MATH REVISION SHEET FOR THE FINAL EXAM 1st TERM Grade9/___ Name: __________________

Exam will be in Algebra 1 lessons :8.2+8.5+8.9

+ Geometry lessons : 7.1+7.2+7.3+7.4

7.1

1.Name the pairs of congruent angles.

A _______________________

B _______________________

C _______________________2. Write the corresponding side lengths in the proportion below.

Use the figure for Exercises 6 and 7. The triangles are similar. 3. Circle the correct similarity statement.

QRS KJL RSQ KJL QSR LKJ4. Write a proportion with all three pairs of corresponding

side lengths.

Identify the pairs of congruent angles and corresponding sides.5. 6.

______________________________________________ ____________________________________________________________________________________________ ____________________________________________________________________________________________ ______________________________________________

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7.ABC is similar to DEF. 8. The two rectangles are similar. What is What is EF? the value of x to the nearest tenth?

_________________________________ _______________________________

7.2

Apply the dilation D to the polygon with the given vertices. Describe the dilation.

1. D: (x, y) → (1.5x, 1.5y)A(–1, 3), B(2, 2), C(–2, –1)

_____________________________________

2. D: (x, y) → (2x, 2y)P(0, 0), Q(–2, 1), R(3, 3)

_____________________________________

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7.3

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Explain how you know the triangles are similar, and write a similarity statement.

1. 2.

__________________________________________ __________________________________________

__________________________________________ __________________________________________

__________________________________________ __________________________________________

__________________________________________ __________________________________________

3. Verify that ABC MNP.__________________________________________

__________________________________________

Name two pairs of congruent angles in Exercises 4 and 5 to show that the triangles are similar by the Angle-Angle (AA) Similarity Postulate.

4. 5.

__________________________________________ __________________________________________

Substitute side lengths into the ratios in Exercise 6. If the ratios are equal, the triangles are similar by the Side-Side-Side (SSS) Similarity Theorem.

6.

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7.4

In Exercises 5 and 6, set up a ratio and substitute values from the figure to find each length.

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1. LS ______________________ 2. BK ______________________

Find the length of each segment in Exercises 1 and 2.

3. 4.

__________________________________________ __________________________________________

3.Show that and are parallel. ______________________________________________________________________________________________________________________________

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ALGEBRA

8.2

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Find the zeros of each quadratic function from its graph.1. 2 3

__________________________ __________________________ __________________________

Find the axis of symmetry of each parabola.4. 5 6

__________________________ __________________________ __________________________

For 5 and 6, find the axis of symmetry of the function’s graph.7. y x2 10x 25 8. y 3x2 6x 5

x b2 a

2

The axis of symmetry is _______________. The axis of symmetry is _______________.

For 7 and 8, find the vertex. (Hint: Refer back to problems 5 and 6.)9. y x2 10x 25 10. y 3x2 6x 5

The x-coordinate is _______________.

y 2

1 0 2 5

The y-coordinate is _______________.

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The vertex is _______________. The vertex is _______________.

11. Find the vertex of y 2x 2 12x 9.__________________________________________

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8.5

Find the solutions from each graph below. 1. 3x2 9x 0 2. x2 4x 4 0 3. 2x2 6x 0

__________________________ __________________________ __________________________

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8.9

Solve using the quadratic formula.1. x2 6x 5 0 2. x2 9x 20 0

a: b: c: a: b: c:

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x x

____________________________________________ __________________________________________

3. 2x2 9x 4 0 4. x2 3x 18 0

a: b: c: a: b: c:

______________________________________________ __________________________________________

Find the number of real solutions of each equation using the discriminant.5. x2 3x 5 0 6. x2 10x 25 0 7. x2 6x 7 0

b2 4ac 2 4 b2 4ac 2 4 b2 4ac ___________

___________ ___________

______________________________ __________________________ __________________________

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Use a table of values to graph y = x

2 2.

x 2 1 0 1 2

y

Matching

Match each vocabulary term with its definition.a. linear equationb. minimumc. dilation

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24

2

± 2

4

2

±

d. parabolae. quadratic equationf. scale factor

g. quadratic functionh. linear functioni. maximum

____ 1. a drawing that uses a scale to represent an object as smaller or larger than the original object (c)

____ 3. the y-value of the lowest point on the graph of the function (b)

____ 1. the ratio of any length in a drawing to the corresponding actual length (f)

____ 2. the shape of the graph of a quadratic function (d)

____ 3. an equation that can be written in the form , where a, b, and c are real numbers and (e)

____ 4. the y-value of the highest point on the graph of the function (i)

____ 5. a function that can be written in the form , where a, b, and c are real numbers and (g)

Answer Key:

1.FE D

2. 3. RSQ KJL

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4.

5.J M; K N; L P;

6.A Q; B R; C S; D T

7.24 8. 8.1

********************************************************************************

7.21.

; dilation with center (0, 0) and scale factor 1.52.

; dilation with center (0, 0) and scale factor 2

*************************************************************************************

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7.3

1.Q T by the Def. of . By the Sum Thm., mS 39°and mU 49°, so S V and R U. QRS TUV by AA .

2. HJG LJK by the Vert. Thm. . GHJ KLJ by SAS .

3. ABC MNP by SSS . 4. B Y; C Z

5. F V; D T

6. ; ; ; ; ; **************************************************************7.41.12 2. 4

3. 14 4. 30.43.

so by the Conv. of the Proportionality Thm*************************************************************

ALGEBRA

8.2

1.4 and 0 2. 23.no zeros 4. x 05.x 4 6. x 5

7.10; 1; 10; 2; 5; x 58.x 19.x 5; 5; 5; 0; y 0; (5, 0)10. (1, 8)11. The vertex is (3, 27)***************************************************************************8.51. 0 , -32. 23. 0 , 3**************************************************************************8.91.1; 6; 5; 6; 6; 1; 5; 1; 1, 5

2. 1; 9; 20; 9; 9; 1; 20; 1; 5, 4

3. 2; 9; 4; , 4 4. 1; 3; 18; 6, 35. 3; 1; 5; 11; no real solutions6. 10; 1; 25; 0; 1 7. 64; 2

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