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MHCA Math Summer Packet

For students entering Pre-calculus CP

The Summer Packet is broken into 7 different sections labeled weeks. If you do 1

section a week, you can complete the entire packet before the start of the school

year without much stress. This will be collected during the school’s Orientation

Days (August 28th

& 29th

). Packets turned in on the 1st official day of school will

lose 10 points for being late. Any packet that is not turned in by the 1st day of

school will receive a 0. The summer packet counts as two quiz grades, and will help

you review the material from last year so it is in your best interest to complete the

packet. If you have any questions regarding the completion of the MHCA Math

Summer Packet please contact Mr. McMahon (fmcmahon@maryhelp.org) or Mrs.

Wszeborowska (mrs.w@maryhelp.org)

Here are some websites to help you with the summer packets. Typing the topic into a web search will also give you more websites to help you.

http://www.khanacademy.org/ http://www.math.com/

http://www.coolmath.com/ http://www.purplemath.com/

http://www.ixl.com/math/algebra-1 http://www.ixl.com/math/geometry

http://www.themathpage.com http://www.mathgoodies.com

Week # 1

Chapter 1 – Equations and Inequalities

Exercises

Evaluate each expression.

1. 20 ÷ (5 – 3) + (3)

A 235 B 85 C

D 255

2. 18 – {5 – [34 – (17 – 11)]}

A B C D

3. Evaluate + 2y if a = 5 and y = –3.

A 58 B –2 C 70 D 10

4. Evaluate |–2b| if b = 8.

A –16 B 6 C 10 D 16

5. Name the sets of numbers to which

belongs.

A rationals C rationals, reals

B naturals, reals D integers, rationals, reals

6. Simplify 2 (x + 3) + 5 (2x – 1) .

A 12x + 1 B 12x + 11 C 12x + 2 D 9x + 1

7. Name the property illustrated by the equation.

5x • (4y + 3x) = 5x • (3x + 4y)

A Associative B Commutative C Distributive D Inverse

For Questions 6–8, solve each equation.

8.

y = 8

A 16 B 4 C

D 10

9. 4 (2x – 9) = 3x + 4

A –32 B –

C

D 8

10. 4|x + 3| = 20

A {2} B {–8} C {2, –8} D ∅

For Questions 9–10, solve each inequality.

11. 2x – 1 ≤ 5 or 7 – x < 1

A 3 ≤ x < 6 B x < 6 C x ≤ 3 or x > 6 D ∅

12.

|2x – 5| ≤ 9

A –4 ≤ x ≤ 14 B –2 ≤ x ≤ 7 C x ≤ –2 or x ≥ 7 D all real numbers

13. Identify the graph of the solution set of 9 > 3 + 2x.

A C

B D

14. A parking garage charges $2 for the first hour and $1 for each additional hour. Fran has $7.50 to spend for

parking. What is the greatest number of hours Fran can park?

A 3 B 5 C 6 D 7

Week # 2

Chapter 2- Linear Relations and Functions

Exercises

1. Find the domain of the relation {(0, 0), (1, 1), (2, 0)}. Then determine whether the relation is a function.

A {0, 1, 0}; function C {0, 1, 2}; function

B {0, 1, 0}; not a function D {0, 1, 2}; not a function

2. Find f(–1) if f(x) = –3x – 5.

A –9 B –8 C –2 D 2

3. Which equation is linear?

A xy = 60 C y = – 3x + 1 B 3x – 2y = 5 D + 1 = x

4. Write y – 4x = 7 in standard form.

A 4x – y = –7 B 4x + y = 7 C y = 4x + 7 D 4x = y – 7

5. Find the x-intercept of the graph of –5x + 10y = 20.

A –2 B 2 C 4 D –4

6. Find the slope of the line that passes through (0, 2) and (8, 8).

A 8 B

C

D

7. If a line rises to the right, its slope is ___?____.

A zero B positive C negative D undefined

8. What is the slope of a line that is perpendicular to the graph of y = 2x + 5?

A –

B

C 2 D –2

9. Line a through (2, 3) is parallel to line b with equation y = –1. Which point below also lies on line a?

A (2, 9) B (–5, 3) C (0, 1) D (1, 4)

10. Write an equation in slope-intercept form for the line that has a slope of –

and passes through (0, 7).

A y = 7x B y = 7x –

C y =

x + 7 D y = –

x + 7

11. Write an equation in slope-intercept form for the line that passes through

(0, 1) and is perpendicular to the line whose equation is y = 2x.

A y = –2x + 1 B y = 2x + 1 C y =

x + 1 D y = –

x + 1

12. Identify the range of y = ⎪x⎥ .

A all real numbers B {x | x ≥ 0} C { y | y ≥ 0} D {y | y ≤ 0}

13. The graph of the linear inequality y ≥ 2x – 1 is the region __?__ the graph of the line y = 2x – 1.

A on or above B on or below C above D below

14. Which inequality is graphed at the right?

A y ≥ |x| – 3 B y ≤ |x| – 3 C y > |x| – 3 D y < |x| – 3

Week # 3

Chapter 3- systems of equations and Inequalities

Exercises 1. A system of linear equations may not have

A exactly one solution. C infinitely many solutions. B no solution. D exactly two solutions.

2. Choose the correct description of the system of equations.

4x + 2y = –6

2x – y = 8

F consistent and independent H consistent and dependent

G inconsistent J inconsistent and dependent

3. Which system of equations is graphed?

A y –

x = 0 C y – 3x = 0

x – y = –2 x – y = 2

B y – 3x = 0 D y –

x = 0

x – y = –2 x – y = 2

4. Which system of inequalities is graphed?

A y > – 1 B y > – 1

y ≥ – x + 1 y ≤ – x + 1

C y ≥ –1 D y > – 1

y ≥ – x + 1 y < – x + 1

5. Find the minimum value of f(x, y) = 3x + y for the feasible region.

A 6 B 4 C 2 D 0

6. Find the maximum value of f(x, y) = 3x + y for the feasible region.

A 2 B 4 C 6 D 12

7. What is the value of y in the 2x + y + z = 1

solution of the system of equations? 2x – y – 3z = –3

x – 2y – 4z = –2

A –10 B –8 C 2 D 5

For Questions 8-15, use the matrices to find the following.

P = [

] Q = [

] R = [

] S = [

]

8. the first row of 4S

A [–2 8 –5] B [12 –4 –20] C [24 –16 36] D not possible

9. the first row of 2P + 2R

A [8 3] B [4 3] C [6 –4] D not possible

10. the first row of SP

A [12 –4 –20] B [–23 21] C [53 –27] D not possible

11. the inverse of matrix R

A P B Q C T D not possible

12. the determinant of Q

A 8 B 4 C 2 D 4

13. Find the value of |

|.

A 13 B 7 C 17 D 3

14. Cramer’s Rule is used to solve the system of equations 2m + 3n = 11 and 3m – 5n = 6. Which determinant

represents the numerator for m?

A |

| B |

| C |

| D |

|

Week # 4

Chapter 4 – Quadratic Functions and Relations

Exercises

1. Find the y-intercept for f(x) = .

A 1 B –1 C x D 0

2. What is the equation of the axis of symmetry of y = –3 + 12?

A x = 2 B x = –6 C x = 6 D x = –18

3. The graph of f(x) = –2 + x opens _____ and has a _____ value.

A down; maximum C up; maximum B down; minimum D up; minimum

4. The related graph of a quadratic equation is shown at the right. Use the graph to determine the solutions of the

equation.

A –2, 3 B –3, 2 C 0, –6 D 0, 2

5. The quadratic function f(x) = has ________ .

A no zeros C exactly two zeros B exactly one zero D more than two zeros

6. Solve – 3x – 10 = 0 by factoring.

A {–5, 2} B (–2, –5) C {–2, 5} D {–10, 1}

7. Which quadratic equation has roots –2 and 3?

A + x + 6 = 0 C – 6x + 1 = 0 B – x – 6 = 0 D + x – 6 = 0

8. Simplify (5 + 2i)(1 + 3i).

A 5 + 6i B –1 C –1 + 17i D 11 + 17i

9. To solve + 8x + 16 = 25 by using the Square Root Property, you would first rewrite the equation as .

A = 25 B + 8x – 9 = 0 C = 5 D + 8x = 9

10. Find the value of c that makes + 10x + c a perfect square.

A 100 B 25 C 10 D 50

11. The quadratic equation + 6x = 1 is to be solved by completing the square. Which equation would be the first

step in that solution?

A + 6x – 1 = 0 B + 6x + 36 = 1 + 36 C x(x + 6) = 1 D + 6x + 9 = 1 + 9

12. Find the exact solutions to – 3x + 1 = 0 by using the Quadratic Formula.

A √

B

√

C

√

D

√

13. What is the vertex of y = 2 + 6?

A (–3, –6) B (3, –6) C (–3, 6) D (3, 6)

14. Which quadratic inequality is graphed at the right?

A y ≥ + 4 B y ≤ – + 4 C y ≤ – – + 4 D y ≤ – – 4

Week # 5

Chapter 5 - Polynomials and Polynomial Functions

Exercises

1. Simplify (2 ).

A B 12 C 18 D 18

2. Simplify

. Assume that no variable equals 0.

A

B

C 5 z D

3. Shen is simplifying the expression (3 + 4 )( – 2 – 1). Which of the following shows the correct product?

A 3 – 6 + 4 – 11 – 4 C 3 + 6 – 4 + 11 + 4

B 3 – 6 + 4 – 11 – 4 D 3 – 6 – 11 + 4 – 4

4. Simplify 3x(2 – y).

A 5 + 3xy B 12x – y C 6 – 3y D 6 – 3xy

5. Simplify ( – 2x – 35) ÷ (x + 5).

A – x – 30 B x – 7 C x + 5 D + 3 – 45x – 175

6. Which represents the correct synthetic division of ( – 4x + 7) ÷ (x – 2)?

A C

B D

7. Factor + 9m + 14 completely.

A m(m + 23) B (m + 14)(m + 1) C (m + 7)(m + 2) D m(m + 9) + 14

8. Simplify

. Assume that the denominator is not equal to 0.

A t – 5 B t – 2 C t – 3 D t + 3

9. State the number of real zeros for the function whose graph is shown at the right.

A 0 B 2 C 1 D 3

10. Write the expression + 5 – 8 in quadratic form, if possible.

A + 5( ) – 8 B + 5( ) – 8 C – 5( ) – 8 D not possible

11. Use synthetic substitution to find f(3) for f(x) = – 9x + 5.

A –23 B –16 C –13 D 41

12. One factor of + 4 – 11x – 30 is x + 2. Find the remaining factors.

A x – 5, x + 3 B x – 3, x + 5 C x – 6, x + 5 D x – 5, x + 6

13. Which describes the number and type of roots of the equation 4x + 7 = 0?

A 1 imaginary root B 1 real root and 1 imaginary root C 2 real roots D 1 real root

14. Find all the rational zeros of p(x) = – 12x – 16.

A –2, 4 B 2, –4 C 4 D –2

Week # 6

Chapter 6 – Inverse and Radical Functions and Relations

Exercises For Questions 1 and 2, use f(x) = x + 5 and g(x) = 2x.

1. Find (f + g)(x).

A 3x + 5 B x + 5 C 2x + 10 D 2 + 5

2. Find (f ⋅ g)(x).

A 2 + 5 B 3 + 10x C 2 + 10x D 2x + 10

3. If f(x) = 3x + 7 and g(x) = 2x – 5, find g[f(–3)].

A –26 B –9 C –1 D 10

4. If f(x) = and g(x) = 3x – 1 find [ g ◦ f](x).

A + 3x – 1 B 9 – 1 C 9 – 6x + 1 D 3 – 1

5. Find the inverse of g(x) = –3x.

A (x) = x + 1 C (x) = x – 1 B (x) = –3x – 3 D (x) = –

x

6. Determine which pair of functions are inverse functions.

A f(x) = x – 4 B f(x) = x – 4

g(x) = x + 4 g(x) = 4x – 1

C f(x) = x – 4 D f(x) = 4x – 1

g(x) = –

g(x) = 4x + 1

7. State the domain and range of the function graphed.

A D = {x │ x > 2}, R = {y │ y > 0} B D = {x │ x < 2}, R = {y │ y > 0}

C D = {x │ x ≥ 2}, R = {y │ y < 0} D D = {x │ x ≥ 2}, R = {y │ y ≥ 0}

8. Which inequality is graphed?

A y ≤ √ B y > √ C y < √ D y ≥ √

9. Use a calculator to approximate √ to three decimal places.

A 15.0 B 14.97 C 14.966 D 14.967

10. Simplify (2 + √ )(3 – √ ).

A 1 + √ B 1 – √ C –1 + √ D –1 – √

11. Write the expression

in radical form.

A √

B 35 C √

D √

12. Simplify the expression

•

.

A

B

C

D

13. If x is a positive number, then √

÷

= ?

A B

x C 1 D

14. If • y = , then y = ?

A – B – C

D

Week # 7

Chapter 7 – Exponential and Logarithmic Functions and Relations

Exercises

1. Find the domain and range of the function whose graph is shown.

A D = {x | x > 0}; R = {y | y > 0} B D = {all real numbers}; R = {y | y > 0}

C D = {x | x > 0}; R = {all real numbers} D D = {all real numbers}; R = {y | y < 0}

2. Which function represents exponential growth?

A y = 9(

)

B y = 4 C y = 12(

)

D y = 10

3. The graph of which exponential function passes through the points (0, 4) and (1, 24)?

A y = 4 B y = 3 C y = 2 D y = 10

4. Solve = .

A –2 B –1 C 0 D 1

5. Solve > 4.

A {x | m < 0} B {x | m > 0} C {x | m > 2} D {

}

6. Write the equation = 64 in logarithmic form.

A = 64 B = 64 C = 3 D = 3

7. Write the equation log12 144 = 2 in exponential form.

A = 12 B

= 144 C = 144 D

= 2

8. Evaluate .

A 3 B 4 C 16 D 64

9. Solve = 2.

A 6 B 5 C 8 D 9

10. Solve 2m > .

A {

} B {x | m < 5} C {x | m > 5} D {x | m > –5}

11. Solve + = .

A 180 B 4 C 5 D 30

12. Solve ≥ 21. Round to the nearest ten-thousandth.

A {x | x ≥ 0.8451} B {x | x ≥ 2.7712} C {x | x ≥ 0.3608} D {x | x ≥ 7.0000}

13. Express in terms of common logarithms.

A log

B C

D

14. Evaluate .

A B C D 4

15. Martin bought a painting for $5000. It is expected to appreciate at a continuous rate of 4%. How much will the

painting be worth in 6 years? Round to the nearest cent.

A $6200.00 B $5360.38 C $37,647.68 D $6356.25

16. Solve = 20. Round to the nearest ten-thousandth.

A 0.4628 B 1.5214 C 0.6990 D 2.161