FOM 11 Practice Test Name: ____________

Midterm Ch.1-4 Date: _____________

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Janice created the following table.

Number 23 28 73

Sum of the Digits 5 10 10

Based on this evidence, which conjecture might Janice make? Is the conjecture valid?

a. A number whose digits sum to a multiple of 10 will be 2 less than a multiple of 5; no, this

conjecture is not valid.

b. The sum of the digits of a number that is 2 less than a multiple of 5 is a multiple of 5; no,

this conjecture is not valid.

c. The sum of the digits of a number that is 2 less than a multiple of 5 is a multiple of 5; yes,

this conjecture is valid.

d. A number whose digits sum to a multiple of 10 will be 2 less than a multiple of 5; yes, this

conjecture is valid.

____ 2. Make a conjecture as to which line segment is longer, A or B.

a. I conjecture that B is longer than A.

b. I conjecture that A and B are the same length.

c. I conjecture that A is longer than B.

____ 3. Ginerva made the following conjecture:

The square of a number is always greater than the number.

Is the following equation a counterexample to this conjecture? Explain.

52 = 25

a. No, it is not a counterexample, because 25 is greater than 5.

b. No, it is not a counterexample, because 25 is less than 5.

c. Yes, it is a counterexample, because 25 is greater than 5.

d. Yes, it is a counterexample, because 5 is less than 25.

____ 4. Which of the following choices, if any, uses inductive reasoning to show

that an odd number and an even number sum to an odd number?

a. 3 + 6 = 9 and 4 + 5 = 9

b. 2x + 2y + 1 = 2(x + y + 1)

c. (2x + 1) + 2y = 2(x + y) + 1

d. None of the above choices

____ 5. What type of error, if any, occurs in the following deduction?

All swimmers can swim one kilometre without stopping.

Joan is a swimmer.

Therefore, Joan can swim one kilometre without stopping.

a. a false assumption or generalization

b. an error in reasoning

c. an error in calculation

d. There is no error in the deduction.

____ 6. What type of error, if any, occurs in the following deduction?

If you combine one haystack with another haystack,

you get one haystack. Therefore, 1 + 1 = 1.

a. a false assumption or generalization

b. an error in reasoning

c. an error in calculation

d. There is no error in the deduction.

____ 7. Determine the unknown term in this pattern.

3, 6, 12, 24, ____, 96, 192

a. 48

b. 36

c. 102

d. 96

____ 8. In a Kakuro puzzle, you fill in the empty squares with the numbers from 1 to 9.

• Each row of squares must add up to the circled number to the left of it.

• Each column of squares must add up the circled number above it.

• A number cannot appear more than once in the same sum.

Complete this Kakuro puzzle by filling in the grey squares.

a. 9, 7, 4, 1

b. 1, 4, 8, 8

c. 2, 3, 7, 9

d. 1, 4, 7, 9

____ 9. Which angle property proves ∠BED = 73°?

a. alternate interior angles

b. vertically opposite angles

c. corresponding angles

d. alternate exterior angles

____ 10. Which are the correct measures for ∠DCE and ∠CAB?

a. ∠DCE = 75°, ∠CAB = 55°

b. ∠DCE = 65°, ∠CAB = 50°

c. ∠DCE = 75°, ∠CAB = 66°

d. ∠DCE = 55°, ∠CAB = 61°

____ 11. Which are the correct measures of the interior angles of ΔCDE?

a. ∠DCE = 46°, ∠CDE = 101°, and ∠CED = 33°

b. ∠DCE = 32°, ∠CDE = 83°, and ∠CED = 65°

c. ∠DCE = 76°, ∠CDE = 91°, and ∠CED = 13°

d. ∠DCE = 56°, ∠CDE = 101°, and ∠CED = 23°

____ 12. With which of the following polygons could you create a tiling pattern?

a. a regular hexagon

b. a regular pentagon

c. a regular octagon

d. none of the above

____ 13. Determine the length of k to the nearest centimetre.

a. 29 cm b. 28 cm c. 27 cm d. 30 cm

____ 14. Determine the measure of θ to the nearest degree.

a. 40° b. 38° c. 36° d. 42°

____ 15. Determine the length of PQ to the nearest tenth of a centimetre.

a. 9.4 cm b. 9.1 cm c. 8.5 cm d. 8.8 cm

____ 16. How you would determine the indicated angle measure, if it is possible?

a. the sine law b. not possible c. primary trigonometric ratios d. the cosine law

____ 17. Which set of measurements will produce just one triangle?

a. ∠A = 25°, a = 9.4 m, b = 10.0 m

b. ∠A = 40°, a = 9.4 m, b = 10.0 m

c. ∠A = 125°, a = 9.4 m, b = 10.0 m

d. ∠A = 70°, a = 9.4 m, b = 10.0 m

____ 18. In ΔEFG, ∠G = 32°, f = 9.5 m, and g = 12.5 m.

Which statement is true for this set of measurements?

a. This is not a SSA situation.

b. This is a SSA situation; no triangle is possible.

c. This is a SSA situation; only one triangle is possible.

d. This is a SSA situation; two triangles are possible.

Short Answer

19. Star claims that whenever you add an odd integer to the square of

an odd integer, the result is an odd number. Is her conjecture reasonable?

Briefly justify your decision.

20. What type(s) of error(s) occurs in the following deduction?

Briefly justify your answer.

4 = 2 + 3

4(4) = 4(2 + 3)

4(4) – 5 = 4(2 + 3) – 20

16 – 5 = 20 – 20

11 = 0

21. Determine the values of a, b, and c.

22. Determine the value of x.

23. Determine the sum of the measures of the interior angles of this 14-sided polygon.

Show your calculation.

24. Determine the measure of α to the nearest degree.

25. In ΔVWX, v = 52.5 cm, w = 48.0 cm, and x = 61.7 cm.

Determine the measure of ∠V to the nearest degree.

26. A canoeist leaves a dock on Lesser Slave Lake in Alberta, and heads in a direction S20°W from the dock for

1.5 km. The canoeist then turns and travels north until he is directly west of the dock.

Determine the distance to the dock, to the nearest tenth of a kilometre.

27. Determine two angles between 0° and 180° that have the sine ratio 0.8480.

28. Determine the indicated side length to the nearest tenth of a centimetre.

Problem

29. Two Jasper National Park rangers in their fire towers spot a fire.

Determine the distances, to the nearest tenth of a kilometre, from each tower to the fire. Show your work.

30. Determine the perimeter of this quadrilateral to the nearest tenth of a centimetre.

31. The posts of a soccer goal are 24 ft apart. A player is standing at a point 50 ft from one post and 42 ft from the

other post. Within what angle must the player kick the ball to score a goal? Express your answer to the nearest

degree. Show your work and draw a diagram.