graphing review - weebly

Graphing Review

1. Using the table of values provided, graph the following line. Be sure to list at least 3 points.

𝑦 =3

4𝑥 + 2

x y

2. Using the table of values provided, graph the following line. Be sure to list at least 3 points.

2𝑥 + 3𝑦 = 6

x y

3. Given 𝑦 = −3𝑥 + 1

a. create a table

b. Find the y-intercept

c. Find the slope

d. Graph (make sure to

label everything!)

3. There exists a line B with slope 3

4. Line C is parallel to line B and has a y-intercept of (0, 5). What is the

equation of the line? (2 marks)

4. The slope between the points ( 3,2 ) and ( -6,y ) is 2

3 . Calculate the value of y.

5. If the point ( 5,3) lies on the line y = mx + 2 find the slope.

6. The slope between the points ( -4, 1 ) and ( x, 4 ) is 3

4. Calculate the value of x.

7. Which one of the graphs matches the equation 𝑥 − 2𝑦 = −4 (2 marks)

8. Which one of the following graph matches the equation 𝑦 = −2

3𝑥 + 2

(2 marks)

a.

b.

c.

d.

9. Given the line A with slope 2

7 determine the equations for the perpendicular line which goes through the

point (14, 3). (2 marks)

Exponents Review

1. Evaluate the following (evaluate means find the answer!)

a. (-2)4

b. –(2)4 c. -2

4

d. (12+12)×82×20÷4 e. 5

-2

f. (1

4)

−3

g. (-2)0 h. -20

i. –(2)0

j. 32+3

-2 k. (22

)2×2

4÷(-2)

4

2. Simplify to positive exponential form

a. (-c)7(-c)

b. 6y-5

(-3y7)2 c. 5(3)

8×6(3)

4

d. (−36𝑚2𝑛2)

2

(12𝑚2𝑛2)3

e. 8(-7)4×4(-7)

11

f. (1

5)

−2

− 52

g. (3𝑠2)2 × (𝑠2

𝑡)

−3

h. 3a+1

× 3-2a+1

i. 1

4× (2−2)−3

3. Use <, =, > to complete the following:

a. 22____2

-2

b.

5−2

23 _____ (2-3

52)-1

Answer Key:

1.

a. 16 b. -16 c. -16

d. 7680 e. 1/25 f. 64

g. 1 h. -1 i. -1

j. 82/9 or 91

9 k. 16 l.

2.

a. C8 b. 54y

9 c. 30(3)

12or 10(3)

13

d. 3

4m

-2n

-2 e. -32(7)

15 f. 0

g. 9𝑡3

𝑠2 h. 3-a+2

i. 24

3.

a. >

b. <

Polynomials Review

1) Simplify

a. 4x + 3z – 8y – 5x +8z – 4y

b. 4x2 +8x – 7xy + 14x2y – 8xy2 + 17yx2 – 7x2 + 14xy

c. 3xy – 2yz + 5xz – 6yz + 4xy – 10 xz

d. yyyy6

1

4

1

3

2

2

1 22

e. 1.8s2t – 7.2st + 0.8st2 – 0.7s2t + 4.2st2 – 4.8st + st2

2) Evaluate the expressions for x = 3 y = 2 and z = -1 (simplify first!)

-3xy + 5yz – 2xz + 6xy + yz – 5xz

3) Write an expression for the perimeter of the figure

4) Simplify

a. (4x + 3) + (2x – 5)

b. (1 – 3t) – (-2 – 5t)

c. (3x + 2) – (x + 4) + (x -7)

d. (17n2 – 17n – 5) + (4n2 -3n +14) – (n2 + 13n + 23)

e. 4a2b – 5(a – b2) + a(a + 5)

f. a(a + b2) – 2(a2 – b2) +ab2

5) Expand

a. -4xy(x2 – y2)

b. 2xy2(y – 2x2y + 3xy) 6) Expand and simplify

a. (x + 3)(x – 4)

b. (5x + 3y)(4x – y)

c.

xx

4

133

2

1

d. (3x – 2)2

e.

2

3

1

x

f. (x + 4)(x2 -3x + 5)

g. 5(a + 1)(a – 1)

h. (x + 1)(x – 1)(x2 + 1)

i. (x – 5)3

q

r

q

p

y

x

7) Expand and simplify

a. 4x(x2 – 3x) – 4(3x2 – 2x)

b.

3

6

1

4

1

3

2

4

18

3

2xxxx

8) Find the area of the figure

9) Divide each polynomial

a. 33

25

9

54

ba

ba

b. 32

445362

16

483216

nm

nmnmnm

10) Expand and simplify

a. 3x(x2 – 3x + 3) –[4x(x2 – 3x + 4) –(x + 2)]

b. (x+4)(x – 2) – (x – 3)(x + 3)

c. (3xy +2x2y)(3x2 – 4xy + 3y2) - 4x[3x(x + 2y)- 2x(x – 3y)]

11) Calculate

a.

341

16

15

15

8

3

5

12) Simplify

b.

75

3322

4

422

yx

yxyx

Answers: 1) a. - x + 11z – 12y b. 31x2y – 8xy2 - 3x2 + 7xy + 8x c. 7xy – 8yz – 5xz d. –y2/4 + y/2 1.1s2t

– 12st + 6st2 2) 27 3) 2p + 4q + 2r 4) a. 6x – 2 b. 3 + 2t c. 3x – 9 d. 20n2 – 33n – 14 e.

4a2b + 5b2 + a2 f. –a2 2ab2 + 2b2 5) a. -4x3y + 4xy3 b. 2xy3 – 4x3y3 + 6x2y3 6) a. x2 – x – 12

b. 20x2 + 7xy – 3y2 c. –x2/8 +3x/4 + 9 d. 9x2 – 12x + 4 e. x2 – 2x/3 + 1/9 f. x3 + x2 – 7x + 20

g. 5a2 – 5 h. x4 – 1 i) x3 – 15x2 – 75x - 125 7) a. 4x3 – 24x2 + 8x b. 73x2/24 - 43x/36 8) 2xy – y2

9) a. -6a2/b b. –n3 + 2mn2 – 3m2n 10) a. -x3 +3x2 – 6x + 2 b. 2x + 1 c. 3x3y – 12x2y2 + 9xy3 –

4x3 – 24x2y 11) 163/84 or 1 12) 128x8/y2

Factoring and rational expressions Review

1) Find the GCF of: 10s4t5, 5s5t4, 15s3t4

Factor:

2) 12ab + 28ac + 36ad

3) x2 - x - 72

4) x3 +9x2 + 8x

5) 4x2 – 4y2

6) m4 - 16

7) 2a2 + 10a - 28

8) 10x + 24y

9) y2 – 15y + 56

10) 2x2 - x - 3

11) –15 + 8x – x2

12) 9 + 25x – 6x2 13)

16

1

9

4 2 x

14) 5xy2 –7x2y

15) 4x2 – 2x - 12

16) x4 – x2

17) 25m2 – (n + 2p)2

Expand and simplify

18) (3x – 4)(2x – 5)

19) Subtract the product of (4x2 – 2)(-3x2 + 2x + 5) from (x4 + 8x3 – x2 – 4x – 5)

20) (-5x – 3y)2

Multiply or divide the following rational expressions

21) 3

3

6

92

x

x

22) 49

882

10

3552

2

m

mmm

23) 4

483

16

16 2

2

2

x

x

x

x

Add or subtract:

24) 2

5

3

3

aa 25)

2

3

4

72

xx

x 26)

107

1

3011

2

128

3222

xx

x

xx

x

xx

x

27) What polynomial must be subtracted from (7x3 + 2x2 – 8x + 7) to give (3x2 – 4x – 9)

Bonus

28) Solve for x: 7

6

232

62

2

xx

xx

Bonus

29) 36

37

17

1

52

5

xx

30) Do the following division. State the result in the form: dividend = divisor x quotient + remainder

(4x3 – 4x + 3) (2x – 1)

Answers

1) 5s3t4 2) 4a(3b + 7c +9d) 3) (x + 8)(x – 9) 4) x(x + 1)(x + 8) 5) 4(x – y)(x + y)

6) (m – 2)(m + 2)(m2 + 4) 7) 2(a – 2)(a + 7) 8) 2(5x + 12y) 9) (y – 7)(y – 8)

10) (x + 1)(2x – 3) 11) -1(x – 3)(x – 5) 12) -1(3x + 1)(2x – 9) 13) (2/3x – ¼)(2/3x + ¼)

14) xy(5y – 7x) 15) 2(2x + 3)(x – 2) 16) x2(x + 1)(x – 1) 17) (5m – n – 2p)(5m + n +2p)

18) 6x2 – 23x + 20 19) 13x

4 – 27x

2 + 5 20) 25x

2 + 30xy + 9y

2 21)

2

3x 22)

7

22

m

m

23) 43

1

x 24)

2

5

a

a 25)

22

610

xx

x 26)

526

25193 2

xxx

xx 27) 7x3 – x2 – 4x + 16

28) x = 3 29) 5, -1/14 30) (2x –1)(2x2 + x – 3/2) + 3/2

Rational Expressions Review:

1. Simplify the following:

a. −36𝑦4

28𝑦3 b. 16𝑥2

28𝑥 c.

39𝑛

13𝑛4

d. 2𝑥−2

𝑥−1 e.

45

10𝑥−10 f.

𝑥−2

3𝑥2−12

g. 𝑥−5

𝑥2−10𝑥+25 h.

𝑥2−7𝑥−30

𝑥2−4𝑥−60 i.

𝑥2−11𝑥+18

𝑥2+2𝑥−8

j. 9𝑥+81

𝑥3+8𝑥2−9𝑥

2 Simplify the following:

a. 2𝑛

3×

3

2𝑛2 b. 39𝑥2

11×

22

13𝑥 c.

6(𝑥+1)

2×

4

𝑥+1

d. (2𝑥+3)

6×

2

6𝑥2+9𝑥 e.

7𝑥2(𝑥+4)

(𝑥−3)(𝑥+4)×

𝑥−3

(𝑥+8)(𝑥+6) f.

1

𝑥+10×

10𝑥+30

𝑥+3

g. 𝑥+7

7𝑥+35×

𝑥2−3𝑥−40

𝑥−8 h.

8𝑥−56

8𝑥+48×

𝑥2+9𝑥+18

8𝑥2+24𝑥


a. 10𝑛

9÷

12𝑛2

15 b.

7𝑥2

7𝑥3+56𝑥2 ÷2

𝑥2+7𝑥−8 c.

𝑥2+10𝑥+16

𝑥2+6𝑥+8÷

1

𝑥+4

d. 10𝑥2+42𝑥+36

6𝑥2−2𝑥−60÷

40𝑥+48

3𝑥2−13𝑥+10 e.

8

4𝑥2−16÷

1

𝑥−2


a. 𝑢−𝑣

8𝑣+

6𝑢−3𝑣

8𝑣 b.

5

3𝑟−6+

5𝑎+1

3𝑟−6 c.

6

𝑥+1−

5

4

d. 𝑥+1

7−

2𝑥−3

7 e.

3

𝑥+7+

4

𝑥+7 f.

2𝑥

𝑥−1−

3𝑥−4

2𝑥+3

g. 7𝑛

𝑛+1+

8

𝑛−3 h.

3

8+

7

𝑥−3 i.

5𝑛+5

5𝑛2+35𝑛−40+

7

𝑛+8

j. 4𝑎−5

6𝑎2+30𝑎+

𝑎−1

6𝑎 k.

𝑥+2

3𝑥2+7𝑥−20−

𝑥+1

9𝑥2−25 l.

𝑥−4

𝑥2−𝑥−20+

𝑥+1

2𝑥2+9𝑥+4

KEY:

1a. -9y/7 b. 4x/7 c. 3/n3 d. 2 e. 9

2(𝑥−1) f.

1

3(𝑥+2) g.

1

𝑥−5

h. 𝑥+3

𝑥+6 i.

𝑥−9

𝑥+4

2a. 1/h b. 6x c. 12 d. 1/9x e. 7𝑥2

(𝑥+8)(𝑥+6) f.

10

𝑥+10 g.

𝑥+7

7

h. 𝑥−8

8𝑥

3a. 50/3n

b. 𝑥−1

2 c. x+8 d.

𝑥−1

8 e.

2

𝑥+2

4a. 7𝑢−4𝑣

8𝑣 b.

5𝑎+6

3𝑟−6 c.

19−5𝑥

4(𝑥+1) d.

–𝑥+4

7 e.

7

𝑥+7 f.

𝑥2−𝑥−4

(𝑥−1)(2𝑥+3) g.

7𝑛2−13𝑛+8

(𝑛+1)(𝑛−3)

or (7𝑛−8)(𝑥−1)

(𝑛+1)(𝑛−3)

h. 3𝑥+47

8(𝑥−3) i.

2(4𝑛−3)

(𝑛+8)(𝑛−1) j.

𝑎2+8𝑎−10

6𝑎(𝑎+5) k.

2(𝑥2+3𝑥+3)

(𝑥+4)(3𝑥−5)(3𝑥+5) l.

3𝑥2−11𝑥−9

(𝑥−5)(𝑥+4)(2𝑥+1)

Radicals Review:

1. Approximate the following:

a. √54

b. √106

2. Convert the following to mixed radicals in simplest form:

a. √125𝑛 b. 2√45𝑝5

c. √−625𝑝3𝑞43 d. √405𝑥5𝑦𝑧74


a. √2 × 6√6 b. 5√28 × 2√21

c. √3 × √21 d. √283

× √63

e. √2 × √3


a. 3√2 + √2 b. √27 + 2√12

c. 3√5 + 4√5 − √5 d. 5𝑏√18𝑎2𝑏 + 𝑎√8𝑏3

e. 7𝑥√8𝑥𝑦2 − 4𝑦√32𝑥3 + 9√8𝑥2𝑦3 f. 3√27𝑐2 − 2√108𝑐2 − √48𝑐2


a. 3√3(4 − 3√5 ) b. 4√15(−3√6 + 5)

c. √15(2√10 − 4√6) d. √𝑥(3√𝑥 + 5)

e. (2 + √3)(3 - 2√5) f. (-7+√3𝑥)(4 + √3𝑥)

g. (2 - √5)(2 + √5) h. (√3 + √5𝑥)(√3 + √5𝑥)


a. √8

√7 b.

√7

8√7 c.

√21

√15

d. √14

3√35 e.

2√5

8√3

7. Determine the unknown side length:

a. b.

8. Convert the following to entire radicals

a. 3√2 b. 5𝑟√2𝑟 c. −12𝑥3√3𝑥

KEY

1a 7.3 b. 10.3

2a. 5√5𝑛 b. 6𝑝2√5𝑝 c. −5𝑝𝑞 √5𝑞3

d. 3xyz√5𝑥𝑦𝑧34

3.a 12√3 b. 140√3 c. 3√7 d. 2√21 e. √6

4a. 4√2 b. 7√3 c. 6√5 d. 47ab√2𝑏 e. -2xy√2𝑥 + 18𝑥𝑦√2𝑦

f. -7c√3

5a. 12√3-9√15 b. -36√10 + 20√5 c. 10√6 − 12√10 d. 3x+5√3 e. 6+4√5 + 3√3 − 2√15

f. −21 − 3√3𝑥 + 3 g. -1

6a. 2√14

7 b.

1

8 f.

√35

5 g.

√10

15 h.

√15

12

7a. 𝑎 = 10 b. 𝑥 = 4

8a. √18 b. √50𝑟3 c. −√432𝑥7

Solving Linear Equations Unit Review:

Part 1 – Type 1 to 4 Equations:

1. 4b − 6 = 14 2. −12m − 10 = 2 3. 3b + 5 = −13 4. 4w − 7 + 3w = 35

5. 12g − 72 = 4g + 8 6. −12 = 3 − 2m − m 7. 6 = −3(d + 2) 8. 75 = 3(−6n − 5)

9. −3(1 + 6r) = 14 − r 10. −4(3m + 2) − 5 = 2m − 3(m − 3)

Part 2 – Removing Fractions and Decimals:

1. 0.25(8y + 4) − 17 = −0.5(4y − 8) 2. h

3+

2

9=

5

6

3. m+3

2= −5 4.

2(n−2)

3=

1

6 5.

4c

5−

4+5c

3= 3 6.

1

8(m + 5) =

7

4

7. 1

2(t − 1) −

2

3(t + 1) = 1 8.

2

d−7=

3

d−2

9. 6

p=

1

p−5−

p+4

p2−5p 10.

1

b2−7b+10+

1

b−2=

2

b2−7b+10

Part 3 – Literal Equations and Transforming Formula:

1. Make x the subject (solve for x) for the following:

a. 𝑎 + 𝑏 = 𝑐𝑥 + 𝑑 b. 𝑐 =5

9(𝑥 − 32)

c. 𝑥

2𝑎+

𝑥

3𝑏= 𝑐 d. 𝑎(𝑥 − 𝑏) + 𝑐(𝑥 + 𝑑) = 𝑒

2. Make v the subject (solve for v):

a. 𝑑 = 𝑔𝑡2 + 𝑣𝑡

Part 4 – Quadratic Equations:

Solve for m:

1. 𝑚2 − 6𝑚 + 8 = 0 2. 𝑣2 + 4𝑣 − 21 = 0 3. 4𝑚2 − 12𝑚 = 0

4. 9𝑝2 − 16 = 0 5. (𝑥 − 8)(𝑥 + 1) = 10 6. (𝑥 − 2)(5𝑥 − 4) + 1 = 0

7. (2𝑥 + 3)(3𝑥 − 2) + 2𝑥 + 3 = 0

8. (5𝑡 − 1)(3𝑡 − 2) = 22 9. 𝑏2 + 5𝑏 − 35 = 3𝑏

11. 5𝑟2 − 44𝑟 + 120 = −30 + 11𝑟

Part 5 – Word Problems:

1. A certain number added to its square is 30. Find the number.

2. The product of two consecutive odd integers is 99. Find the integers.

3. The length of a rectangle exceeds its width by 4 inches. Find the dimensions of the rectangle it its

area is 96 square inches.

4. The ages of three family children can be expressed as consecutive integers. The square of the age of

the youngest child is 4 more than eight times the age of the oldest child. Find the ages of the three

children.

5. The height of a triangle is 5 less than its base. The area of the triangle is 42 square inches. Find its

base and height.

Answer Key:

Part 1:

1) B=5 2) m=-1 3) b=- 6 4) w=6 5) g=10 6) m=5

7) d= -4 8) n= -5 9) r= -1 10) M= -2

Part 2:

1) Y= 5 2) h = 11/6 3) m= -13 4) n = 9/4 5) c = -5 6) m = 9

7) t= -8 8) d=17 9) p = 4 1/3 10) B =6

Part 3:

1.

a. 𝑥 =𝑎+𝑏−𝑑

𝑐

b. 𝑥 =9

5𝑐 + 32

c. 𝑥 =6𝑎𝑏𝑐

3𝑏+2𝑎

d. 𝑥 =𝑒+𝑎𝑏−𝑐𝑑

𝑎+𝑐

2. a. 𝑣 =𝑑

𝑡− 𝑔𝑡

Part 4:

1) m= 2, 4 2) v= 3, -7 3) m = 0, 3 4) p = 4/3, -4/3 5) x= -2, 9

6) x = 9/5, 1 7) 𝑥 =1

3, −

3

2 8)𝑡 =

5

3, −

4

5 9) 𝑏 = 5, −7 10) 𝑟 = 5, 6

Part 5:

1) n = 5, -6 2) The #’s are 9 and 11 3) w=8 L=12 4) The ages are 10, 11 and 12

5) base= 12, height = 7

graphing review - weebly

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