且 叫 AGN … TE

且 叫 AGN … TE

1. Evaluate each expression without using a calculator (a)

(-3)'

(b) -3⁴ (c) 3-⁴

(2 \-2 晶，ι (e) 1 了) (f) 16-;月 n-划，、J-a、J

d

2. Simplify each expression. Write your answer without negative exponents (約占百 -13吉

(b) (3α3b³)(4ab²)2

例(中~r2

3. Expand and simpl方 (a) 3(x

+

6)

+

4(2x - 5)

(c) 以 + Jb)(J(i - Jb)

(e) (x

+ 2?

4. Factor each expression‘

(a) 4x² - 25

(c) x3 - 3x2 - 4x

+

12 (e) 3x3/2 - 9x 1/2

+

6x- 1/2

5. Simplify th陪 rational ex戶'ession.

X2+3x+2

(a) 勻《

x-- x 一」

x² X

+

1

(c) 一?一一一一一一

x" - 4 x

+

2

(b) (x

+

3)(4x - 5) (d) (2x

+

3)2

(b) 2X2

+

5x 一 12 (d) x⁴

+

27x (f) x3y - 4xy

2x² - X 一 1 x

+

3 (b) 勻 ﹒一一一-

Xι -9 2x+1 y x

x v

(d) 一一一」一

1 1 y x 6. Rationalize the expression and simplify^‘

(的 一哼--、 10

、 5 - 2

7. Rewrite by completir啥也esquare (a) x²

+

x

+

1

(a)

x 十 5 =

14 -

~x

8. Solve the equation. (Find only the real solutions.)

(b) 2x2 - 12x

+

11

2x 2x-1

(b) 一一一=一一一一

x

+

1 x

(d) 2X2

+

4x

+

1 ⁼ 0 (f) 31x-41 = 10

(c) 正 -x-12=0 (e) x⁴ - 3x2

+

2 = 0

(g) 2x(4 - x)一1/2- 3 )4士了=0

9. Solve each ínequality‘Write your answer using ínterval notation‘

(的 -4

<

5 - 3x逗17 (b) x2

<

2x

+

8

(c) x(x一 l)(x

+

2)

>

0 (d) 1 x - 41

<

3

2x - 3

(e) 一一一一-石l

x

+

1

10. State whether each equation ís 仕ueor false‘

(a) (p

+

q

)2

= p2

+

q2

J -

H

EC G=

AW肘

(c) 占訂苦了 =a+b

4主j DIAGN 。刊 C

TEST: ANALYTIC

GEOMET 盯

1. Find an equation for the line也atpasses through the point (2, - 5) and (a) has slop巳 -3

(b) ís parallel to也ex-axis (c) ís parallel to the y-axis

(d) ís parallel to the line 2x - 4y = 3

2. Find 叩 equati叩 for 血eαrcle 也athas center (一 1 ，4) and passes 伽ough 血epαnt(3, -2).

3. Find the center and radius of the circle with equation x² +

f -

6x + 10y + 9 = 0^‘

4. Let A(-7,4) andB(5, -12) be points in the plane.

(a) Find the slope of the ^{line 也at}contains A and B.

(b) Find an equ ati on of the line 也atpasses through A and B. What are 吐.Jeintercepts?

(c) Find the midpoint of 也esegrnent AB^‘ (d) Find the leng也 ofthe segrnent AB.

(e) Find an equation of the perpendicular bisector of AB.

(f) Find an equation of the circle for which AB is a di羽田ter.

5. Sketch the region in 也exy-plane defined by the equation or inequal泌的‘

(a) 一 l 石y"，;:3

(c)

Y

< 1 - ~x

(e) X2

+

y2

<

4

(b) ¹ x ¹

<

4 and ¹ y ¹

<

2 (d) y ;;主 x²一1

(f) 9x²

+

16y2 = 144

4三J- DIAGNOSTIC

TEST: FUNCTIONS y

1 / 1 \

\

^。I

ⁱ

^λ

1'\

/

FIGURE FOR PROBlEM 1

1. The graph of a function

f

is gi恥enat the left (a) State the value of f(一 1)。

(b) Estima能出ev叫 ueof f(2)‘

(c) For what values of x 旭 f(x)= 2?

(d) Estimate the values of x such 伽tf(x) ⁼ O.

(e) State the domain andrange of

f.

f(2

+

h) - f(2)

2. If f(x) = 針， evaluate 也e differen臼 quotient" ，叩dsimplify y∞r answ釘﹒

3. Find the domain of the function.

2x

+

¹ Hx

(的 f(x)=一一一一一 (b) g(x) =τ片寸

正 +x-2 口 λ (c) h(x) =

.J4='X 十 ~τ

4. How are graphs of the functions obtained from the graph of f?

(a) y = - f(x) (b) y = 2f(x) 一 1 (c) y = f(x - 3)

+

2 5. Without using a calcu1ator, make a rough sketch of the graph.

(a) y = x³ (b) y = (x

+

1)3 (c) Y = (x - 2)3

+

3 (副 y= 4 - x²

(e) 尸 /x (f)尸 2 /X

(g) y = -2' (h)

Y

= 1

+

^{[ 1}

11 -

x² if x逞。 6. Letf(x) =

i

12x+1 ifx> O

(a) Evaluate f( -2) 阻df(l)自 (b) Sketch th巴 graphof

f.

7. If f(x) = x² + 2x - 1 and g(x) = 2x - 3，且ndeach of the following functions^‘

(的 fog (b)gof (c) gogog

孔丘J DIAGNOSTIC

TEST: TRIGONOMETRY

d

b

FIGURE FOR PROBlEM 5

1. Convert from degrees to radians (a) 300⁰ (b) -18。

2. Convert from radians to degrees.

(a) 5Tr/6 (b) 2

3. Find the 1ength of an arc of a cir^c1e with radius 12 cm if the 旺csubtends a central ang1e of 30。‘

4. Find 血eexact values.

(a) tan(Tr/3) (b) sin(h /6) (c) sec(h/3) 5. Express the lengths a and b in the figure in terms of 8.

6. If sinx = } and sec y =

L

where x 叩dY lie between 0 and Tr/2, evalua能 sin(x + y).

7. Prove the identities^‘

(a) tan 8 sin 8 + cos 8 = sec 8 2 tanx

(b) 一一一-:;-= sin 2x

1 十 tan"x

8. Find all values of x such that sin 2x = sin x and 0 ^",;: X ",;: 2Tr.

9. Sketch the graph of the function ^{y 言 1} + sin 2x without using a calculator