Algebra Competency Exam for 8th Grade Students Incoming eighth grade students requesting placement in Honors Geometry are required to take an Algebra Competency Examination. The purpose of the examination is to assess algebra competency and thus verify placement in either an additional algebra class or a geometry class. This exam is designed to assess the student’s knowledge of the following concepts of algebra:

• Rewriting algebraic expressions • Solving equations and inequalities • Working with Cartesian graphs • Understanding functions • Operations with radicals

Students are best prepared for advanced mathematics if they are competent in the above areas with and without the aid of technology. The Algebra Competency Exam will consist of 2 parts. Part 1 will consist of 20 multiple choice questions and the student will be able to use a calculator. Part 2 will consist of 30 free response questions, calculators will not be allowed and students will be required to show their work. The following are some sample problems. PART 1 Multiple Choice (choose one answer) Multiple Choice Directions: You may use your calculator for all of these problems. Use any methods you like. 1. If p = 2 and r = -5 then =

+

p

rp

A. -5 B. -

2

5

C. -2

3

D. 2

3

E. None of the above

2. If -2x + 5 > -11 which of the following must be true? A. x > - 3 B. x > 8 C. x < 3 D. x < 8 E. None of the above. 3. If k = ),60(

5

3+n which of the following gives n in terms of k?

A. 603

5!

k

B. 123

5!

k

C. 605

3+

k

D. 125

3+

k

E. None of the above 4. Simplify: ( )23

27!!

"

A. - 64

49

B. 64

49

C. 49

64

D. 1764 E. None of the above. 5. Which of the following is a factor of 2x 2 - 4x – 6? A. x + 1 B. x + 3 C. 2x – 1 D. 2x + 3 E. None of the above

6. Simplify: 12 A. 3 2 B. 2 3 C. 4 3 D. 6 2 E. None of the above. 7. Find the value of the expression: 5x 2 - 2yz when x =

2

1! , y = -2 and z = 5.

A. 21.25 B. -21.25 C. 25 D. -18.75 E. None of the above.

8. If

6

179=!

nn then n =

A. 12

1

B. 3

1

C. 6 D. 12 E. None of the above. 9. Find the equation of the straight line through the points (-2, 3) and (-1, - 4). A. y =

7

19

7

1+! x

B. y = -7x – 11 C. y = -7x -14 D. y =

7

23

7

1+! x

E. None of the above.

10. Solve the following equation. Round your solutions to the nearest tenth. 2x 2 = -3x + 1

A. 1.8, 0.3 B. -1, - 0.5 C. 0.3, - 1.8 D. – 1.6, 0.1 E. None of the above.

PART 2 Free response. (Show your work!!) Free Response Directions: No calculators are to be used in this section.. You will be graded on your methods. Be sure to clearly show how you arrived at your answer. Simplify the following five problems: 1. 2

8

53

2

1+

2. 3

4

31

16

1÷

3. 7.956 ÷ 1.8 4. 3.056 ! 1.03 5. -2[5 – (3 + 1)] 6. Solve the linear equation: )1(

2

14)2(

8

3!=!+ xx

7. Solve the following quadratic equation: 2a 2 + 7a – 4 = 0

8. The length of a rectangular room is 4 feet greater than its width. If the area of the room is 96 square feet, what is the length of the room in feet? 9. Find the equation of a line, in standard form, that is parallel to the line 2x – y = 5 and passes through the point (-2, 1). 10. Find the equation of a line with slope -2 and y-intercept of 3. Answer in standard form. 11. One number is 3 more than twice another, and their sum is 54. Find the larger number. 12. Simplify each of the following and write the answers using positive exponents only.

(a) (3x 232 )!!y (b)

2

1

22

8

2!

!

!

""#

$%%&

'

xy

yx

13. Simplify: (a) (3 2 - 2 3 ) 2 (b) 14

3

2

21+

14. Simplify: )12(4

2322

2

+÷!

!!x

x

xx

15. It takes a boat 2 hours to travel 20 miles down a river and 3 hours to return upstream to its starting point. What is the rate of the current in the river? 16. Solve the following system of equations: 4x + 3y = 3 2x – 6y = -1