Pre calculus review

MAC 1147 TEST 4 REVIEW

LESSONS 8, 9, 10, 11

1. Find focus, directrix, and graph

A. x2 = -9py

B. x2 = 2p7

C. y2 = 6px

D. y2 = -4px

2. Wriye the equation of the parabola given vertex at (0,0) and directrix at x=4.

3. Find focus, vertex, and graph each ellipse.

A. 𝑥2

16 +

𝑦2

49 = 1 B.

𝑥2

81 +

𝑦2

16 = 1

4. Write the equation of an ellipse with focus at (5,0) and vertices at (8,0), centered at

(0,0).

5. Find focus, vertices, asymptotes, and graph each hyperbola

A. 𝑥2

16 −

𝑦2

9 = 1 B.

𝑦2

36 −

𝑥2

9 = 1

6. Find the equation of a hyperbola with intercept at (8,0) and focus at (11,0)

7. Evaluate the determinant | 2 3 4 |

| 0 5 1 |

| 6 0 7 |

8. Find the area of a triangle with coordinates A(2,5) B( 7,2) and C( 4, 8)

9. Solve by Cramer rule

A. 4x – 7y = 11 D= Dx= Dy =

5x + 7y = 3 x = y =

B. 4x – 3y +2z = 25 D= Dx= Dy = Dz=

x + y – z = 4 x = y = z =

3x + 2y – 5z = 4

10. Solve each non-linear system

A. y = √𝑥 − 1 and y= x – 3

B. y= x2 -7x +5 and y = 2x – 3

C. y= 3x2 +x – 5 and y = 2x2 –x – 2

D. x2 – y2 = 4 and 3x2 + y2 = 16

11. Find the fraction decomposition

A. 𝑤𝑥+2

𝑥2−3𝑥−4

B. 2𝑥+5

𝑥3+3𝑥2

C. 𝑥+1

𝑥(𝑥+1)2