## Algebra 2: Midterm Exam (study guide)

What is the number of real solutions?

– x² + 9x + 7 = 0

– x² + 9x + 7 = 0

use b^2-4ac

What is the number of real solutions?

8x² – 11x = -3

8x² – 11x = -3

use b^2-4ac

What is the number of real solutions?

x² = -7x + 7

x² = -7x + 7

use b^2-4ac

What is the number of real solutions?

– 4x² – 4 = 8x

– 4x² – 4 = 8x

use b^2-4ac

What is the expression in factored form?

2x² + 16x + 30

2x² + 16x + 30

2(x+3)(x+5)

What is the expression in factored form?

– 4x² + 8x + 32

– 4x² + 8x + 32

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What is the expression in factored form?

3x² + 26x + 35

3x² + 26x + 35

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What is the expression in factored form?

9x² – 18x + 9

9x² – 18x + 9

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What is the expression in factored form?

x² – 64

x² – 64

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What are the solutions of the quadratic equation?

x² – 9x + 18 = 0

x² – 9x + 18 = 0

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What are the solutions of the quadratic equation?

3x² + 25X + 42 = 0

3x² + 25X + 42 = 0

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What are the solutions of the quadratic equation?

4x² – 18x + 20 = 0

4x² – 18x + 20 = 0

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Solve by using tables. Give each answer to a most two decimal places.

2x² + 5x – 3 = 0

2x² + 5x – 3 = 0

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Solve by using tables. Give each answer to a most two decimal places.

– 7x² – 2 = -10x

– 7x² – 2 = -10x

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What is the solution of each equation?

3x² = 21

3x² = 21

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What is the solution of each equation?

108x² =147

108x² =147

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Solve the equation.

x² + 18x + 81 = 25

x² + 18x + 81 = 25

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Solve the equation.

x² – 8x + 16 = 16

x² – 8x + 16 = 16

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Solve the equation.

0.125r – 0.0625 + 0.25r = 0.25 + r

0.125r – 0.0625 + 0.25r = 0.25 + r

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Solve the equation.

– 5y – 9 = – ( y – 1 )

– 5y – 9 = – ( y – 1 )

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Solve the quadratic equation by completing the square.

x² + 10x + 14 = 0

x² + 10x + 14 = 0

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Solve the quadratic equation by completing the square.

– 3x² + 7x = – 5

– 3x² + 7x = – 5

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Rewrite the equation in vertex form. Name the vertex and y- intercept.

y = 3/5x² + 30x + 382

y = 3/5x² + 30x + 382

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Use the quadratic formula to solve the equation.

– 2x² – 5x + 5 = 0

– 2x² – 5x + 5 = 0

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Use the quadratic formula to solve the equation.

2x² + x – 4 = 0

2x² + x – 4 = 0

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Use the quadratic formula to solve the equation.

– 4 x² + x = – 4

– 4 x² + x = – 4

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Simplify the number using the imaginary unit i.

√(-144)

√(-144)

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Simplify the number using the imaginary unit i.

√(-360)

√(-360)

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Simplify the expression.

(-1 + 6i) + ( -4 + 2i)

(-1 + 6i) + ( -4 + 2i)

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Simplify the expression.

(1 + 2i) – (5 + 3i)

(1 + 2i) – (5 + 3i)

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Simplify the expression.

(-5i) (6i)

(-5i) (6i)

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Simplify the expression.

(6 – 4i) (-1 + 6i)

(6 – 4i) (-1 + 6i)

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Simplify the expression.

-1+3i

————

4 – i

-1+3i

————

4 – i

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Simplify the expression.

-5 +4i

———–

-6i

-5 +4i

———–

-6i

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What are the solutions?

9x² + 16 = 0

9x² + 16 = 0

__________________

What are the solutions?

½ x² – x + 5 = 0

½ x² – x + 5 = 0

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Which algebraic expression models the given word phrase?

40 fewer than a number t

40 fewer than a number t

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Which algebraic expression models the given word phrase?

You start with $15.00 and save $8.00 each week. What algebraic expression models the total amount you save?

You start with $15.00 and save $8.00 each week. What algebraic expression models the total amount you save?

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Write an algebraic model for the situation and evaluate it for the given information?

You are going shopping for some new sweaters, t-shirts, and pants. Sweater (s) cost $30, t-shirts (t) cost $19, and pants (p) cost $18. What algebraic expression models the total cost of the clothes that you buy?

Suppose you bought 26 sweaters, 9 t-shirts, and 23 pairs of pants. How much did you spend?

You are going shopping for some new sweaters, t-shirts, and pants. Sweater (s) cost $30, t-shirts (t) cost $19, and pants (p) cost $18. What algebraic expression models the total cost of the clothes that you buy?

Suppose you bought 26 sweaters, 9 t-shirts, and 23 pairs of pants. How much did you spend?

__________________

Is the relation a function?

{(15, 11), (5, 1), (4,11) ,(9,9),(5,5)}

{(15, 11), (5, 1), (4,11) ,(9,9),(5,5)}

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What is the slope of the line that passes through the given points?

(-12,12) and (2,4)

(-12,12) and (2,4)

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What is the slope of the line that passes through the given points?

(7,-9) and (7,-1)

(7,-9) and (7,-1)

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What is an equation of the line in slope intercept form?

m = ½ and the y-intercept is (0,-2)

m = ½ and the y-intercept is (0,-2)

__________________

see graph

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Write the equation in slope intercept form.

What are the slope and y-intercept?

-8x +3x = -10

What are the slope and y-intercept?

-8x +3x = -10

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Write the equation in slope intercept form.

What are the slope and y-intercept?

¾x + 4/5y = 4

What are the slope and y-intercept?

¾x + 4/5y = 4

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What is the graph of the equation?

3x – y = 3

3x – y = 3

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What is the graph of the equation?

-5x + 5y =4

-5x + 5y =4

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Write an equation of the line, in point-slope form, that passes through the 2 given points.

points: (-9,4) , (13, -7)

points: (-9,4) , (13, -7)

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What is an equation of the line, in point-slope form, that passes through the given point and has the given slope?

point: (9,6) ; slope: 1/3

point: (9,6) ; slope: 1/3

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