Garden Grove Unified School District
Precalculus Q4 Benchmark Review 2009-10
Scientific Calculators are permitted on the exam
1. Std MA 5.1 Which of the following
equations is an ellipse whose major axis is
horizontal?
2
3. Std MA 5.1 Write the following equation in
standard form and identify the type of conic.
9y 2  4x 2  8x  18y  41  0
2
a) 9x  4y  36
b) 9x 2  4y 2  36


c)
4x 2  9y 2  36
 4. Std MA 5.1 Find the foci of the graph of
(x  6) 2 (y  7) 2

1
100
121
2
2
d) 4x  9y  36


2. Std MA 5.1 Which of the following is the
(y  3) 2 (x  1) 2

graph of

 1?
16
9
5. Std MA 5.1 Find the equations of the
asymptotes of the hyperbola represented by
(x  5) 2 (y  1) 2

1
25
9


6. Std MA 5.1
Given: 9x2  y2  36x  6y 18  0

a)
b)
c)
d)
identify the conic
find the coordinates of the center
find the coordinates of the foci
find the coordinates of the vertices
7. Std MA 5.2 What is the equation of the locus
of points in a plane whose distance from (-4,6)
and the x-axis are equal? (Leave in x 2  4 py
form)
8. Std MA 5.2 What is anequation of the locus
of points whose sum of the distances from any
point on the conic to (-2,2) and (8,2) is 12?
9. Std MA 5.2 What is the equation of an
ellipse, centered at (2,1), if the vertical major
axis is 6 and the length of the horizontal minor
axis is 4?
Precalculus Q4 BM Review 2009-10
Garden Grove Unified School District
Precalculus Q4 Benchmark Review 2009-10
Scientific Calculators are permitted on the exam
10. Std MA 5.2 What is the equation of a
hyperbola, centered at (1, -2), if the length of the
horizontal transverse axis is 4 and the length of
the conjugate axis is 2?
16. Std MA 8.0 What is
lim
x 4  x 3  3x 2  5x
x x 3  x 2  3x  5
?
 x 2  36  
17. Std MA 8.0 What is lim  
 ?

x 5   x  6  
11. Std MA 3.0
n(n  1)(n  2)
,
3
complete the inductive step of its proof:
If (1)(2)  (2)(3)  ...n(n  1) 


(1)(2)  (2)(3)  ...  k(k  1)  (k  1)(k  2) 
_____________________

19. Std Alg 14.0 What is the approximate value
of the expression below if log m  0.6990 and
n
 m  
log n p  1.0792? log n    
 p  

12. Std MA 3.0 Erin is proving n!  2n for
every integer ≥ 4 by math induction. What
would be the first normal step?

13. Std MA 3.0 If Pk 
18. Std MA 8.0If f (x)  x 2  3x , what is the
f (2  h)  f (2)
value of lim
?
h
h0

(k  1) 2 (2k  1)
, what
3
20. Std Alg 14.0 If log c a  0.3010 and

log c b  .9542, what is 2 log c ab?
is Pk1 ?



14. Std MA 3.0 Identify the order of the steps
in a mathematical induction proof:

_____A. Assume S n is valid for n = k
_____B. Verify that the conjecture S n is true for
the first possible case
_____C. Prove that S n is valid for n = k + 1
_____D. Summarize what you have shown 


n 1
15. Std MA 8.0 Suppose an  4 
for
n
n {1,2, 3,...}. What is the limit of this sequence
as n increases?


21. Std Alg 14.0 What is the value of
 2log 4 ?
log10  log 4 16
2


Precalculus Q4 BM Review 2009-10

22. Std Alg 14.0 Solve for x:
log 5 3  log 5(x  2)  log 512
23. Std Alg 20.0 The length of a side of a cube
is represented by (3x  4y) . What is the volume
of the cube in expanded form?
24. StdAlg 20.0 What is the value of n if
56x 6 y 5 is the middle term in the expansion of
(x 2  y) n ?
Garden Grove Unified School District
Precalculus Q4 Benchmark Review 2009-10
Scientific Calculators are permitted on the exam
25. Std Alg 20.0 What is the middle term in the
expansion of (2x  4y)6 ?
26. Std Alg 20.0 What is the coefficient of the

x 2 y 2 term of the expansion of (2x  y) 4 ?

27. Std Alg 22.0 What is the value of 64 +16 +

4+1+… ?
28. Std Alg 22.0 What is the sum of the
20
arithmetic series  (2n  5) ?
n 1
29. Std Alg 22.0 What is the sum of the odd
integersbetween 36 and 74?
30. Std Alg 22.0 Find the sum of the series
2 1 1
  
 ...
3 9 54

Precalculus Q4 BM Review 2009-10
Garden Grove Unified School District
Precalculus Q4 Benchmark Review 2009-10
Scientific Calculators are permitted on the exam
Answer Key
17. 11
1. C
2. D
18. 1
2
3.
2
(y  1)
(x  1)

 1 hyperbola
9
4
19. – 0.3802
20. 2.5104
4. (6,7  21)

21. – 1
3
3
5. y  x  4 and y   x  2
5
5

6. a) hyperbola
c) (2  10,  3)

b) (2, -3)
d) (3, -3) (1, -3)
7. (x  4) 2  12(y  3)

2
8.

9.





(x  2) 2 (y  1) 2

1
4
9
(x  1) 2 (y  2) 2

1
4
1
(k  2) 2 (2k  3)
3
15. 5
16.  
Precalculus Q4 BM Review 2009-10


25. 10240x3y3
26. 24

27. 85
1
3
28. 520

(k  1)(k  2)(k  3)
3
14. B, A, C, D

24. 8
2
12. For n = 4, the formula is true because 4! ≥
24
13.
23. 27x 3  108x 2y  144xy 2  64y 3
(y  2)
(x  3)

1
36
9
10.
11.
22. 2
29. 1,045
30. 

4
7