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WorksheetsMOCK UP BRAINQUEST 2
Total questions: 166
Worksheet time: 3hrs 46mins
Which of the following equations is NOT a quadratic equation?
2x2 + 2 = 0
x2 + 4x = -4
4 = x2
x2 - 2x + 1
Which of the following equations is NOT a quadratic equation?
2x2 + 2 = 0
x2 + 4x = -4
64 = x2
x2 - 2x + 1
It is a polynomial equation of degree two that can be written in the form
ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.
Linear Equation
Linear Inequality
Quadratic Equation
Quadratic Inequality
In the quadratic equation 2x2 – 9x – 5 = 0, which is the quadratic term?
2x2
x2
– 9x
– 5
Solve by extracting the roots:
4m2 = 100
m=25, -25
m=96
m=-96
m=5, -5
Solve by extracting the roots:
3x2 = 192
-32 or 32
-8 or 8
-64 or 64
No Solution
Find the solutions of the equation x2 - 16 = 0 by extracting the square root.
x = 4 and x = -4
x = 4
x = -4
no answer
Find the roots of the quadratic equation 2s2 = 50.
s = 25 and s = -25
s = 5 and s = -5
s = 5 and s = 25
s = -5 and s= -25
What equation has the roots of x = 7 and x = -7?
x2 - 14 = 0
x2 - 49 = 0
x2 + 49 = 0
x2 = 14
What are the roots of the quadratic equation 3t2 = 12?
t =4 and t = -4
t = 2 and t = -2
t = 3 and t = -3
t = 9 and t = -9
What is the solution of the equation a2 – 60 = 21?
positive or negative 4
positive or negative 6
positive or negative 7
positive or negative 9
What is the first step in solving the quadratic equation x2−3=−2x ?
Factor the expression on left side of the equation.
Add 2x to both sides to set the equation equal to 0.
Use the zero product property.
Multiply both sides of the equation by 2x.
Which of the following properties must be used to solve for the quadratic equation (x−3)(x+2)=0 ?
Associative Property
Commutative Property
Inverse Property
Zero Product Property
What are the root/s of the quadratic equation x2+4x+4=0 ?
x = 2
x = -2
x = -4, 1
x = -4, -1
What are the solutions of the quadratic equation (x−3)(x+2)=0 ?
x=3,-2
x=-3,2
x=2,3
x=3,2
Solve for the root/s of x2−9x=0 by factoring.
9
0, 9
-9, 0
-9
x2+5x+6=0 are
Which of the following expressions is a perfect square trinomial?
2x² - 4x - 7
x² - 2x + 1
6x² - 9x - 2
x² - 4x - 8
What must be added to the equation x² - 4x = 0 to make it a perfect square trinomial?
4
-4
2
-2
Write the following quadratic expression in completed square form...
x2 + 4x + 10
(x + 4)2 + 6
(x + 2)2 + 6
(x + 4)2 - 6
(x + 2)2 - 6
The discriminant is...
ax2 +bx+c
b – 4ac
b2 +4ac
b2 – 4ac
The roots of x2 + 6x + 9 = 0 will be
real or imaginary
unequal and irrational
real, rational and unequal
real, rational and equal
Which is true for the equation x2−5x+12=0?
There are two real roots
There is one one repeated root
There are no real roots
There are two rational roots
What is the value of b2−4ac for equation p2=3p+2?
1
17
6
14
What is the value of the discriminant for the equation 4x2−12+9=0?
0
−12
144
1
What is the SUM of the roots of quadratic equation x2 + 13x + 42 = 0?
-42
-13
13
42
What is the PRODUCT of the roots of x2 – 15x + 26 = 0?
-26
-15
15
26
Determine the SUM of the roots of the given quadratic equation below:
−311
311
−34
Determine the PRODUCT of the roots of the given quadratic equation below:
−311
−34
34
Determine the SUM of the roots of the given quadratic equation below:
−23
23
−41
What is the sum of the roots of the quadratic equation x2+5x + 4 = 0 ?
4
5
-4
-5
What is the product of the roots of the quadratic equation x2−6x = 27 ?
-27
27
6
-6
1. All equations are mathematical statements that the quantities being compared are equal.
2. All quadratic equations are solvable by completing of squares.
Both statements are true.
Both statement are false.
Statement 1 is true; statement 2 is false.
Statement 1 is false; statement 2 is true.
Solve the following quadratic equation...
x2 + 9x + 20 = 0
x = -2
x = -10
x = -5
x = -4
x = -1
x = -20
x = 4
x = 5
What is another word for zeros?
y-intercepts
roots
vertex
axis of symmetry
In the quadratic formula, if b2-4ac>0, then the quadratic equation has
two imaginary solutions
two different real solutions
two equal real solutions
none of these
To complete the perfect square trinomial in the expression x2-22x+_____, we need to add
11
44
144
121
The graph of a quadratic function is called
a line
a hyperbola
a parabola
an ellipse
Complete the square for
x2 + 12x + ____
x2 + 12x + 144
x2 + 12x - 36
x2 + 12x + 36
x2 + +12x - 144
The area of a rectangular pathway is 350 sq. meters and its perimeter is 90 meters. What is the sum of the roots of quadratic equation?
450
90
440
80
Translate "three more a number is seventeen" into mathematical equation.
x + 3 = -17
x - 3 = 17
x + 3 = 17
x - 3 = -17
Translate: The square of a number is one hundred fifty more than five times a number.
x2 = 5x + 150
x2 = 5x + 50
2x = 5x + 150
x2 = 5x + 15
Ate Marwin and Ate Daisy are both working on the school canteen. Together they can finish cleaning the canteen in 4 hours. It takes ate Marwin working alone in 6 hours longer than it takes Ate Daisy working alone. Determine the quadratic equation formed on the given problem.
x2 + 6x + 12 = 0
x2 + 2x + 24 = 0
x2 - 6x + 12 = 0
x2 – 2x – 24 = 0
The length of a rectangle is 7 inches more than its width, its area is 228 square inches. Determine the length of the given rectangle.
18 m
19 m
20 m
21 m
Which of the following graph is the same as the interval [−5,4] ?
Which of the following is the same as the given graph?
(−2, 3)
[−2, 3]
undefined
(−∞, −2)∪(3, ∞)
Write the interval notation for the graph?
[-3, 2)
-3<x<2
(-∞, -3] U (2, ∞)
x > 2 or x < -3
It is a second-degree function of the form f(x)=ax2 + bx + c , where a, b, and c are real numbers and a = 0 .
Linear Function
Quadratic Function
Cubic Function
Constant Function
In a quadratic function in the form f(x)=ax2+bx+c , if a > 0, then the parabola opens ________.
upward
downward
to the left
to the right
The parabola has a turning point called the _______ which is either the lowest point or the highest point of the graph.
axis of symmetry
vertex
domain
range
The standard form of a quadratic equation is
y=x²
y=ax²+bx+c
y=mx+b
y=x
a, b, and c for
the quadratic equation:
4x2 – 8x = 3
What is the domain of the graph?
x > 0
y ≤ 8
All real numbers
No solution
What is the range of the graph?
x > 0
y ≤ 8
All real numbers
y >8
What is the equation of the axis of symmetry for this parabola?
x = −1
x = 0
y = −1
y = 5
What is the vertex (turning point) of this parabola?
(−1, 3)
(3, −1)
(5, 0)
(0, 5)
What is the vertex (turning point) of this parabola?
(−1, 0)
(3, 0)
(1, −4)
(−4, 1)
Which parent function is this?
Quadratic
Cubic
Linear
Rational
Which parent function is this?
Quadratic
Cubic
Linear
Rational
Which parent function is this?
Quadratic
Cubic
Linear
Rational
The following symbols are used to denote inequality except _______________________.
>
=
<
≥
Which of the following is an example of quadratic inequality?
2x² + 3x + 4 > 0
15x ≤ 10
x² - x +15 < -30
x² + 4x - 5 = 0
Which of the following odes not belong to the group?
x2 - 3x + 4 > 0
2x2 > 4
x2 + 6x < 3
x3 + 4x + 8 < 0
Which symbol indicates "is greater than" in quadratic inequality?
<
≤
>
≥
2x + 5 ≤ x − 3 , is
Quadratic inequality
Not quadratic inequality
b2 − 4b + 4 = 0 , is
Quadratic inequality
Not quadratic inequality
Which of the following is a quadratic inequality?
x2− x −6
3x2 − 4x − 7 = 0
(x −4)(x−2) > 0
x≤6
Which of the following is NOT a quadratic inequality?
(x−5)(x−1)>0
x2−2x −5≥0
x2 −2x +5=0
x2 − 8x − 16 ≤ 0
Write the inequality.
x >−1
x < −1
x≤−1
x≥−1
Write the inequality.
x < −1
x>−1
x≤−1
x≥−1
Write the inequality.
x<−1
x>−1
x≤−1
x≥−1
Write the inequality.
x<1
x>1
x≤1
x≥1
Write the inequality.
x<−1
x>−1
x≤−1
x≥−1
Graph the solution set on the number line.
x>2
Graph the solution set on a number line.
x≥−3
Graph the solution set on a number line.
x <−4
Write the statement in the form of equation. Use k as the constant of variation. (choose 1 equation only, use small letter and no spacing)
c is directly proportional to d
(a)
Write the statement in the form of equation. Use k as the constant of variation. (choose 1 equation only, use small letter and no spacing)
w varies directly as z
(a)
Does y varies directly as x? Type YES or NO
(a)
Does y varies directly as x? Type YES or NO (use capital letter)
(a)
Does y varies directly as x? Type YES or NO (use capital letter)
(a)
Does y varies directly as x? Type YES or NO (use capital letter)
(a)
Does y varies directly as x? Type YES or NO (use capital letter)
(a)
Solve for the unknown variable:
If y varies directly as x and y = 96 when x = 4, what is the value of y when x = 30?
(a)
Solve for the unknown variable:
If a varies directly as b and a = 12 when b = 20, what is the value of b if a = 123? (no space)
(a)
Solve for the unknown variable:
If z varies directly as r and z = 243 when r = 27. What is the value of z when r = 780? (do not use comma)
(a)
The distance covered by a moving object with a constant rate varies directly as the time it travelled. Milo walked 40 meters in 15 seconds. How long will it take him to walk 128 meters with a constant rate? (use small letter for the unit of measure, (a) seconds)
A school committee is assigned the task of selecting a DJ for their annual dance night. They were able to find a DJ who charges 5000 pesos for every 3 hours. How much will the school pay if the dance lasts for 9 hours? (use the word pesos in small letter as unit of measure, (a) pesos)
If y varies jointly with the product of x and z, and y = 105 when x = 5 and z = 7, find y when x = 9 and z = 10.
270
180
360
255
If y varies jointly with the product of x and z, and y = 1000 when x = 10 and z = 20, find y when x = 8 and z = 10.
100
200
300
400
The variable x is in joint variation with y and z. When the values of y and z are 4 and 6, x is 16. What is the value of x when y = 8 and z =12?
32
64
48
96
A is in joint variation with B and square of C. When A = 144, B = 4 and C = 3. Then what is the value of A when B = 6 and C = 4?
12
24
36
48
If a varies jointly as b and the square root of c, and a = 21 when b = 5 and c = 36, find a when b = 9 and c = 225.
126
196
256
289
z varies jointly with x and y. If x = 2, y = 3 and z = 4, find z when x = -6 and y = 2.
-6
-8
-10
-12
z varies jointly with x and y. If x = 5, y = -1, and z = 10. Find z when x = -1/2 and y = 7.
5
6
7
8
z varies jointly with x and y. If x = 7, y = 3 and z = -14, find y when z = -8 and x = 3.
3
4
5
6
z varies jointly with x and y. If x = 8, y = -3 and z = -6, find x when z = 12 and y = -16.
-3
-4
-6
-9
The equation for a Joint Variation is represented as:
y = kx
y = k/x
y = kxz
y = kx/z
Write the mathematical equation of the given statement: (no spacing, use / for fraction bar)
f is directly proportional to b and inversely proportional to e
(a)
Write the mathematical equation of the given statement: (no spacing, use / for fraction bar)
The time (t) needed to answer a set of problems is directly proportional to the number (N) of problems, and inversely proportional to the number of students (P) working on the solutions.
(a)
Solve for the constant of variation, k.
A varies directly as D and inversely as F. A=10.5, when D=2 and F=4
(a)
Solve for the constant of variation, k.
D is directly proportional to e2 and inversely proportional to f. D=12, when e=2 and f=7.
(a)
Given that z varies directly with y and inversely with x when x = 12, y=36 and z=15, find the value of z when x= -8 and y=24.
(a)
If a varies jointly as b and c, and inversely as d when a=140, b=5, c=4, and d=3, find a when b=10, c=8, and d=12.
(a)
The volume of gas varies directly as the temperature and inversely as the pressure. If the volume is 180 cu cm when the temperature is 270 K and the pressure is 15 lbs/sq cm, what is the volume when the temperature is 220 K and the pressure is 25 lbs/sq cm? (Write your final answer in this form: _ cu cm )
(a)
The resistance of a wire varies directly as its length and inversely as the square of the diameter. If a 15-ft long wire and a diameter of 1/2 inch has a resistance of 3 ohms, what is the resistance of a wire with a length of 25 ft and a diameter of 2 inches? (Write your final answer in fraction and of the form: _ ohms )
(a)
2−2
41
−41
3−2
91
61
4−3
641
461
5−1
5
51
3−4
91
811
Simplify
11−1
111
−11
11
12
4−21=
41
161
4
16
Simplify
3x5y−9
3x5y91
3x5y9
y93x5
x53y9
t−5r−2s3
r2s3t5
r2s3t5
r2s3t5
r2s3t51
Simplify
(3m−3n2)2
3m6n4
9m6n4
m53n4
m69n4
Rewrite using a positive exponent.
7−10
7101
710
7−101
-70
Simplify
−161
161
-16
16
2−1
21
11
-1
-2
Evaluate.
0
1
7
70
Rewrite as a positive exponent: 3−2
-2
-6
91
21
Rewrite as a positive exponent: 6−2
361
−12
61
121
Which is the same as 5−2
25
101
251
-25
921 is the same as
9 so the value is 3
9 × 2 1 so the value is 4.5
2521 is the same as
25 ÷ 2 so the answer is 12.5
25 so the answer is 5
100 is the same as
10031
10021
10×10
3100
2646
26
66
86
303903
33
1203
603
303
82162
22
42
82
242
