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Equations, Inequalities & Formulae

Equations, Inequalities & Formulae — Free MYP1 Mathematics Practice Questions

1QuestionGraphing Inequalities on a Number LineConcept Practice
2 marks~3 minCriterion A
A school bus picks up students who live at least 5 km from school. Let dd be the distance, in kilometres, a student lives from school.
a
Identify what the inequality d≥5d \geq 5 means for a student wanting to use the bus. [1]
b
Describe why the value 5 km matters in deciding who can use the bus. [1]
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2QuestionUnderstanding Inequality SymbolsConcept Practice
2 marks~3 minCriterion C
A number line is shown with a closed circle at 33 and shading extending to the left.
a
Identify what the closed circle at 33 tells you about the number 33. [1]
b
State the inequality shown by the number line. [1]
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3QuestionInterpreting Inequalities in Real-Life ScenariosConcept Practice
2 marks~3 minCriterion D
Mia has between 10 dollars and 25 dollars to spend each week on snacks and a movie ticket. She writes the inequality 10≤amount<2510 \leq \text{amount} < 25 to model her spending.
a
Give an example of one real-life situation that can be shown using an inequality. [1]
b
Describe one reason why a simple inequality may not perfectly match real spending. [1]
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4QuestionCreating and Solving Multi-Step Word ProblemsConcept Practice
2 marks~3 minCriterion B
Look at these sums of three consecutive numbers:

1+2+3=61 + 2 + 3 = 6

2+3+4=92 + 3 + 4 = 9

3+4+5=123 + 4 + 5 = 12

4+5+6=154 + 5 + 6 = 15
a
Identify the relationship between each sum and the middle number. [1]
b
Use this relationship to state the value of 7+8+97 + 8 + 9 without adding the numbers. [1]

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5QuestionChecking Solutions in the Context of the ProblemConcept Practice
4 marks~6 minCriterion C
A student says the answer to "Twice a number plus 5 is 17" is x=6x = 6.
a
Identify the value of 2x+52x + 5 when x=6x = 6. [1]
b
State whether x=6x = 6 is correct. [1]
c
Describe in one sentence why x=6x = 6 does or does not make sense as the answer to the problem. [2]

Solutions

6QuestionChecking Solutions in the Context of the ProblemConcept Practice
2 marks~3 minCriterion A
A rectangle has a width of xx cm and a length of (x+2)(x + 2) cm. Its perimeter is 20 cm.
a
Write an equation for the perimeter of the rectangle in terms of xx. [1]
b
Calculate the value of xx and state whether both side lengths are positive. [1]
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7QuestionInterpreting and Rewriting Real-Life FormulasConcept Practice
2 marks~3 minCriterion C
The formula for the perimeter of a rectangle is P=2l+2wP = 2l + 2w.
a
Identify what PP represents in this formula. [1]
b
Describe in one sentence what 2l+2w2l + 2w tells you about the rectangle. [1]

Solutions

8QuestionApplying the Speed Distance Time FormulaConcept Practice
2 marks~3 minCriterion B
A car travels at a constant speed. The table below shows how far it goes each hour.

Time (hours)1234
Distance (km)5101520
a
Identify the pattern in the table. [1]
b
Calculate the distance the car travels in 6 hours. [1]

Solutions

9QuestionApplying the Speed Distance Time FormulaConcept Practice
2 marks~3 minCriterion D
A family is driving 120 km to visit relatives. Their average speed is 60 km/h.
a
Identify the formula they would use to find the travel time. [1]
b
Describe one reason why the actual travel time might be longer than the calculated time. [1]
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10QuestionApplying the Speed Distance Time FormulaConcept Practice
2 marks~3 minCriterion A
A car travels from point A to point B, a distance of 60 km, at a speed of 30 km/h.

Using the formula

time=distancespeed,\text{time} = \frac{\text{distance}}{\text{speed}},

calculate the time taken for the journey. Give your answer in hours. [2]
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11QuestionSolving Equations with Decimals and FractionsConcept Practice
2 marks~3 minCriterion B
Each equation has the form x+d=sx + d = s.

dd: 0.5, 0.6, 0.7, 0.80.5,\ 0.6,\ 0.7,\ 0.8
ss: 1.5, 1.8, 2.1, 2.41.5,\ 1.8,\ 2.1,\ 2.4
a
Identify the relationship between dd and ss. [1]
b
Write the next two equations in the sequence, including their solutions. [1]

Solutions

12QuestionSolving Equations with Decimals and FractionsConcept Practice
2 marks~3 minCriterion D
You buy a notebook for $6.50\$6.50 and a pencil case for $3.25\$3.25. You pay with a $20\$20 note and receive $8.25\$8.25 in change.
a
Write an equation to find the cost, xx dollars, of a third item you also bought. [1]
b
Solve your equation and describe whether your answer makes sense in this shopping situation. [1]
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13QuestionSolving Equations with Decimals and FractionsConcept Practice
2 marks~3 minCriterion A
A rectangle has one side measuring xx cm and the other side measuring 3.53.5 cm. Its perimeter is 19.219.2 cm.

Calculate the value of xx. [2]
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14QuestionClearing Fractions in EquationsConcept Practice
2 marks~3 minCriterion D
Three friends share a pizza bill equally. Each person pays 13\frac{1}{3} of the total cost.
a
Give an example of a real-life situation where you would need to solve an equation with fractions. [1]
b
Describe one reason why the answer from your equation might not work perfectly in real life. [1]

Solutions

15QuestionClearing Fractions in EquationsConcept Practice
2 marks~3 minCriterion B
Look at these equations and their solutions.

x2=4⇒x=8\dfrac{x}{2} = 4 \Rightarrow x = 8 \quad x3=6⇒x=18\dfrac{x}{3} = 6 \Rightarrow x = 18 \quad x4=8⇒x=32\dfrac{x}{4} = 8 \Rightarrow x = 32 \quad x5=10⇒x=50\dfrac{x}{5} = 10 \Rightarrow x = 50
a
Identify the pattern that connects the bottom number and the right-hand side number to the solution for xx. [1]
b
Calculate the solution for x6=12\dfrac{x}{6} = 12. Show your working. [1]

Solutions

16QuestionClearing Fractions in EquationsConcept Practice
2 marks~3 minCriterion C
Look at the equation below.

x3+12=5\frac{x}{3} + \frac{1}{2} = 5
a
State what the least common denominator (LCD) means. [1]
b
Identify the LCD of the equation above. [1]

Solutions

17QuestionExpanding Brackets Before SolvingConcept Practice
2 marks~3 minCriterion A
A rectangle has side lengths of (x+3)(x + 3) cm and 55 cm. Its perimeter is 3636 cm.
a
Write an equation for the perimeter of the rectangle. [1]
b
Expand the brackets and solve for xx. Show all your working. [1]
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18QuestionSolving One-Step InequalitiesAssessment Practice
6 marks~9 minCriterion B
A conjecture states: "Adding the same number to both sides of an inequality always keeps the inequality sign the same."
a
Identify whether each result is True or False. [2]

3<73 < 7, add 22: 5<9\quad 5 < 9

−2<5-2 < 5, add −3-3: −5<2\quad -5 < 2

4>−34 > -3, add −5-5: −1>−8\quad -1 > -8
b
State the general rule about what happens to an inequality when you add the same number to both sides. Use the word "preserves" in your answer. [2]
c
Describe how a number line shows why this rule works. [2]

Solutions

19QuestionTranslating Word Problems into EquationsAssessment Practice
2 marks~3 minCriterion D
A student has exactly 50 dollars to spend on notebooks at 3 dollars each and pens at 2 dollars each. The equation 3x+2y=503x + 2y = 50 models this situation.
a
Identify one limitation of using this equation in a real shopping situation. [1]
b
Describe how this limitation changes what the student can actually buy. [1]
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20QuestionSolving One-Step Addition and Subtraction EquationsAssessment Practice
4 marks~6 minCriterion C
Maya has read 5 pages of a 20-page chapter. She writes the equation x−5=20x - 5 = 20 to find how many pages she still needs to read.
a
Calculate the value of xx. [1]
b
State one reason why Maya's equation does not match the real situation. [1]
c
Describe how you would change the equation to better match the real situation. [2]
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