MATHEMATICS - SOLVING TWO STEP EQUATIONS

Solving Two Step Equations Worksheet

  • 10 questions
  • Understand that a situation can be represented either in words or as an equation. Move between the two representations and solve the equation (integer coefficients, unknown on one side).
  • Difficulty: Hard
  • Board: CAIE
  • Attempt online on the examination portal

Here are the first 3 questions. Click “View all questions” to see the complete assessment.

Q1.

A ride costs a fixed 8 dollars plus 5 dollars for each zone travelled. The total cost is 63 dollars. If z is the number of zones, which equation and solution represent the situation?

  1. A) 5z + 8 = 63, so z = 11.
  2. B) 5z − 8 = 63, so z = 71/5.
  3. C) 8z + 5 = 63, so z = 29/4.
  4. D) 5(z + 8) = 63, so z = 23/5.

Q2.

Which situation is represented by 6n − 11 = 43, and what is the value of the number?

  1. A) Subtract 6 from 11 times a number to get 43; the number is 49/11.
  2. B) Subtract 11 from 6 times a number to get 43; the number is 9.
  3. C) Add 11 to 6 times a number to get 43; the number is 16/3.
  4. D) Subtract 11 from a number and multiply the result by 6 to get 43; the number is 109/6.

Q3.

When 14 is subtracted from 5 times an integer, the result is 61. Which equation represents this statement, and what is the integer?

  1. A) 5x − 14 = 61, so x = 15.
  2. B) 14x − 5 = 61, so x = 33/7.
  3. C) 5(x − 14) = 61, so x = 131/5.
  4. D) 14 − 5x = 61, so x = − 47/5.

Q4.

There are 4 cartons containing the same number of bottles. After 9 bottles are removed from each carton, 52 bottles remain altogether. If b was the original number in each carton, which equation and solution are correct?

  1. A) 4b − 9 = 52, so b = 61/4.
  2. B) 4(b − 9) = 52, so b = 22.
  3. C) b − 36 = 52, so b = 88.
  4. D) 4(b + 9) = 52, so b = 4.

Q5.

A team begins a contest with a penalty of 15 points. It then earns 6 points in each round and finishes with 33 points. If r is the number of rounds, which equation and solution model the situation?

  1. A) 6r − 15 = 33, so r = 8.
  2. B) 6(r − 15) = 33, so r = 41/2.
  3. C) −15 − 6r = 33, so r = − 8.
  4. D) 6r + 15 = 33, so r = 3.

Q6.

Which verbal statement represents −7p + 5 = 47, and what is the value of p?

  1. A) Negative 7 times the sum of a number and 5 is 47; p = − 82/7.
  2. B) Seven times the sum of a number and 5 is 47; p = 12/7.
  3. C) Five more than negative 7 times a number is 47; p = − 6.
  4. D) Five less than negative 7 times a number is 47; p = − 52/7.

Q7.

A rope is cut into 9 equal pieces, with an extra length of 4 cm left over. The original rope is 103 cm long. If each equal piece has length l cm, which equation and solution are correct?

  1. A) l/9 + 4 = 103, so l = 891 cm.
  2. B) 9l = 103 + 4, so l = 107/9 cm.
  3. C) 9(l + 4) = 103, so l = 67/9 cm.
  4. D) 9l + 4 = 103, so l = 11 cm.

Q8.

An integer is multiplied by −6. Then 13 is subtracted, giving a result of 35. Which equation represents the process, and what is the integer?

  1. A) 6x − 13 = 35, so x = 8.
  2. B) −6x + 13 = 35, so x = − 11/3.
  3. C) −6x − 13 = 35, so x = − 8.
  4. D) −6(x − 13) = 35, so x = 43/6.

Q9.

The diagram shows a level balance. Each identical bag has mass x. Which equation represents the balance, and what is the mass of one bag?

Diagram for question 9: The diagram shows a level balance. Each identical bag has mass x. Which equation represents the balance, and…
  1. A) 5x + 3 = 32, so x = 29/5 kg.
  2. B) 3(x + 5) = 32, so x = 17/3 kg.
  3. C) 3x − 5 = 32, so x = 37/3 kg.
  4. D) 3x + 5 = 32, so x = 9 kg.

Q10.

The flow diagram shows the operations performed on an input x. Which equation represents the diagram, and what is the input?

Diagram for question 10: The flow diagram shows the operations performed on an input x. Which equation represents the diagram, and…
  1. A) −4x − 7 = 39, so x = − 23/2.
  2. B) 4x + 7 = 39, so x = 8.
  3. C) −4(x + 7) = 39, so x = − 67/4.
  4. D) −4x + 7 = 39, so x = − 8.

What this assessment covers

Concepts Tested

  • solving two step equations
  • Understand that a situation can be represented either in words or as an equation. Move between the two representations and solve the equation (integer coefficients, unknown on one side).

Question Mix

  • Hard questions included

Skills you build

  • Apply

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