Algebra high school practice test

3 3

x y
1. Simplify the complex fraction .
4 4

y2 x

3y  x  y 3 x  y  3 x  y  3y  x  y 3y  x  y
A) B) C) D) E)
4 x  y 2
 4 x  y 2
 4 x  4 x  y 2
 4 x  y

2. A rectangular frame for a painting has a perimeter of 82 inches. If the length of the frame is 25
inches, find the width of the frame.

A) 18 in. B) 57 in. C) 16 in. D) 41 in. E) 66 in.

3. Compute a zero of the quadratic function f  x   23x 2  576 .

24 24 23 24 23 24 24 23
A) x  i B) x  C) x  D) x  E) x  i
23 23 23 23 23

4. Coordinates of the vertex for the parabola y = x2 + 12x + 40 are:

A) ( 6, 4) B) (-6, 4) C) (-4, 6) D) ( 4, 6) E) ( 0, 4)

5. Solve: 3  x – 10   3 x – 27

A) 0 > 3 B) –3  x  10 C) x  –20 D) x  –10 E) no solution

6. Solve the radical equation x 2  1  10 to find all real solutions.

A) x  9; x  9 B) x  11 C) x  9 D) x  3 E) x  3; x  3

7. Write the slope-intercept form of the equation of the line through the given point parallel to
the given line.
point: (4, 6) line: –40x – 8y = –4

1 59 1
A) y  x+ B) y  x C) y = –40x – 15 D) y = –5x + 26 E) y = –5x
40 10 5

8. Find the remainder of p(x)  q(x). Here, p( x)  x3  x  9 and q( x)  x  2 .

A) -15 B) 15 C) 3 D) 0 E) -3




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, 9. Evaluate f  – x  for the following function. f ( x)  6 x 2

A) 6x 4 B)  6x 3 C) 6x 3 D)  6x 2 E) 6x 2

10. Write the slope-intercept form of the equation of the line through the given point
perpendicular to the given line.
point: (4, 9) line: 9x + 45y = 8

1 85 1 49
A) y  x+ B) y  x+ C) y = 5x – 11 D) y = 9x + 45 E) y = 5x
9 9 5 5

11. Given that f ( x)  3 x  1 and g ( x)  x3  1 determine the value of ( f o g)(0) (if possible).

A) 0 B) 2 C) 1 D) x3  1 E) not possible

12. The volume of a gas varies directly with the temperature. If the volume is 30cc at 40 C,
what is the volume if the temperature is 64 C?

256 64 3
A) 48 cc B) 64 cc C) cc D) cc E) cc
3 3 256

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13. Use the zero x   to completely factor the polynomial f ( x)  5x3  x2  35x  7 .
5
A) (5x  1)( x2  7) B) (5x 1)( x2  7) C) (5x  1)( x2  7)
D) (7 x  1)( x2  5) E) (7 x  1)( x2  5)

 –8 x + 5 y  6
14. Solve the system of equations. 
 –16 x +10 y  2

 7 7 1 5   5 1 7 7
A)  – ,  B)  ,  C)  ,  D)  , –  E) no
 16 10   2 16   16 2   16 10 
solution

15. Solve the inequality x 2  10  x .
 1 41   1 41   1 41   1 41 
A)  ,    ,   B)  ,      ,  
 2 2  2 2 3 3  3 3
   
 1 41   1 41   1 41  1 41 
C)  ,       ,   D)  ,   E)   ,  
 2 2  2 2 2 2 
   3 3 




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