## SAT SUBJECT TEST MATH LEVEL 2

**PART 2**

**REVIEW OF MAJOR TOPICS**

**CHAPTER 2 **

Geometry and Measurement

Geometry and Measurement

**2.1 Coordinate Geometry**

**Answers and Explanations**

Transformations and Symmetry

1. **(B)** Horizontal translation (right) is accomplished by subtracting the amount of the translation (5) from *x* before the function is applied.

2. **(D)** Vertical stretching is accomplished by multiplying the function by the stretching factor after the function is applied.

3. **(D)** The graph of *y* = *f* (–*x*) – 2 reflects *y* = *f* (*x*) about the *y*-axis and translates it down 2.

4. **(D)** The horizontal shrinking by a factor of 2 is the multiplication of *x* by 2 before the function is applied. The reflection about the *x* -axis is the negation of the function after it is applied. The translation down 3 is the addition of –3 after the function is applied.

Conic Sections

1. **(D)** This is the standard equation of an ellipse with center (2, –1), *a*^{2} = 5, *b*^{2} = 4, and *y* -orientation. Since *c*^{2} = *a*^{2} – *b*^{2} = 1, the foci are 1 unit above and below the center.

2. **(C)** Complete the square in both *x* and *y* to put the equation in standard form:

This hyperbola has *x*-orientation, with *a*^{2} = 4 and *b*^{2} = 3. Its asymptotes are .

3. **(B)** The directrix is a vertical line 4 units to the right of the focus. Therefore, the parabola has an *x*-orientation (the *y*-term is square). The vertex of (4, –3) is 2 units right of the focus, so *p* = –2.

4. **(A)** Since the vertices have the same *y*-coordinate, the major axis is horizontal, has length 8, and *a*^{2} = 16. Therefore, the center of the ellipse is (–1, 2). Since the minor axis has length 6, *b*^{2} = 9.

5. **(D)** Complete the square in both *x* and *y* to get the standard equation:

The transverse axis has length 4, so the vertices of the hyperbola are 2 units left and right of the center (1, –3).

6. **(C)** Expand the right side of the equation and bring all but the constant term to the left side. Complete the square in both *x* and *y* to get , the standard equation of a hyperbola.

Polar Coordinates

1. **(A)** The angle must either be coterminal with (60 ± 360*n*) with *r* = 2 or (60 ± 180)° with *r* = –2. A is the only answer choice that meets these criteria.

2. * **(A)** With your calculator in degree mode, evaluate *x* = *r* cos = 2 cos 200 –1.88 and *y* = *r* sin 200 = 2 sin 200 –0.68.

3. * **(D)** With your graphing calculator in POLAR mode, enter as *r*_{1}, and observe that the graph is a vertical line with holes where cos = 0.