Level 4 Algebra

2019 Junior Algebra Equations L3&4 Practise.pdf
2019 Junior Algebra Equations L3&4 Practise Answers.pdf

• Find and justify a word formula which represents a given practical situation.

We can solve these word problems using number skills:

  • 42 heads, with two legs per head is 84 feet. We need 124 feet. 124-84=40 & 40/2=20. There must be 20 rabbits and 22 chickens.
  • 34 heads with two legs per head is 68 feet. We need 114 feet. 114-68=44 & 44/2=22. There must be 11 donkeys and 23 children.

We can solve using simultaneous equations:

  • This would be Level 5 OR Level 6 of the NZC.
  • The working makes the Level shift from Level 4 to Level 5 or 6.
  • Rabbits have 4 feet, so if "r" is the number of rabbits then 4r is the number of rabbit feet.
  • Chickens have 2 feet, so it "c" is the number of chickens then 2c is the number of chicken feet.
  • The total number of feet is 124
    • 4r+2c=124
  • Rabbits and Chickens have one head, so the number of rabbits plus the number of chickens equals 42.
    • r+c=42
  • Now we need to solve r+c=42 and 4r+2c=124
  • We can rearrange r+c=42 to give c=42-r
  • We can replace the "c" in "4r+2c=124" with "42-r"
    • 4r+2(42-r)=124
    • 4r+84-2r=124
    • 2r=124-84
    • 2r=40
    • r=40/2
    • r=20
    • There are 20 Rabbits.
    • c=42-r
    • c=42-20
    • c=22
    • There are 22 Chickens.
    • Check 22 Chickens plus 20 Rabbits = 42 Heads.
    • Check 22 Chickens gives 44 feet and 20 Rabbits gives 80 Feet.
    • 44+80=124 feet. Correct.
  • Donkeys have 4 feet, so if "d" is the number of donkeys then 4d is the number of donkey feet.
  • Children have 2 feet, so it "c" is the number of children then 2c is the number of children feet.
  • The total number of feet is 114
    • 4d+2c=114
  • Donkeys and Children have one head, so the number of donkeys plus the number of children equals 34.
    • d+c=34
  • Now we need to solve d+c=34 and 4d+2c=114
  • We can rearrange d+c=34 to give c=34-d
  • We can replace the "c" in "4d+2c=114" with "34-d"
    • 4d+2(34-d)=114
    • 4d+68-2d=114
    • 2d=114-68
    • 2d=46
    • d=46/2
    • d=23
    • There are 23 donkeys.
    • c=34-d
    • c=34-23
    • c=11
    • There are 11 children.
    • Check 11 Children plus 23 Donkeys = 34 Heads.
    • Check 11 Children gives 22 feet and 23 Donkeys gives 92 Feet.
    • 22+92=124 feet. Correct.
  • Let g represent the number of girls.
  • Let b represent the number of boys.
  • b+g=672
  • 2g=b (There are twice as many boys as girls)
  • 2g+g=672
  • 3g=672
  • g=672/3
  • g=224 There are 224 Girls.
  • b=2g
  • b=448 There are 448 Boys.
  • Check 448+224=672 Correct

• Solve simple linear equations that involve more than one step.

• Solve simple linear inequalities that do not involve reversing the inequality sign.

Level 5

• Form linear equations to model a given situation.

• Solve linear equations that require multiple steps.

• Solve linear equations that contain algebraic fractions.

• Use equations to represent practical situations.

  • These are word problems.
  • Use letters to represent numbers that you are trying to calculate.
  • Read the question multiple times before and after forming your equation.
  • Once you have formed your equation you can solve it.
  • Remember to answer the question.

• Solve simple linear inequalities that involve reversing the inequality sign.

  • If you multiply or divide by a negative sign you must FLIP the inequality.
  • Remember 2<3 but -2>-3
  • Otherwise inequalities require the same skill set as solving.