# QCE Multiple Choice Practice Questions for Unit 3 & 4 General Maths External Assessment

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### Question 6

The student who reported a study time of 10 minutes made six errors. The predicted score for this student would have a residual of:

(a) −7.6

(b) −1.6

(c) 0

(d) 1.6

(e) 7.6

### Question 7

Which of the following statements that relate to the regression line are not true?

(a) The slope of the regression line is −0.12

(b) The equation predicts that a student who spends 40 minutes studying will make approximately four errors

(c) The least squares regression line does not pass through the origin

(d) On average, a student who does not study for the test will make around 8.8 errors

(e) The explanatory variable in the regression equation is number of errors

### Question 8

This regression line predicts that, on average, the number of errors made:

(a) decreases by 0.82 for each extra minute spent studying

(b) decreases by 0.12 for each extra minute spent studying

(c) increases by 0.12 for each extra minute spent studying

(d) increases by 8.8 for each extra minute spent studying

(e) decreases by 8.8 for each extra minute spent studying

### Question 9

Given that the coefficient of determination is 0.8198, we can say that close to:

(a) 18% of the variation in the number of errors made can be explained by the variation in the time spent studying

(b) 33% of the variation in the number of errors made can be explained by the variation in the time spent studying

(c) 67% of the variation in the number of errors made can be explained by the variation in the time spent studying

(d) 82% of the variation in the number of errors made can be explained by the variation in the time spent studying

(e) 95% of the variation in the number of errors made can be explained by the variation in the time spent studying

### Question 10

For the recurrence relation tn+1 − tn = 6 with t1 = 3, the nth term is:

(a) tn = 6 − 3n

(b) tn = 3 + 3n

(c) tn = 6n − 3

(d) tn = −3 + 3n

(e) tn = −4 + 7n

### Question 11

What does the letter r stand for in terms of regressions?

(a) Correlation coefficient

(b) Coefficient of determination

(c) Covariance

### Question 12

What is an explanatory variable?

(a) A variable that explains the purpose of an experiment

(b) A variable that can be used to predict a response variable

(c) A variable that is predicted by the response variable

### Question 13

Eli borrowed some money. He will be charged compound interest at the rate of 7.08% per annum, compounding monthly. After one year, Eli repaid \$6674.95 as principal and interest. The amount borrowed was closest to:

(a) \$6000

(b) \$6100

(c) \$6200

(d) \$6300

(e) \$6400

### Question 14

The balance of a reducing-balance loan after n months, An, can be modelled by the recurrence relation A0 = 250000, An+1 = 1.003125 × An − 2300. The total interest that has been paid after one repayment is closest to:

(a) \$781

(b) \$1519

(c) \$1558

(d) \$2300

(e) \$3042

### Question 15

A loan of \$180000 is charged compound interest at the annual percentage interest rate of 3.24% per annum, compounding monthly. The loan is repaid with monthly repayments of \$1200. If An is the balance of the loan after n months, which one of the following is a recurrence relation model for this loan?

(a) A0 = 180000, An+1 = 1.0324 × An − 1200

(b) A0 = 180000, An+1 = 1.00324 × An − 1200

(c) A0 = 180000, An+1 = 1.27 × An − 1200

(d) A0 = 180000, An+1 = 1.027 × An − 1200

(e) A0 = 180000, An+1 = 1.0027 × An – 1200

### Question 16

The minimum spanning tree for a graph is…

(a) the spanning tree that has the smallest possible total weight for that graph

(b) the spanning tree that has the biggest possible total weight for that graph

### Question 17

Prim’s algorithm is…

(a) an algorithm used to predict the value of the vertices of a graph

(b) an algorithm used to predict the length of the branches of a graph

(c) an algorithm that is used to determine the minimum spanning tree for a graph

### Question 18

Euler’s Formula states that…

(a) v = the number of faces, f = the number of vertices and e = the number of edges in a planar graph, then v + f − e = 2

(b) v = the number of vertices, f = the number of faces and e = the number of edges in a planar graph, then v + f − e = 2

(c) v = the number of vertices, f = the number of faces and e = the number of edges in a planar graph, then v + f − e = 4

### Question 19

A walk is…

(a) A route through a graph, from one vertex to another, along the edges of the graph

(b) A path through a graph, from a vertex to the other, along the outside of a graph

(c) A cycle

### Question 20

A trail…

(a) is a walk with repeated edges

(b) is a walk that has no repeated edges.

(c) is a cycle

### Question 21

A path…

(a) is a walk that has repeated edges and repeated vertices

(b) is a walk that has no repeated edges and no repeated vertices

(c) is a walk that has no repeated edges and repeated vertices

### Question 22

When are outliers present?

(a) Outliers are present when the values do not stand out from the general body of data.

(b) Outliers are present when almost half the values stand out from the general body of data

(c) Outliers are present when there are individual values that stand out from the general body of data

### Question 23

The EST is…

(a) The latest starting time for an activity is the earliest time after the start of the project that an activity can begin.

(b) The earliest starting time for an activity is the earliest time after the start of the project that an activity can begin.

(c) The earliest starting time for an activity is the earliest time after the start of the project that an activity can end.

### Question 24

The formula for LST is…

(a) LST = duration – LFT

(b) LST = LFT + duration

(c) LST = LFT – duration

### Question 25

The LFT is…

(a) The latest starting time for an activity is the latest time after the start of the project that an activity can finish without affecting the overall completion time of the project.

(b) The earliest starting time for an activity is the latest time after the start of the project that an activity can finish without affecting the overall  time of the project.