Download Mathematics 20-1 Final Exam Multiple Choice Questions

Mathematics 20-1 Final Exam p.1
Mathematics 20-1: Final Exam
Name: _________________________
Date: _________________
This exam consists of 24 multiple choice questions worth 2 marks each and 8 written response questions
worth a total of 26 marks. There is a tear-off formula sheet at the back of the exam.
Multiple Choice Answer Section (48 marks)
Place the letter corresponding to the best answer on the line.
1. _____
4. _____
7. _____
11. _____
13. _____
15. _____
18. _____
22. _____
2. _____
5. _____
8. _____
12. _____
14. _____
16. _____
19. _____
23. _____
3. _____
6. _____
9. _____
17. _____
20. _____
24. _____
10. _____
21. _____
SCORING GUIDE: TO BE FILLED OUT BY TEACHER
Unit
Multiple
Choice
Questions
1: Sequences & Series
1–3
/6
1
/4
/10
2: Trigonometry
4–6
/6
2
/3
/9
3: Quadratic Functions
7 – 10
/8
3
/3
/11
4: Quadratic Equations
11 – 12
/4
4
/3
/7
5: Radical Expressions & Equations
13 – 14
/4
5
/3
/7
6: Rational Expressions & Equations
15 – 17
/6
6
/3
/9
7: Absolute Value & Reciprocal Functions
18 – 21
/8
7
/4
/12
8: Systems of Equations
n/a
8
/3
/3
9: Linear & Quadratic Inequalities
22 – 24
n/a
n/a
/6
/26
/74
Totals:
MC
Score
n/a
/6
/48
Written
Questions
Written
Score
Total
Mark
Score on
Final
Exam
Mathematics 20-1 Final Exam p.2
Mathematics 20-1 Final Exam p.3
Mathematics 20-1 Final Exam
Multiple Choice Questions (2 marks each)
Record your answers on the front cover of the exam.
1. What are the missing terms of the arithmetic sequence: __, 3, 9, __, __?
a) 1, 27, 81
b) 9, 3, 9
c) -6, 12, 17
d) -3, 15, 21
2. What is the sum of the first five terms of the geometric series 16 807 – 2401 + 343 – ...?
a) 19 607
b) 14 707
c) 16 807.29
d) 14 706.25
3. The 20th term of a geometric sequence is 524 288 and the 14th term is 8192. The value of the third
term could be
a) 4 only
b) 8 only
c) +4 and -4
d) +8 and -8
Mathematics 20-1 Final Exam p.4
4. Which angle in standard position has a different reference angle than all the others?
a) 125°
b) 155°
c) 205°
d) 335°
5.
Which is the exact value of cos 150°?
a)
6.
1
2
b)
√3
2
c)
−
d)
−
√3
2
1
2
The expression that could be used to determine the measure of angle 𝜃 in the diagram is:
a)
sin 𝜃
70
=
sin 28
34
𝜃
b) 𝜃 2 = 342 + 702 − 2(34)(70) cos 28°
c) cos 𝜃 =
d)
sin 𝜃
34
=
70 cm
702 +342 −282
2(70)(34)
sin 28
70
28°
34 cm
Mathematics 20-1 Final Exam p.5
7. What points on the graph of this quadratic function
represent the locations of the zeros of the function?
a) (0, 5) and (1, 0)
b) (0, 1) and (0, 5)
c) (1, 0) and (5, 0)
d) (5, 0) and (0, 1)
8. Which function is NOT a quadratic function?
a) 𝑓(𝑥) = 2(𝑥 + 2)2 − 7
b) 𝑓(𝑥) = (𝑥 − 3)(2𝑥 + 5)
c) 𝑓(𝑥) = 5𝑥 2 − 20
d) 𝑓(𝑥) = 3(𝑥 − 9) + 6
9. Identify the range for the function 𝑦 = −6(𝑥 − 6)2 + 6.
a) {𝑦|𝑦 ≤ 6, 𝑦 ∈ 𝑅}
b) {𝑦│𝑦 ≥ 6, 𝑦 ∈ 𝑅}
c) {𝑦|𝑦 ≤ −6, 𝑦 ∈ 𝑅}
d) {𝑦|𝑦 ≥ −6, 𝑦 ∈ 𝑅}
10. What conditions on a and q will give the function 𝑓(𝑥) = 𝑎(𝑥 − 𝑝)2 + 𝑞 have no x-intercepts?
a) 𝑎 > 0 and 𝑞 > 0
b) 𝑎 < 0 and 𝑞 > 0
c) 𝑎 > 0 and 𝑞 = 0
d) 𝑎 < 0 and 𝑞 = 0
Mathematics 20-1 Final Exam p.6
11. What is one of the factors of 𝑥 2 − 3𝑥 − 10?
a) 𝑥 − 5
b) 𝑥 + 5
c) 𝑥 − 10
d) 𝑥 + 10
1
2
7
2
12. The roots, to the nearest hundredth, of − 𝑥 2 + 𝑥 + are
a) 1.83 and 3.83
b) -1.83 and 3.83
c) 1.83 and -3.83
d) -1.83 and -3.83
3
13. What is the entire radical form of −3(√2)?
3
a) √54
3
b) √18
c)
3
√−18
3
d) √−54
14. What is the simplest form of the expression −2𝑥√6𝑥 + 5𝑥√6𝑥, 𝑥 ≥ 0?
a) 3√6𝑥
b) 6√12𝑥
c) 3𝑥√6𝑥
d) 6𝑥√12
Mathematics 20-1 Final Exam p.7
15. Simplify the rational expression
a)
b)
c)
d)
b)
c)
d)
𝑥 2 −2𝑥−24
for all permissible values of x.
𝑥+1
𝑥−4
𝑥−1
𝑥+4
𝑥+1
𝑥+4
𝑥−1
𝑥−4
16. Simplify
a)
𝑥 2 −7𝑥+6
8
3𝑦
+
5𝑦
4
−
5
8
for all permissible values of y.
30𝑦 2 −15𝑦+64
24𝑦
30𝑦 2 +79
24𝑦
15𝑦 2 +64
24𝑦
5𝑦+3
24𝑦
17. Determine the solution(s) of the equation
a) 𝑥 = −2, 𝑥 = 5
b) 𝑥 = −5, 𝑥 = −1, 𝑥 = 1
c) 𝑥 = −2, 𝑥 = 3
d) 𝑥 = 2
𝑥
𝑥 2 +6𝑥+5
=
2
.
𝑥 2 −1
Mathematics 20-1 Final Exam p.8
18. The value of the expression |−9 − 3| − |5 − 23 | + |−7 + 1 − 4| is
a) 13
b) 19
c) 21
d) 25
19. The range of the function 𝑓(𝑥) = |𝑥 − 3| is
a) {𝑦|𝑦 > 3, 𝑦 ∈ 𝑅}
b) {𝑦|𝑦 ≥ 3, 𝑦 ∈ 𝑅}
c) {𝑦|𝑦 ≥ 0, 𝑦 ∈ 𝑅}
d) {𝑦|𝑦 > 0, 𝑦 ∈ 𝑅}
20. The absolute value equation |1 − 2𝑥| = 9 has solution(s):
a) x = -4
b) x = 5
c) x = -5 and x = 4
d) x = -4 and x = 5
21. One of the vertical asymptotes of the graph of the reciprocal function 𝑦 =
a) x = 0
b) x = 4
c) x = 8
d) x = 16
1
𝑥 2 −16
is:
Mathematics 20-1 Final Exam p.9
22. What linear inequality does the graph show?
3
a) 𝑦 ≤ 4 𝑥 + 4
3
b) 𝑦 ≥ 4 𝑥 + 4
3
c) 𝑦 < 4 𝑥 + 4
3
4
d) 𝑦 > 𝑥 + 4
23. What is the solution set for the quadratic inequality 6𝑥 2 − 7𝑥 − 20 < 0?
4
5
a) {𝑥|𝑥 ≤ − 3 𝑜𝑟 𝑥 ≥ 2 , 𝑥 ∈ 𝑅}
4
5
4
5
b) {𝑥|− 3 ≤ 𝑥 ≤ 2 , 𝑥 ∈ 𝑅}
c) {𝑥|− 3 < 𝑥 < 2 , 𝑥 ∈ 𝑅}
4
5
d) {𝑥|𝑥 < − 3 𝑜𝑟 𝑥 > 2 , 𝑥 ∈ 𝑅}
24. For the quadratic function q(x) shown in the graph,
which of the following is true?
a) There are no solutions to 𝑞(𝑥) > 0.
b) All real numbers are solutions to 𝑞(𝑥) ≥ 0.
c) All real numbers are solutions to 𝑞(𝑥) ≤ 0.
d) All positive real numbers are solutions to 𝑞(𝑥) < 0.
Mathematics 20-1 Final Exam p.10
Mathematics 20-1 Final Exam p.11
Written Response (marks as indicated)
Record your answers below. Remember to show all your work.
1. Consider the sequence 5, __, __, __, __, 160.
a) Assume the sequence is arithmetic. Determine the unknown terms of the sequence.
b) What is the general term of the arithmetic sequence?
c) Assume the sequence is geometric. Determine the unknown terms of the sequence.
d) What is the general term of the geometric sequence?
/4
Mathematics 20-1 Final Exam p.12
2. In ΔPQR, P = 56°, p = 10 cm, and q = 12 cm.
a) Sketch a diagram of the triangle.
b) Determine the length of the unknown angles to the nearest degree.
c) Determine the measures of the unknown side to the nearest tenth of a centimetre.
/3
Mathematics 20-1 Final Exam p.13
3. Write the quadratic function 𝑦 = 3𝑥 2 + 36𝑥 + 13 in the form 𝑦 = 𝑎(𝑥 − 𝑝)2 + 𝑞 by completing
the square.
/3
Mathematics 20-1 Final Exam p.14
4. Solve the quadratic equation 3𝑥 2 + 5𝑥 + 1 using the quadratic formula. Express your answers as
exact roots.
/3
Mathematics 20-1 Final Exam p.15
5. Given the equation 𝑥 − 4 = √𝑥 + 2
a) Solve the equation.
b) State any extraneous roots.
c) Identify the values of x for which the radical is defined.
/3
Mathematics 20-1 Final Exam p.16
6. Given the equation 2 −
5
𝑥 2 −𝑥−6
=
𝑥+3
,
𝑥+2
a) Solve the equation.
b) Identify all non-permissible values.
/3
Mathematics 20-1 Final Exam p.17
7. Consider the function 𝑓(𝑥) = |2𝑥 − 7|.
a) Sketch the graph of the function on the grid
to the right.
b) Determine all the x- and y-intercepts.
c) State the domain and range.
d) What is the piecewise notation form of the function?
/4
Mathematics 20-1 Final Exam p.18
8. Solve the following system algebraically.
𝑦 = 7x − 11
5𝑥 2 − 3𝑥 − 𝑦 = 6
/3