Al Zuhour Pvt School
Mathematics Department
Diagnostic Test
Grade 12 pre-calculus
Name: ______________________
Class: ______________________
𝑥2
50
Grade 12
Diagnostic Test
Standard Code : N.CN
Question 1:
Find the solutions of the equation 8𝑥 2 + 30 = 6 in simplest form
A. ±√3
B. ±3
C. ±i√3
D. ±3i
Standard: N.CN.1,2
DOK: 1
Points: /2
Question 2:
What is the number of solutions of the equation 𝑥 2 + 8𝑥 + 6 = 0 by using Discriminant?
A. Two non-real solutions
B. One real solution
Standard: N.CN.1,2
C. 2 real solutions
DOK: 2
D. 3 real solutions
Points: /2
Question3:
Solve the equation 𝑥 2 + 16𝑥 + 106 = 6 by completing the Square method.
A. ±6I
B. 6 ±8i
Standard: N.CN.1,2
C. ±10
DOK: 2
D. -8 ±6i
Points: /3
Standard Code : F.IF
Question4:
Identify vertical Asymptotes and holes of f(x) =
A vertical asymptote at x= 1 and hole at x=-2
𝑥 2 −2𝑥−8
𝑥 2 +𝑥−2
Standard:
F.IF-7,F.IF.5
DOK: 2
Points: /4
B vertical asymptote at x= 2 and hole at x=-1
C vertical asymptote at x=-1 and hole at x=2
D vertical asymptote at x= -1 and hole at x= 4
1
Question 5:
State the Domain of the expression
Standard: F.IF-7,
F.IF.5
DOK: 2
Points: /3
8𝑥−24
𝑥 2 +7𝑥−30
A. (-∞ , ∞)
B. x ≠ 3, -10
C. (3, -10)
D. (-10 , ∞)
Question6:
1
What are the Horizontal and vertical asymptotes of the graph of g(x) = 5( ) + 7
𝑥−2
A. x=5 , y=-2
B. x=7 , y=2
Standard: F.IF.7
C. x=2 , y=7
DOK: 1
D. x=-2 , y= -7
Points: /3
Standard Code : F.BF
Question7:
Write g(x) =
A g(x)=
B g(x)=
C g(x)=
4
3𝑥+19
4
𝑥+5
3
𝑥+5
4
D g(x)=
3𝑥+19
𝑥+5
𝑥+5
in
g(x) = a(
1
𝑥−ℎ
) + 𝑘 form
+3
−3
Standard: F.BF.3
DOK: 2
Points: /3
+4
+3
Standard Code : F.TF
Question 8:
Write in Degrees the measure of the angle
A. 405°
B. -350°
C. 225°
D. -405°
−9𝜋
4
Standard: F.TF.1,2
DOK: 2
Points: /2
2
Question 9:
What the positive and negative co-terminal angles from the options
A. -123, 455
B. -222, 498
C. -310,114
D. -122,389
Standard: F-TF.3
DOK: 2
Points: /2
Question10:
.Use the given point to find the value of tan 𝜃
A. -6
3
B. 4
C. -8
D. -0.75
Standard: F.TF.3
DOK: 1
Points: /2
Question11:
𝟑𝝅
Given that sin θ = −0.442 where
< 𝜽 < 𝟐𝝅
𝟐
find cos θ. If necessary, round to 3 decimal places.
A. -0.978
B. 0.235
C. 0.897
D. -0.789
Standard: F-TF.6
DOK: 2
Points: /3
3
Question12:
You are measuring the height of a Sitka spruce tree in Alaska. You stand 45 feet from the base of the tree. You
measure the angle of elevation from a point on the ground to the top of the top of the tree to be 59°. To estimate
the height of the tree, you can write a trigonometric ratio that involves the height h and the known length of 45
feet.
A. 75.9
B. 25.7
C.69.3
D. 48.6
Standard: F.TF.7
DOK: 2
Points: /2
Question13:
Identify the equation of the given graph.
3
1
A. y= 4 sin 2 𝑥
3
1
B. y=4 cos 2 𝑥
C. y=– 0.75 cos 2x
3
D. 𝑦 = 4 sin 2𝑥
Standard: F.TF.5,6,7
DOK: 3
Points: /3
Question14:
Which quadrant that sine and cosine are negative.
A.
B.
C.
D.
Ⅰ
Ⅱ
Ⅲ
Ⅳ
Standard: F.TF.8
DOK: 1
Points: /2
4
Question15:
Standard: F.TF.7,8
DOK: 3
Points: /3
A.25.6
B.30.75
C.19.75
D.27.5
Standard Code : A-APR
Question16:
Find the quotient of the expression
A.(X-2)
𝑥 2 +4𝑥
𝑥−2
𝑥 2 +2𝑥−8
÷ 𝑥 2 −2𝑥−8
𝑥 2 +2
B. 𝑋+2
Standard: A-APR.6,7
DOK: 2
Points: /4
𝑋+2
C.𝑋−2
𝑋(𝑋+2)
D. (𝑋−2)2
Question17:
Find the sum of
A.
B.
C.
D.
3𝑋+1
𝑥−1
𝑥 2 −𝑥
+
𝑥+2
𝑥+1
in simplest form .
𝑋+1
𝑥 2 +3𝑋+1
𝑋(𝑋+1)
Standard: A-APR.7
DOK:
Points: /4
𝑥 2 −3𝑋−1
𝑥 2 +1
𝑥 2 +3𝑋−1
𝑋−1
5
Standard Code : A-SSE
Question18:
A.
B.
C.
8
𝑥+1
40
𝑥(𝑥+1)
40
𝑋(𝑋+8)
D.
Standard: A.SSE.1, 2A.CED.1,
DOK: 3
Points: /3
8
𝑋(𝑋+40)
6