Vector Arithmetic and Scalar Multiplication
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Vector Arithmetic and Scalar Multiplication — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionAdding and Subtracting Column VectorsAssessment Practice
6 marks~9 minCriterion A
The diagram shows the graph of f(x)=x2−4x+cf(x) = x^2 - 4x + c for 0≤x≤50 \le x \le 5, where cc is a constant.
a
Given that the graph passes through the point (5,6)(5, 6), find the value of cc. [1]
b
Hence write down the coordinates of the yy-intercept and find the coordinates of the vertex of f(x)f(x). [3]
c
State the values of kk for which f(x)=kf(x) = k has exactly one solution in the domain 0≤x≤50 \le x \le 5, justifying your answer. [2]
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Solutions

2QuestionAdding and Subtracting Column VectorsAssessment Practice
6 marks~9 minCriterion B
A pattern of growing L-shapes is made from unit squares. The first three figures are shown in the diagram.
a
Write down the number of unit squares in Figure 4. [1]
b
Find a rule for the total number of unit squares SS in Figure nn. Give your rule in the form S=an2+bn+cS = an^2 + bn + c, where aa, bb and cc are integers to be found. [3]
c
A student claims that no figure in this pattern can contain exactly 100 unit squares. Justify whether this claim is correct, using your rule from part (b). [2]
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Solutions

3QuestionAdding and Subtracting Vectors GraphicallyAssessment Practice
6 marks~9 minCriterion C
The diagram shows a right triangle ABCABC drawn on a coordinate grid, where A=(0,0)A = (0, 0), B=(6,0)B = (6, 0), and C=(6,8)C = (6, 8).
a
Write down the length of BCBC. [1]
b
Find the length of ACAC, giving your answer in exact form. [2]
c
A second triangle PQRPQR is similar to triangle ABCABC, with ACAC corresponding to PQPQ. Given that PQ=15PQ = 15, the area of triangle PQRPQR is calculated to be 5454 square units. Justify whether this area is correct. [3]
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Solutions

4QuestionAdding and Subtracting Column VectorsAssessment Practice
8 marks~12 minCriterion D
A set of 30 students each recorded the number of hours, xx, they spent on social media in one week and their score, yy, on a wellbeing survey (scored out of 100). The mean number of hours is xˉ=14\bar{x} = 14 and the mean wellbeing score is yˉ=62\bar{y} = 62.

A student suggests modelling the relationship with the linear equation
y=−2.5x+cy = -2.5x + c
where cc is a constant.
a
Show that c=97c = 97, given that the line of best fit passes through (xˉ, yˉ)(\bar{x},\, \bar{y}). [2]

The table below gives data for three students and the scores predicted by the model y=−2.5x+97y = -2.5x + 97.

Student A: hours x=8x = 8, actual score =79= 79, predicted score =77= 77

Student B: hours x=14x = 14, actual score =62= 62, predicted score =62= 62

Student C: hours x=20x = 20, actual score =41= 41, predicted score =47= 47
b
Calculate the percentage error for Student A and for Student C, using the formula
percentage error=∣predicted−actual∣actual×100%.\text{percentage error} = \frac{|\text{predicted} - \text{actual}|}{\text{actual}} \times 100\%.
Give each answer correct to 2 decimal places. [3]
c
A fourth student, Student D, spent 28 hours on social media. Using the model, determine the predicted wellbeing score for Student D. Advise whether this prediction should be trusted, referring to both the percentage errors found in part (b) and the position of x=28x = 28 relative to the data. [3]
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Solutions

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