Arithmetic calculations
Questions 1 to 20: Select the best answer to each question. Note that a question and its answers may be split across a page
break, so be sure that you have seen the entire question and all the answers before choosing an answer.
1. Solve the triangle shown below. Round lengths to the nearest tenth and angle
measures to the nearest tenth of a degree.
[image]
A. A = 62, B = 36.2, C = 81.8
B. A = 60, B = 38.2, C = 81.8
C. A = 38.2, = 60, C = 81.8
D. A = 60, B = 81.8, C = 38.2
2. Use the substitution method to solve the system of equations below.
4x – 3y = –77
x = –2y
A. (–14, 7)
B. (14, 7)
C. (14, –7)
D. (–14, –7)
3. Find the area of a triangle with these measurements: C = 100°, a = 1 yard, and b = 8 yards. Round your
answer to the nearest square unit.
A. 80 yd2
B. 8 yd2
C. 4 yd2
D. 40 yd2
4. Use the addition method to solve the system below:
4x + 27y = 27
8x – 3y = –3
A. (0, 1)
B. (1, 1)
C. (0, 0)
D. (1, 0)
5. What is the standard form equation of a parabola with directrix x = –2 and focus (2,0)?
A. x
2
= –8x
B. y
2
= –8x
C. y
2
= 8x
D. x
2
= 8x
6. Find the rectangular coordinates of a point whose polar coordinates are (3, –270°).
A. (3, 3)
B. (–3, 0)
C. (3, 0)
D. (0, –3)
7. Use the limit definition to compute ƒ'( x) if ƒ (x) = 6x2
– 9.
A. 6x
B. 12x
C. 6x – 9
D. 12x – 9
8. Write an equation for the ellipse with vertices (–2,0), (–2,–6), (–4,–3), and (0,–3).
A.
B.
C.
D.
9. Solve the system of equations given below.
4x + 4y + z = 16
4x - 5y - z = -37
3x + y + 4z = 15
A. {–2, –4, 5}
B. {–2, 5, 4}
C. No Solution
D. {2, –5, –4}
10. Use properties of limits to compute the following limit exactly.
[equation]
A. ?2/7
B. ?2/14
C. ?7/14
D. ?7/2
11. Find the foci of the hyperbola
A. (10,1) and (0,1)
B. (1,10) and (0,1)
C. (1,10) and (1, 0)
D. (–10, –1) and (0, –1)
12. Using the vectors given below, find u · v.
u = –7i + 12j and v = 8i – 15j
A. –236
B. 12
C. –180
D. –15
13. Use Gauss-Jordan elimination to solve the system below:
x – y + 3z = 0
2x + 2y – z = 9
–x + 5y – 10z = 4
A. {1, 6, 7}
B. {1, 1, 1}
C. {0, 0, 0}
D. {ø}
14. Eliminate the parameter from the parametric equations x = 1
∕2
t + 6 and y = cos t – sin t.
A. y = sin (2x – 12) – cos (2x – 12)
B. y = cos (2x +12) + sin (2x + 12)
C. y = cos (2x – 12) + sin (2x – 12)
D. y = cos (2x – 12) – sin (2x – 12)
15. Graph the solution set of the system of inequalities below.
y < –x + 8
y > 8x – 3
A.
B.
C.
D.
16. Estimate the following limit using a table.
A. –4
B. 4
C. –2
D. 2
17. Find the area of a triangle with the measurements given below. Round your answer to the nearest
square unit.
C = 110°, a = 7 yards, and b = 8 yards
A. 56 yd2
B. 26 yd2
C. 62 yd2
D. 13 yd2
18. Find the foci of the hyperbola
A. (2 ± √5, –3)
B. (3 ± √5, –2)
C. (–2, 3 ± √5)
D. (–2 ± √5, 3)
19. Plot the complex number –1 – 2i.
A.
B.
End of exam
C.
D.
20. If the sequence below is a geometric sequence, find the common ratio.
A. 0.33
B. 0.5
C. 2
D. 4