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End-of-Course Test
1. Graph y = 2(x + 1)2 – 3. Identify the vertex.
2. Solve the equation x2+ – 5x + 4 = 0.
3. Write the product (4 – 7i)(–2 + 3i) as a complex number in standard form.
4. Solve 2x2 + 6x + 3 = 0 by completing the square.
5. Use the quadratic formula to solve the equation 4x2 – 4x – 11 = 0.
 64m 3 

6. Simplify 
6 
27
n


2/3
.
7. Find the product (x – 2)(3x + 2)(x + 2).
8. Factor completely 54y3 – 128.
9. Divide 2x4 + 2x3 – 13x2 – x + 6 by x + 2 using synthetic division.
10. Find all the real zeros of f(x) = 2x4 + 5x3 – 11x2 – 20x + 12.
11. Write the expression
3
81xz4
in simplest form. Assume all variables
8x 2 y
are positive.
12. Find an equation for the inverse of the relation y = 7x – 4.
f ( x)
f ( x)
, and state the domain of
.
g ( x)
g ( x)
14. Given f(x) = 2x – 3 and g(x) = x2 – 2, find g(f(5)).
13. Let f(x) = 3x2 and g(x) = x3/2. Find
15. Solve the equation
1
16. Graph y = –2  
2
17. Expand log 3
4
x2  8 = 2.
x1
2 x3
.
5 y
+ 3. State the domain and range.
18. Evaluate log2 64.
19. Use the change-of-base formula to evaluate log2 17.
20. Solve the equation 42x – 1 = 360.
5
21. Graph y =
+ 2. State the domain and range.
x 1
9 x  27
4 x 2  16
22. Simplify the product
.
•
2 x 2  8 x  8 6 x  18
5 3
2  2
x x .
23. Simplify the complex fraction
2 5
 3
x2 x
3
6

24. Solve 2
x 9 x 3
25. Determine whether the function g(x) = 2x3 – 3x is even, odd, or
neither.
43
26. Find the sum of the series  (8  n) .
n  40
6
27. Find the sum of the series  2k .
k 1
28. Find the 9th term of the geometric sequence 10, –20, 40, –80,. …
29. Use the formula for the sum of an infinite geometric series to write
the repeating decimal 0.729729729… as a fraction in lowest terms.
30. Write a recursive rule for the sequence 3, 5.5, 8, 10.5, 13, … .
31. Convert
7
to degrees.
6
32. Find the values of the other 5 trigonometric functions of x if
5
tan x = –
and cos x < 0.
12
33. Solve ΔABC with B = 49°, C = 90°, and c = 13.3.
34. Find c in ΔABC where A = 64°, C = 55°, and b = 18.
35. Evaluate the function cos (–150°) without using calculator.
36. Write an equation of the graph of y = sin 3πx translated down 2
units and right 3 units, and then reflected in the x-axis.
Answers
21.
End-of-Course Test
; domain: all real numbers
except –1; range: all real
numbers except 2
; (–1, –3)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
1,4
13 + 26i
3  3
2
1 2 3
2
16n4
9m 2
3x2 + 2x2 – 12x – 8
2(3y – 4)(9y2 + 12y + 16)
28
2x3 – 2x2 – 9x + 17 –
x2
1
–3, –2, , 2
2
3z 3 2 x 2 y 2 z
2 xy
x4
7
1/2
3x ; all positive real numbers
47
±2 6
16.
; domain: all real numbers;
range: y ≤ 3
17.
log3 2 + 3 log3 x – log3 5 –
18.
19.
20.
6
4.09
2.62
3( x  2)
( x  2)
2x  3
23.
3x  2
7
24.
2
25. Add
26. –134
27. 126
28. 2560
27
29.
37
30. a1 = 3, an = an – 1 + 2.5
31. 210°
5
12
13
32. sin x =
, cos x =  , csc x =
,
13
5
13
13
12
sec x =  , cot x = 
A = 41°, a =
12
5
8.7, b = 10.0
33. 16.86
3
34. 
2
35. y = –sin (3πx – 3) + 2
22.
1
log3 y
2