worksheet 8.1 algebra name:worksheet 8.1 algebra name: _____ 1 substitution full setting out please....

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WorkSHEET 8.1 Algebra Name: ___________________________ 1 Substitution

Full setting out please.

2 If 𝑎 = 2, and 𝑏 = 3 determine the value of the expression 2𝑎 + 4𝑏.

2𝑎 + 4𝑏

= 2 × 2 + 4 × 3

= 4 + 12

= 16

3 If 𝑑 = 3, and 𝑔 = 5 determine the value of the expression 4𝑑 − 2𝑔

4𝑑 − 2𝑔

= 4 × 3 − 2 × 5

= 12 − 10

= 2

4 If 𝑔 = 2, and ℎ = 3 determine the value of the expression 5ℎ − 2𝑔

5ℎ − 2𝑔

= 5 × 3 − 2 × 2

= 15 − 4

= 11

5 If , then:

𝑑 + 3𝑒 =

𝑑 + 3𝑒

= 3 + 3 × 2

= 3 + 6

= 9

6 If , then:

4𝑑 − 2𝑒 =

4𝑑 − 2𝑒

= 4 × 3 − 2 × 2

= 12 − 4

= 8

3 and 2d e= =

3 and 2d e= =

WorkSHEET 8.1 Algebra


7 If 𝑥 = 2, determine the value of the expression 4𝑥 + 3.

4𝑥 + 3

= 4 × 2 + 3

= 11

8 If 𝑥 = 3, determine the value of the expression 2𝑥 + 7.

2𝑥 + 7

= 2 × 3 + 7

= 13

9 If 𝑥 = 4, determine the value of the expression 3𝑥 − 10.

3𝑥 − 10

= 3 × 4 − 10

= 2

10 If 𝑥 = 5, determine the value of the expression 4𝑥 − 6.

4𝑥 − 6

= 4 × 5 − 6

= 14

11 If 𝑥 = 2, determine the value of the expression 𝑥! + 3𝑥 + 4.

𝑥! + 3𝑥 + 4

= 2! + 3 × 2 + 4

= 4 + 6 + 4

= 14

12 If 𝑥 = 3, determine the value of the expression 𝑥! + 5𝑥 − 6.

𝑥! + 5𝑥 − 6

= 3! + 5 × 3 − 6

= 9 + 15 − 6

= 18

13 If 𝑥 = 4, determine the value of the expression 𝑥! − 2𝑥 − 5.

𝑥! − 2𝑥 − 5

= 4! − 2 × 4 − 5

= 16 − 8 − 5

= 3

14 If 𝑥 = 2, determine the value of the expression 𝑥! − 5𝑥 − 7.

𝑥! − 5𝑥 − 7

= 2! − 5 × 2 − 7

= 4 − 10 − 7

= −13



15 Substitution – Problem Solving

Full setting out please.

16 The velocity of a car ( 𝑣 stands for Velocity which is speed) is given by the formula;

𝑣 = 𝑢 + 𝑎𝑡 Find the velocity of the vehicle where;

𝑢 = 50 𝑎 = 8

and 𝑡 = 6

Yes, this is a real equation you will use in Science. It doesn’t matter that you do not know what all the letters mean, but you can Substitute to get an answer … :

𝑣 = 𝑢 + 𝑎𝑡 By substitution,

𝑣 = 50 + 8 × 6

= 50 + 48

= 98 The car is travelling 98 km/h

17 The interest a Bank account receives (𝐼 stands for Interest) is given by the formula;

𝐼 = 𝑃𝑅𝑇 Find the Interest received when;

𝑃 = 5000

𝑅 =4100

and 𝑇 = 2

Yes, this is a real equation you will use in Financial Maths. It doesn’t matter that you do not know what all the letters mean, but you can Substitute to get an answer … :

𝐼 = 𝑃𝑅𝑇 By substitution,

𝐼 = 5000 ×4100 × 2

Use your calculator

= 640 The interest earned is $640



18 The sum of the angles in a polygon is given by , where is the number of sides. Find the sum of the angles of a triangle (a 3-sided polygon).

Given; 𝑆 = 180(𝑛 − 2)

Set 𝑛 = 3 𝑆 = 180(3 − 2)

= 180 × 1

= 180

Therefore, the sum of all angles in a triangle is 180 degrees. Yes, we already knew that, but this formula is how we know it! If your solution didn’t look like this, then do it again. You need to show your substitution into the equation and then get an answer. Setting out is IMPORTANT!

19 The sum of the angles in a polygon is given by , where is the number of sides. Find the sum of the angles of a quadrilateral (a 4-sided polygon).

Given; 𝑆 = 180(𝑛 − 2)

Set 𝑛 = 4 𝑆 = 180(4 − 2)

= 180 × 2

= 360

Therefore, the sum of all angles in a quadrilateral is 360 degrees.

20 The sum of the angles in a polygon is given by , where is the number of sides. Find the sum of the angles of a pentagon (a 5-sided polygon).

Given; 𝑆 = 180(𝑛 − 2)

Set 𝑛 = 5 𝑆 = 180(5 − 2)

= 180 × 3

= 540

Therefore, the sum of all angles in a pentagon is 540 degrees.

21 The sum of the angles in a polygon is given by , where is the number of sides. Find the sum of the angles of a hexagon (a 6-sided polygon).

Given; 𝑆 = 180(𝑛 − 2)

Set 𝑛 = 6 𝑆 = 180(6 − 2)

= 180 × 4

= 720

Therefore, the sum of all angles in a hexagon is 720 degrees.

)(S)2(180 -= nS n

)(S)2(180 -= nS n

)(S)2(180 -= nS n

)(S)2(180 -= nS n



22 Combining Like Terms

23 By combining like terms, simplify;

3𝑥 + 5𝑥

3𝑥 + 5𝑥

= 8𝑥

24 Simplify;

5𝑥 − 3𝑥

5𝑥 − 3𝑥

= 2𝑥

25 Simplify;

4𝑥 − 7𝑥

4𝑥 − 7𝑥

= −3𝑥

26 Simplify;

3𝑥 + 7 + 5𝑥

3𝑥 + 7 + 5𝑥

= 8𝑥 + 7

27 Simplify;

5𝑥 + 7 − 3𝑥

5𝑥 + 7 − 3𝑥

= 2𝑥 + 7

28 Simplify;

7𝑥 − 9 − 4𝑥

7𝑥 − 9 − 4𝑥

= 3𝑥 − 9

29 Simplify;

3𝑥 − 9 − 8𝑥

3𝑥 − 9 − 8𝑥

= −5𝑥 − 9

30 Simplify; 7𝑥 + 4 + 3𝑥 + 12

7𝑥 + 4 + 3𝑥 + 12

= 10𝑥 + 16

31 Simplify; 2𝑥 + 3 + 4𝑥 + 5

2𝑥 + 3 + 4𝑥 + 5

= 6𝑥 + 8

32 Simplify; 7𝑥 + 8 + 9𝑥 + 10

7𝑥 + 8 + 9𝑥 + 10

= 16𝑥 + 18

33 Simplify; 3𝑥 + 4 − 5𝑥 − 2

3𝑥 + 4 − 5𝑥 − 2

= −2𝑥 + 2



34 Simplify; 4𝑥 + 6 − 9𝑥 − 1

4𝑥 + 6 − 9𝑥 − 1

= −5𝑥 + 5

35 Simplify; 5𝑥 + 4 − 3𝑥 − 2

5𝑥 + 4 − 3𝑥 − 2

= 2𝑥 + 2

36 Simplify; 15𝑥 + 14 − 7𝑥 − 11

15𝑥 + 14 − 7𝑥 − 11

= 8𝑥 + 3

37 Simplify; 8𝑥 + 4 − 6𝑥 − 3

8𝑥 + 4 − 6𝑥 − 3

= 2𝑥 + 1

38 Simplify; 2𝑥 + 7 − 9𝑥 − 5

2𝑥 + 7 − 9𝑥 − 5

= −7𝑥 + 2

39 Simplify; 𝑥 + 1 − 2𝑥 − 2

𝑥 + 1 − 2𝑥 − 2

= −𝑥 − 1

40 Simplify; 25𝑥 + 30 − 10𝑥 − 20

25𝑥 + 30 − 10𝑥 − 20

= 15𝑥 + 10

41 Simplify; 3𝑥 − 2 − 5𝑥 − 2 − 2𝑥 + 5

3𝑥 − 2 − 5𝑥 − 2 − 2𝑥 + 5

= −4𝑥 + 1

42 Simplify; 4𝑥 − 3 − 6𝑥 − 2 − 𝑥 + 7

4𝑥 − 3 − 6𝑥 − 2 − 𝑥 + 7

= −3𝑥 + 2

43 Simplify; 9𝑥 − 2 − 5𝑥 − 7 − 2𝑥 + 5

9𝑥 − 2 − 5𝑥 − 7 − 2𝑥 + 5

= 2𝑥 − 4

44 Simplify; 10𝑥 + 3 − 5𝑥 − 2 − 2𝑥 + 5

10𝑥 + 3 − 5𝑥 − 2 − 2𝑥 + 5

= 3𝑥 + 6

45 Simplify; 3𝑥 − 2 − 5𝑥 − 2 − 2𝑥 + 5

3𝑥 − 2 − 5𝑥 − 2 − 2𝑥 + 5

= −4𝑥 + 1



46 Expanding Brackets

47 Expand; 5(𝑥 + 2)

5(𝑥 + 2)

= 5𝑥 + 10

48 Expand; 3(𝑥 + 3)

3(𝑥 + 3)

= 3𝑥 + 9

49 Expand; 3(𝑥 + 2)

3(𝑥 + 2)

= 3𝑥 + 6

50 Expand; 3(𝑥 + 4)

3(𝑥 + 4)

= 3𝑥 + 12

51 Expand; 7(3𝑥 − 2)

7(3𝑥 − 2)

= 21𝑥 − 14

52 Expand; 5(2𝑥 + 2)

5(2𝑥 + 2)

= 10𝑥 + 10

53 Expand; 3(4𝑥 + 7)

3(4𝑥 + 7)

= 12𝑥 + 21

54 Expand; 2(3𝑥 − 5)

2(3𝑥 − 5)

= 6𝑥 − 10

55 Expand; 8(2𝑥 − 1)

8(2𝑥 − 1)

= 16𝑥 − 8

56 Expand; 7(3𝑥 − 2)

7(3𝑥 − 2)

= 21𝑥 − 14

57 Expand; 25(2𝑥 − 3)

25(2𝑥 − 3)

= 50𝑥 − 75



58 Expanding Brackets and Combining Like terms

59 Simplify; 3𝑥 + 5(𝑥 + 2)

3𝑥 + 5(𝑥 + 2)

= 3𝑥 + 5𝑥 + 10

= 8𝑥 + 10

60 Simplify; 5𝑥 + 3(𝑥 + 3)

5𝑥 + 3(𝑥 + 3)

= 5𝑥 + 3𝑥 + 9

= 8𝑥 + 9

61 Simplify; 3(𝑥 + 2) + 5

3(𝑥 + 2) + 5

= 3𝑥 + 6 + 5

= 3𝑥 + 11

62 Simplify; 2𝑥 + 3(𝑥 + 3)

2𝑥 + 3(𝑥 + 3)

= 2𝑥 + 3𝑥 + 9

= 5𝑥 + 9

63 Simplify; 5𝑥 + 7(3𝑥 − 2) + 3

5𝑥 + 7(3𝑥 − 2) + 3

= 5𝑥 + 21𝑥 − 14 + 3

= 26𝑥 − 11

64 Simplify; 7(3𝑥 − 2) + 5𝑥 + 3

7(3𝑥 − 2) + 5𝑥 + 3

= 21𝑥 − 14 + 5𝑥 + 3

= 26𝑥 − 11

65 Simplify; 5𝑥 + 3 + 7(3𝑥 − 2)

5𝑥 + 3 + 7(3𝑥 − 2)

= 5𝑥 + 3 + 21𝑥 − 14

= 26𝑥 − 11

66 Simplify; 3(𝑥 + 4) + 5(𝑥 − 2)

3(𝑥 + 4) + 5(𝑥 − 2)

= 3𝑥 + 12 + 5𝑥 − 10

= 8𝑥 + 2



67 Simplify; 3(2𝑥 − 4) + 5(3𝑥 − 1)

3(2𝑥 − 4) + 5(3𝑥 − 1)

= 6𝑥 − 12 + 15𝑥 − 5

= 21𝑥 − 17

68 Simplify; 3(𝑥 + 4) + 5(𝑥 + 2)

3(𝑥 + 4) + 5(𝑥 + 2)

= 3𝑥 + 12 + 5𝑥 + 10

= 8𝑥 + 22

69 Simplify; 2(𝑥 + 3) + 3(𝑥 + 1)

2(𝑥 + 3) + 3(𝑥 + 1)

= 2𝑥 + 6 + 3𝑥 + 3

= 5𝑥 + 9

70 Simplify; 4(𝑥 + 3) + 2(𝑥 − 2)

4(𝑥 + 3) + 2(𝑥 − 2)

= 4𝑥 + 12 + 2𝑥 − 4

= 6𝑥 + 8

71 Simplify; 3(𝑥 − 4) + 5(𝑥 − 2)

3(𝑥 − 4) + 5(𝑥 − 2)

= 3𝑥 − 12 + 5𝑥 − 10

= 8𝑥 − 22

72 Simplify; 2(𝑥 − 4) + 3(𝑥 − 2)

2(𝑥 − 4) + 3(𝑥 − 2)

= 2𝑥 − 8 + 3𝑥 − 6

= 5𝑥 − 14

73 Simplify; 3(2𝑥 − 4) + 4(3𝑥 − 2)

3(2𝑥 − 4) + 4(3𝑥 − 2)

= 6𝑥 − 12 + 12𝑥 − 8

= 18𝑥 − 20

74 Simplify; 5(12𝑥 − 20) + 10(4𝑥 − 5)

5(12𝑥 − 20) + 10(4𝑥 − 5)

= 60𝑥 − 100 + 40𝑥 − 50

= 100𝑥 − 150



75 Simplifying – Different

76 Simplify; 2 × 3𝑥

2 × 3𝑥

= 2 × 3 × 𝑥

= 6𝑥

77 Simplify; 2𝑥 × 3

2𝑥 × 3

= 2 × 𝑥 × 3

= 2 × 3 × 𝑥

= 6𝑥

78 Simplify; 2 × 6𝑥

2 × 6𝑥

= 2 × 6 × 𝑥

= 12𝑥

79 Simplify; 2𝑥 × 3𝑦

2𝑥 × 3𝑦

= 2 × 𝑥 × 3 × 𝑦

= 2 × 3 × 𝑥 × 𝑦

= 6𝑥𝑦

80 Simplify; 2𝑦 × 3𝑥

2𝑦 × 3𝑥

= 2 × 𝑦 × 3 × 𝑥

= 2 × 3 × 𝑥 × 𝑦

= 6𝑥𝑦

81 Simplify; 2𝑥 × 3𝑦 × 4𝑧

2𝑥 × 3𝑦 × 4𝑧

= 24𝑥𝑦𝑧

82 Simplify; 3𝑦 × 4𝑧 × 5𝑥

3𝑦 × 4𝑧 × 5𝑥

= 60𝑥𝑦𝑧



83 Is this enough simplification practice? NO … I’d have to do these questions multiple times to have confidence to do them all in the test without error.

84 Since I can do these questions in class, it means that I can do the in the test.

NO … I’d have to do these questions multiple times to have confidence to do them all in the test without error.

85

86 Expand; 5(𝑥 + 2) Factorise; 5𝑥 + 10

5(𝑥 + 2) = 5𝑥 + 10

5𝑥 + 10 = 5(𝑥 + 2)

87

88 What is the connection between Expanding and Factorising that you can see?

Yes, they are the opposite process. Expanding and factorising are the exact opposite process to each other!

89

90 Is there anything in the year 8 achievement standard on this?

Yes, A year 8 student needs to be able to make a connection between expanding and factorising.

91

92 What is the connection between Expanding and Factorising that you can see?

Yes, they are the opposite process. Expanding and factorising are the exact opposite process to each other!



93 Words in Algbra

94 If tickets to a tennis match cost $23 for adults and $11 for children, write an expression for the cost of the following. (a) p adult tickets (b) q children tickets (c) x adult and y children tickets

Answers: (a) $ (b) $ (c) $( )

95 Bob is now d years old. (a) Write an expression for his age in 6 years

time. (b) How old is Bob 6 years ago?

(c) How old was Bob 3 years ago?

Answers: (a) (b) 𝑑 − 6

(c)

96 Kate is 𝑘 years old. Bob is double Kate’s age, plus 3 more years Write an expression showing how old Bob is.

ANSWER:

2𝑘 + 3

97 Kate is 𝑘 years old. Bob is double Kate’s age, plus 3 more years. By writing Bob’s age as an expression, use

substitution to find Bob’s age, if Kate is 9 years old.

ANSWER: Bob’s age as an expression

2𝑘 + 3 By substitution; Bobs age is

2 × 9 + 3 = 21

Bob is 21 years old

23p11q23 11x y+

6d +

3d -

worksheet 8.1 algebra name:worksheet 8.1 algebra name: _____ 1 substitution full setting out please....

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