Mathematics IV (Advanced Algebra,Trigonometry And Statistics)
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Mathematics is a broad subject and it includes trigonometry, statistic and algebra. The test below covers all this three sections and is designed to help you improve your skills. Give it a try and see if you should enroll into the mathematics competition this year. All the best and work hard!
- 1.What constant term must be added to a-14a+___= 0 to make it a perfect square trinomial?
- A.
-49
- B.
7
- C.
49
- D.
-7
- 2.Where is the vertex of the parabola f(x)=3(x-1)^2 +4?
- A.
(3,4)
- B.
(1,4)
- C.
(-1,4)
- D.
(-3,1)
- 3.Which parabola does not have its axis of symmetry on the y-axis?
- A.
Y=-x^2
- B.
Y=x^2+2
- C.
Y=2x^2
- D.
Y=(x-2)^2
- 4.What quadratic function has a maximum point?
- A.
F(x)=-x^2+3
- B.
F(x)=(x-4)^2+6
- C.
F(x)=2x^2+3
- D.
F(x)=(x)^2
- 5.Which of the following is NOT a perfect square trinomial?
- A.
A^2+10a+25
- B.
Y^2+8y+7
- C.
A^2-18a+81
- D.
H^2-13h+169/4
- 6.Find the product of (6x-3) and (x+5).
- A.
6x^2-15
- B.
6x^2+30x-15
- C.
6x^2-27x-15
- D.
6x^2+27x-15
- 7.Which of the following equations of a parabola has the widest graph?
- A.
Y=4x^2
- B.
Y=x^2
- C.
Y=2x^2
- D.
Y=1/4x^2
- 8.Factor x^2-64.
- A.
(x-8)(x-8)
- B.
(x-4)(x+16)
- C.
(x+8)(x-8)
- D.
(x+4)(x-16)
- 9.What is the axis of symmetry of f(x)=(x+1)^2+1?
- A.
X=1
- B.
X=2
- C.
X=-1
- D.
X=-2
- 10.Which of the following is equal to (x+2)(x+2) or (x+2)^2?
- A.
X^2+2x+4
- B.
X^2+4x+4
- C.
X^2+4x+2
- D.
X^2+4x-4
- 11.Which of the following quadratic functions has the narrowest graph?
- A.
F(x)=x^2
- B.
F(x)=1/2x^2
- C.
F(x)=4x^2
- D.
F(x)=1/4x^2
- 12.What is the turning point of the parabola?
- A.
Vertex
- B.
Origin
- C.
Line of symmetry
- D.
Axis
- 13.Which of the following trinomials is a perfect square trinomial?
- A.
X^2+8x+7
- B.
X^2-8x+16
- C.
X^2+8x+15
- D.
X^2+12x+27
- 14.Which of the following quadratic functions has the vertex at the origin?
- A.
F(x)=4x^2
- B.
F(x)=-3+14x^2
- C.
F(x)=(x-0)^2+2
- D.
F(x)=2(x-4)^2+5
- 15.What is the quadratic function with zeros 2 and -3?
- A.
F(x)=x^2+x-6
- B.
F(x)=x^2+5x-6
- C.
F(x)=x^2-x-6
- D.
F(x)=x^2-x+6
- 16.Which function is not quadratic?
- A.
F(x)=2x^2
- B.
F(x)=x-2
- C.
F(x)=x^2+4x-12
- D.
F(x)=5(x+3)^2
- 17.What are the roots of x^2-5x-6=0?
- A.
6 and -1
- B.
-6 and 1
- C.
-2 and -3
- D.
2 and 3
- 18.Find the solution set of the equation x^2+6x-7.
- A.
-1,-5
- B.
1,-7
- C.
-1,7
- D.
13,-19
- 19.The nature of roots of 3x^2+5x+1=0
- A.
Imaginary conjugates
- B.
Real,unequal,rational
- C.
Real,equal,rational
- D.
Real,unequal,irrational
- 20.What is the equation of the quadratic function whose graph is congruent to the graph of f(x)=x^2 with vertex at (0,3)?
- A.
F(x)=x^2+3
- B.
F(x)=-x^2+3
- C.
F(x)=x^2-3
- D.
F(x)=-x^2-3
- 21.The vertex is the minimum point when the parabola opens downward.
- A.
True
- B.
False
- 22.The polynomial of degree 2 is called square root function.
- A.
True
- B.
False
- 23.The vertex is the maximum point when the parabola opens upward.
- A.
True
- B.
False
- 24.The line of symmetry acts as a mirror which divides the parabola into two symmetrical parts.
- A.
True
- B.
False
- 25.The vertex of the quadratic function f(x)=ax^2 is at the origin.
- A.
True
- B.
False
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