Joint mathematics assignment in the fourth grade.

The use of a calculator is allowed. Carefulness, spelling and writing will be considered in the scoring.

Only the MCQ of the geometric part is to be returned on the subject.

## Exercise 1 shared homework

a) Calculate A and B, showing all steps of the calculations on the copy.

b) Use your calculator to perform the following calculation.

No justification is required, only the result must be written on the copy.

(give the rounding of C to the nearest 0.01)

## Exercise 2 ”Joint homework”

a) Remove the parentheses and reduce the expression M.

b) Expand and reduce N and P.

c) Calculate N when x is equal to 3.

## Exercise 3 ”Joint homework”

Show that each sentence below is false with a counterexample:

a) “when divided by 0.1 the result is smaller than the starting number.”

b) “A number is always greater than its inverse

c) “When you multiply a number by – 1 the result is always smaller than the starting number”.

d) “When you multiply a number by 4, the result is always greater than the original number.

## Exercise 4 shared homework

A calculation program is given:

• Choose a number.
• Multiply the sum obtained by the chosen number
• Add 1 to this product
• Write the result.

1) Write the calculations to verify that if we run this program with the number – 1 , we get 0.

2) Give the result provided by the program when the chosen number is -6

3) Give the result provided by the program when the chosen number is 4

4) Write the expression obtained for any number a.

## Exercise 5 ”Joint homework”.

1. Determine the nature of the triangle RST, R, S and T points of the circle C of center O

2. Furthermore, RT = 65 mm and RS = 72 mm are given. Show that RT = 97 mm. Make a full-scale figure

3. Construct a point A such that AR = 53 mm and AT = 81 mm. Is the ART triangle rectangular? Justify.

## Exercise 6 ”Joint homework”.

1. Prove that ABC is a right triangle
2. Calculate BD
3. Prove that points A, B, C and D are on the same circle whose center and radius you will specify.

## Exercise 7 shared homework

ABCD is a rectangle and the unit is the meter.

AB = 25, BC = 12, DK = 24 and KC = 7

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