y =4 x +3 y =3 x +6 1.Solvethesystemofequations BasicAlgebra , 2)and(7 , 8). x +9 y − 13=0(c)Alinepassingthroughpoints(1 y =2 x − 8(b)3 1.Defineslopeforaline.2.Whatistheslopeforeachofthefollowinglines?(a) BasicGeometry SurveyofPre-CalKnowledge NameandStude

Name and Student ID:

Survey of Pre-Cal Knowledge

Basic Geometry

1. Define slope for a line.

2. What is the slope for each of the following lines?

(a) y = 2x − 8 (b) 3x + 9y − 13 = 0

(c) A line passing through points (1, 2) and (7, 8).

Basic Algebra

1. Solve the system of equations

y = 3x + 6 y = 4x + 3

2. Solve the system of equations

y = 3x − 2 y = x²

3. Solve and sketch the region satisfying x²− 4x + 3 > 0 on the real line.

4. Solve and sketch the region satisfying y ≥ x and y ≤ −2x + 1 on the xy plane.

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Trigonometry

1. ? radian = 360^◦.

2. cos 0 =? sin^π₂ =? tan^π₄ =?

3. If sin x = ¹₄, cos x =?, csc x =? cot x =?

4. if cos x = ¹₃, sin 2x =?, tan 2x =?

5. Sketch the graph of y = f (x) = 2 cos(2x) − 1.

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6. List all x so that (a) sin 3x = 0 (b) tan 4x = 1

Exponential and Logarithmic Functions 1. e ≈?

A. 4.883 B. 3.141 C. 2.718 D. 1.602 × 10⁻¹⁹ 2. Power rules

(a) aⁿbⁿ =?

(b) a^xa^y =?

(c) ^a_a^xy =?

3. Logarithms

(a) log₁₀25 + log₁₀4 =?

(b) ^{ln e}

3 2

ln√ e =?

(c) log₃4 · log₄5 · log₅9 =?

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