1

Grade 9

Maths

6 JULY MATHS ONLINE HOLIDAY

Worksheet 7 Day 6a and b 7-8 July 2020 Function & relationships

Worksheet 8 Day 7a and b 9-10 July 2020 Function & relationships

Worksheet 9 Day 1a and b 13-14 July 2020 Function & relationships

Worksheet 10 Day 2a and b 15-16 July 2020 Function & relationships Worksheet 11 Day 3a and b 17&20 July 2020 Function & relationships

Worksheet 12 Day 4a and b 21-22 July 2020 Function & relationships

23 July 2020 STUDY ALL WORKSHEETS 24 July 2020 ONLINE TEST

2

TOPIC: FUNCTIONS AND RELATIONSHIPS The relationship between input and output values under a given rule can be represented in any of the following ways: (a) verbally (b) in flow diagrams (c) in tables (d) by means of equations

If we consider the relationship where input values 4 ; 5 ; 6produce output values

11;13 ;15using the rule “multiply each input

Note: If we reverse the operations we can determine the input value when given the output value. The reverse rule is as follows: Subtract 3 from each output value and then divide by 2.

Therefore, if the output value is 11, the input value is (113) 2 4 .

For the output value 13, the corresponding input value is (133) 2 5

For the output value 15, the corresponding input value is (15 3) 2 6

In the examples that follow, you will be required to determine output values when given the input values. You will also be required to determine the input values when given the output values. The use of equations will be much easier to do than using inverse operations.

3

4

EXAMPLE

5

EXAMPLE

6

GRADE 9 GREY COLLEGE 7-8 July 2020

MATHS Day 6a and b

Do the following in Book 1 (or on paper) Worksheet 7

a) Determine the output values in the following diagrams:

1 2

b) For each of the following equations, determine the output values corresponding to

the input values x2 ; 1; 0 ;1; 2 ; 3:

1) 𝑦 = −4𝑥 − 1

2) 𝑦 = 4𝑥 + 5

c) If the rule for finding y in the table below is 𝑦 = −9𝑥 + 6, determine the output

values (𝑦) for the given input values (𝑥).

d) If the rule for finding y in the table below is𝑦 =1

3𝑥 − 2, determine the output

values (𝑦) vir for the given input values(𝑥).

7

FINDING INPUT VALUES WHEN GIVEN OUTPUT VALUES AND A RULE

EXAMPLE

8

EXAMPLE

9

GRADE 9 GREY COLLEGE 9-10 July 2020

MATHS Day 7a and b

Do the following in Book 1 (or on paper) Worksheet 8

(a) Determine the input value in the following flow diagrams:

1. 2.

3.

(b) The equation 𝑦 = 𝑥 + 3 is given. If the output values are y4 ; 7 ; 10 ; 13, determine the input values.

(c) The equation 𝑦 = −2𝑥 + 6 is given. If the output values are y10 ; 12 ; 14, determine the input values.

(d) The equation 𝑦 = −1

5𝑥 − 1 is given. If the output values are y0 ; −1 ; −2 ; −3,

determine the input values.

10

FINDING THE RULE WHEN GIVEN INPUT AND OUTPUT VALUES

EXAMPLE

11

EXAMPLE

12

EXAMPLE

13

GRADE 9 GREY COLLEGE 13-14 July 2020

MATHS Day 1a and b

Do the following in Book 1 (or on paper) Worksheet 9

a) Determine the rule in the following flow diagrams

1. 2.

3.

b) Determine the rule in each of the following tables.

1.

2.

14

c) Calculate the value of 𝑎 and b in each of the following tables:

15

THE GRAPHICAL REPRESENTATION OF RELATIONSHIPS

EXAMPLE

16

GRADE 9 GREY COLLEGE 15-16 July 2020

MATHS Day 2a and b

Do the following in Book 1 (or on paper) Worksheet 10 4

a) For each of the following general rules for number patterns, determine the first four

terms and hence represent the relationship graphically. The value of n is a natural

number. 1. 𝑇𝑛 = 𝑛 + 1

2. 𝑇𝑛 =6𝑛−4

2

3. 𝑇𝑛 = 𝑛2 4. 𝑇𝑛 = 2𝑛

b) For each of the following flow diagrams, determine the missing information. Assume

that the input and output values are natural numbers.

1. 2.

c) For each of the following equations, determine the missing values and hence represent

the relationship graphically. Assume that the input and output values are natural

numbers. 1) 𝑦 = 𝑥 + 2 where x2 ; 3 ; 4 ; 5

2) 𝑦 = 2𝑥 − 1 where x1 ; 3 ; 5 ; 7

17

RELATIONSHIPS INVOLVING FORMULAE

EXAMPLE

18

EXAMPLE

19

GRADE 9 GREY COLLEGE 17&20 July 2020

MATHS Day 3a and b

Do the following in Book 1 (or on paper) Worksheet 11

(a) A formula in Physics is = 𝑢 + 𝑎𝑡 . Calculate:

(1) 𝑣 if 𝑢 = 8, 𝑎 = 13 𝑎𝑛𝑑 𝑡 = 4 (2) 𝑎 if 𝑢 = 16, 𝑣 = 46 and 𝑡 = 10

(b) Americans use a different unit for measuring temperature to us. They use the Fahrenheit

scale ( F) whereas we use the Celsius scale ( C). The formula which can be used to

convert a temperature inFtoC, or C to F, is 𝐹 =9

5𝐶 + 32. Convert:

(1) 35C toe F

(2) 20C toe F

(3) 104F toe C

(c) The circumference of a circle is given by the formula C 2r.

(1) If r = 28 and we take the value of 𝜋 to be 22

7 , calculate the value of C.

(2) If C = 60𝜋, calculate the value of r.

(d) The perimeter of a rectangle is given by the formula P 2(L B) , where L= length and B = breadth.

(1) Calculate the perimeter if the length is 10 cm and the breadth is 6 cm. (2) Calculate the breadth if the perimeter is 16 cm and the length is 5 cm.

20

EQUIVALENT FORMS

21

GRADE 9 GREY COLLEGE 21-22 July 2020

MATHS Day 4a and b

Do the following in Book 1 (or on paper) EXERCISE 6

1. Consider the following table:

(1) Determine a rule connecting x and y .

(2) Show that your rule in (1) and the rule y 4 (x 2)(3) are equivalent.

(b) Consider the rules y 2x 2 and y 4 (x 1)(2) .

Using input values of your choice, draw a flow diagram for each rule to show that they are

equivalent. Hence show that they are equivalent using Algebra.

(c) Consider the rules a b2 1 and a (b 1)2 2b . By using the input values

b2 ; 1; 0 ;1; 2 ; 3, show that the rules are equivalent by calculating the corresponding

output values for each rule.

(d)

(e) Consider the following equations:

A y (x 2)2 3 B. y x2 2x 8

C. y (x 4)(x 2) D. y x2 4x 1

(1) Use the input values x1; 0 ;1; 2 to determine which of these equations are

equivalent