intersection. b) Use Maple to help you find all solutions of the equation. 4. Consider the function. a) Find the domain of. b) Find and its domain. What is the range of? c) To check your result in b), plot and the line on the same set of axes. (Hint: To get a nice graph, choose a plotting range for bothand.) Be sure to label each curve. 5. Section 1.6 #62 6. Section 2.1 #4. In d), use Maple to plot the curve and the tangent line. Draw the secant lines by hand on your Maple graph. 7. Section 2.2 #24. Use Maple to plot the function. 8. Section 2.2 #36 9. Section 2.3 #14 10. Section 2.3 #26 11. Section 2.3 #34 12. Section 2.3 #36 Recommended Problems Appendix A all odd-numbered exercises 1-37, 47-55 Appendix B all odd-numbered exercises 21-35 Appendix D all odd-numbered exercises 23-33, 65-71 Section 1.5 #19, 21 Section 1.6 all odd-numbered exercises 15-25, 35-41, 51, 53 Section 2.1 #3, 5, 7 Section 2.2 all odd-numbered exercises 5-9, 15-25, 29-37 Section 2.3 all odd-numbered exercises...

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...find the national average cost of food for an individual, as well as for a family of 4 for a given month. http://www.cnpp.usda.gov/sites/default/files/usda_food_plans_cost_of_food/CostofFoodJan2012.pdf 5. Find a website for your local city government. http://www.usa.gov/Agencies/Local.shtml 6. Find the website for your favorite sports team (state what that team is as well by the link). http://blackhawks.nhl.com/ (Chicago Blackhawks) 7. Many of us do not realize how often we use math in our daily lives. Many of us believe that math is learned in classes, and often forgotten, as we do not practice it in the real world. Truth is, we actually use math every day, all of the time. Math is used everywhere, in each of our lives. Math does not always need to be thought of as rocket science. Math is such a large part of our lives, we do not even notice we are computing problems in our lives! For example, if one were interested in baking, one must understand that math is involved. One may ask, “How is math involved with cooking?” Fractions are needed to bake an item. A real world problem for baking could be as such: Heena is baking a cake that requires two and one-half cups of flour. Heena poured four and one-sixth cups of flour into a bowl. How much flour should Heena take out of the bowl? In this scenario of a real world problem, we have fractions, and subtraction of fractions, since Heena has added four and one-sixth cups of flour, rather than the needed...

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Math

... h(x)= 7-x/3 First we need to compute (f-h)(4) (f*h)(4)=f(4)-h(4), each function can be done separately f(4)=2(4)+5 f(4)=8+5 f(4)=13 H h(4)=(7-4)/3 same process as above h(4)=3/3=h(4)=1 (f-h)(4)=13-1 (f-h)(4)=12 this is the solution after substituting and subtracting The next part we need to replace the x in the f function with the g (f*g)(x)=f(g(x)) (f*g)(x)=f(x2-3) (f*g)(x)=2x2-1 is the result Now we need to do the h function (h*g)(x)=h(g(x)) (h*g)(x)=h(x2-3) (h*g)(x)=7-(x2-3) (h*g)(x)=10-x2 end result The inverse function-- f-1(x)=x-5h-1(x)=-(3-7) By doing problems this way it can save a person and a business a lot of time. A lot of people think they don't need math everyday throughout their life, but in all reality people use math almost everyday in life. The more you know the better off your life will...

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