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General Rules and nth Terms — Free MYP2 Mathematics Practice Questions
1QuestionEvaluating Terms Using nth Term RuleConcept Practice
2 marks~3 minCriterion A
A tile pattern follows the rule , where is the number of tiles in term .
Term 1: 2 tiles Term 2: 6 tiles Term 3: 18 tiles Term 4: 54 tiles
Term 1: 2 tiles Term 2: 6 tiles Term 3: 18 tiles Term 4: 54 tiles
a
Calculate the number of tiles in term 5. [1]
b
Calculate the number of tiles in term 6. [1]
Solutions
2QuestionSolving Problems with nth Term in ContextAssessment Practice
4 marks~6 minCriterion D
A student models plant height using the formula , where is the height in centimetres and is the week number. The measured heights are:
Week 1: 5 cm, Week 2: 8 cm, Week 3: 11 cm, Week 4: 13 cm, Week 5: 14 cm
Week 1: 5 cm, Week 2: 8 cm, Week 3: 11 cm, Week 4: 13 cm, Week 5: 14 cm
a
Calculate the predicted heights for weeks 4 and 5 using the formula. [1]
b
Describe how the predicted heights compare with the actual heights for weeks 4 and 5, and identify the trend in the difference. [2]
c
Explain whether the formula is suitable for predicting the plant's height at week 10, identifying one limitation of assuming constant growth. [1]
Solutions
3QuestionUsing nth Term to Predict Future TermsConcept Practice
3 marks~5 minCriterion C
A tile pattern is plotted on a graph. The points lie on a straight line passing through and , where the horizontal axis shows the step number and the vertical axis shows the number of tiles.
a
Identify the gradient (rate of change) of the line. [1]
b
Calculate the th term rule for the pattern. [1]
c
A classmate says: "Step 20 will have twice as many tiles as step 10." Explain whether your classmate is correct. [1]
Solutions
4QuestionUsing nth Term to Predict Future TermsAssessment Practice
8 marks~12 minCriterion B
The first four figures of a tile pattern are shown below.
Figure 1: 1 tile Figure 2: 3 tiles Figure 3: 7 tiles Figure 4: 13 tiles
Figure 1: 1 tile Figure 2: 3 tiles Figure 3: 7 tiles Figure 4: 13 tiles
a
State the number of tiles in Figure 5 and Figure 6. [2]
b
Calculate the values of , , and in the general rule , where is the number of tiles in Figure . Show your working. [4]
c
Explain how the constant second difference in the sequence confirms that the rule for is quadratic. Use your rule to find . [2]
Solutions
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