WorksheetsMath 9 Final Exam draft
Total questions: 162
Worksheet time: 8hrs 12mins
Find the angles b, c and d.
b=80o, c=42o, d=80o
b=42o, c=58o, d=80o
b=42o, c=42o, d=80o
Find the colored angle B
< B=120o
< B=45o
< B=60o
In a group of 20 children, 11 have a scooter and 13 have a pair of roller skates. 4 children have neither. Use a Venn diagram to find how many children have both.
x = 16
x = 24
x = 8
On the following diagram, shade these sets: (A ∪ B)′
Write this recurring decimal as fraction in the simplest form:
0.8˙98
908
998
Write this recurring decimal as fraction in the simplest form:
0.73˙10066
9966
9066
Solve the following equation by factorizing: 5x2 − 125 = 0
x=±5
x=±25
x=±125
Complete the square for Quadratic formula, giving your answers in surd form: x2 − 8x + 11=0
x=4+√5
x=4±√5
x=4−√5
Use the quadratic formula to solve the equation:
x2 + 3x + 2 = 0
1, 2
1, -2
-1, -2
Use the quadratic formula to solve the equation, your answers correct to (3 s.f.):
2x2 − 4x + 1 = 0
x = 1.71 or x = 0.293
x = -0.293 or x = -1.71
x = -0.293 or x = 0.293
Solve the equation: 2x2 + 8x = 0
x=±4
x= -4 or x= 0
x= 4 or x = 0
Solve the quadratic inequality and represent the solution set on a number line:
2x2 > 18
Solve the quadratic inequality and represent the solution set on a number line:
x2 + x − 2 ≤ 0
1. Which of the following is a quadratic equation?
4x – 12
3x² - 9 = 0
x⁵ = 4x – 1
2x³ = 3x
2. The highest degree of the equation 4x = 3x² + 8 is?
2
4
3
8
3. What is the value of a in 2x(x – 3) + 7 = 0?
2
1
3
7
4. What are the roots of x² = 25?
±3
±2
±5
±4
5. If (x – 4) is a factor of x² - 5x + 4 = 0, what is the other factor?
x + 2
x - 4
x + 1
x - 1
6. What is the missing term of x² + 8x to make it a perfect square trinomial?
4
16
9
25
7. In the given 6x² = 10 + 11x, what is the value of b?
-11
6
-10
11
8. The graph of a quadratic function is called _____.
straight line
circle
parabola
ellipse
9. The vertex of a quadratic function is
(x,y)
(a,b)
x = h
(h,k)
10. If the parabola opens upward the point/vertex is at
maximum
minimum
low
high
11. In the function y = -x² - 4x + 7, what is the value of h?
-2
4
2
7
12. What is the discriminant in the equation x² - 2x + 1 = 0?
0
25
1
8
13. Without solving for the roots, give the sum of the roots of the equation x² - 4x – 21 = 0.
-4
1
4
-1
14. What is the product of the roots in the equation 6a² - 5a = 21?
72
−27
−72
27
15. The equation of the roots (2, 3) is
x² + 5x + 6 = 0
x² - x – 6 = 0
x2+x−6=0
x² - 5x + 6 = 0
What are the values of a, b and c in the equation 5 = (4x + 1)² + 6?
2, 8 and 16
-16, 8 and 2
8, 2 and 16
16, 8 and 2
Find the roots of 2x² - 14 = 18
±2
±4
±3
±5
What is the nature of the roots in x² - 4x = -5
imaginary
real, rational and unequal
real, rational and equal
real, irrational and unequal
The perimeter of a rectangular garden is 36 ft. and the area is 80 ft. Find the dimensions of the garden.
w = 8 ft.; l = 9 ft.
w = 8 ft.; l 10 ft.
w = 7 ft.; l = 8 ft.
w = 9 ft.; l = 10 ft.
What is the sum and product of the equation (a – 4)(a – 2) = 8?
4 and 20
6 and -72
6 and 80
20 and 8
What is the sum and product of the roots of quadratic equation 2x² = 5x + 3?
25and −23
25and 23
−25and 23
−25and −23
Determine the axis of symmetry in f(x) = -2x² + 3x – 1.
−43
43
34
−34
What is the vertex of the parabola of the function y – 4 = 4x² - 8x?
(1, 0)
(-1, 4)
(2, -1)
(-4, -3)
What are the roots/zeros of the function y = 2x² - 3x – 5?
52 and 1
5 and 2
2 and 1
25 and −1
What are the values of a, b and c in 3(x – 2)² = 6?
3, 12 and 6
-3, 12 and 6
3, -12 and 6
3, 12 and -6
Every Quadratic equation has exactly one root
A quadratic equation ax2 + bx + c = 0 has equal roots, then b2 - 4ac = 0
How many solutions can a quadratic have?
1 solution
3 solutions
0 solutions
2 solutions
If discriminant of a quadratic equation is negative, then roots of the equation are __________.
Distinct Roots
Equal roots
Unequal roots
none
a, b, and c for
the quadratic equation:
4x2 – 8x = 3
What is a second degree polynomial equation?
Linear Equations
Quadratic Inequalities
Quadratic Equations
Quadratic Functions
Which of the following is an example of quadratic equations?
x + 9 = 0
x + y =12
x3 + 5x2 - 14 =0
x2 - 2x = 7
Which of the following is NOT an example of quadratic equations?
2x2 - 3 = 2x
-8x - 15 = -x2
x + 3y = 45
x2 + 7x + 10 = 0
Check all the examples of quadratic equations.
y2 - 8y + 16 = 0
x = 15
x2 - 12 = 4x
y - 6 = y2
What is the standard form of 9x - 16 = 3x - x2?
x2 +12x -16 = 0
2x2 + 9x -16 = 0
x2 + 6x -16 = 0
-x2 + 6x - 16= 0
Check whether the following is quadratic equation: (2x−1)(x−3)=(x+5)(x−1)
YES
NO
x2 + 6x - 13 = 3
x2 + 6x - 13 = 3
Solve by factoring: x2 = 7x + 18
-7 and -18
9 and 2
9 and -2
2 and 7
x2 + 4x - 40 = -8
Solve by the Extraction of Roots method: x2 = 16
± 4
± 8
4
8
Solve by the Extraction of Roots method: -5x2 = -50
± 5
± 10
± √10
-10
a2 + 10a + 21 = 0
What is the standard form of a quadratic equation?
y = mx + b
y = a(x - h)2 + k
ax2 + bx + c = 0
ax2 + bx = c
What is the standard form of the quadratic equation
x2 -2x = 5 ?
x2 - 2x + 5 = 0
x2 +2x - 5 = 0
x2 +2x + 5 = 0
x2 -2x - 5 = 0
What is the value of "a" in the quadratic equation 7x + 1 = - x2 ?
7
-7
1
-1
Between what two numbers does the 45 fall?
6 and 7
7 and 8
8 and 9
9 and 10
What are the roots / solutions of the quadratic equation x2 - 10 = 15 ?
x = + 3
x =+ 5
x =+ 7
x = 0 and x = 5
What are the factors AND solutions of x2 + 2x – 3 = 0
(x - 2)(x + 1) = 0;
x=2, x=-1
(x + 2)(x - 1) = 0; x=-2, x=1
(x + 1)(x - 3) = 0; x=-1, x=3
(x - 1)(x + 3) = 0; x=1, x=-3
What must be added to
x2 – 8x + _______ to make it a perfect square trinomial?
8
16
64
-64
What is the first step to solving THIS equation by completing the square? a2 + 10a + 21 = 0
Set the equation equal to zero
Divide 10 by 2 and add the result to both sides
Add a2 and 10a together
Subtract 21 both sides
The graph of a quadratic function is called ____________.
a line
a parabola
a hyperbola
a cubic
A parabola has a vertex at (-3,2). Where is the axis of symmetry?
y = -2
x = 3
x = -3
y = 2
Which transformation transforms the graph of f(x) = x2 to the graph of g(x) = (x + 4)2?
a vertical translation 4 units up
a vertical translation 4 units down
a horizontal translation 4 units to the left
a horizontal translation 4 units to the right
Write an equation
The distance D travelled by a car is directly proportional to its speed s.
D=ks
D=k/s
K=Ds
S=kd
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.
180
255
270
360
Simplify: (-4r5)(2r8)
-8r13
-8r40
-2r13
2y40
If f varies directly as g and inversely as the square of h, and f = 20 when g = 50 and h = 5, what is the value of the constant k?
2
5
8
10
Identify the shaded area...
A
B
A'
B'
Identify the shaded area...
A
B
A'
B'
Identify the shaded area...
A
B
A'
B'
Identify the shaded area...
A∩B
A∪B
A'∩B'
A'∪B'
Identify the shaded area...
A∩B
A∪B
A'∩B'
A'∪B'
Which one of the following illustrates the Commutative Law of Addition?
5 + 7 = 7 + 5
5 + 7 = 4 + 8
5 + 7 = 3 + 9
5 + 7 = 10 + 2
Which of the following illustrates the Commutative Law of Multiplication?
3 x 4 = 6 x 2
3 x 4 = 12 x 1
3 x 4 = 2 x 6
3 x 4 = 4 x 3
What is the distributive property?
For any numbers a, b, c,
a(b + c) = ab + ac
For any numbers a, b, and c,
a(b + c) = a + (b + c)
For any numbers a, b, c,
abc = a + b + c
For any number a, b, and c,
a(b + c ) = a(c + b)
How can 5(3 +2) be expressed using the distributive property?
5(3) x 5(2)
(5 x 3) x (5 x 2)
5(3) + 5(2)
(5 + 3) x (5+2)
-2 + 4
-2
2
0
-4
Given a=b+c , solve for b .
b=c−a
b=a+c
undefined
Given m−n=p , solve for m .
m=np
m=p−n
m=p+n
Given 2m+n=r , solve for m .
m=2r−n
m=r−n−2
m=2r−n
Given n=2rt , solve for r .
r=n−2t
r=2tn
r=t2n
Solve 3 - 7x = 5
X = 5 - 7
X = 7x - 5
X= 84
X = −72
x2 - 16
(x + 4) (x - 4)
(x + 8) (x - 2)
(x + 4)2
x + 4(x - 4)
x2 - 9
(x + 3)2
(x + 3) (x - 3)
(x - 3)2
x + 3(x - 3)
49x2 - 144y2
(7x + 16y) (7x - 16y)
(7x + 12y)2
(12x + 7y) (12x - 7y)
(7x + 12y) (7x - 12y)
x2 + 7x - 30
x2 + 9x - 36
Factor
r2 -16r + 60
(r - 15)(r + 4)
(r - 6)(r + 10)
(r - 6)(r - 10)
(r +30)(r - 2)
What are the three types of special parallelograms?
Rectangle, Square, and Rhombus.
Rectangle, Trapezoid, and Square.
Square, KIte, and Square.
Kite, Trapezoid, and Rhombus.
if quadrilateral MARY is a parallelogram, what is the measure of the segment RY if the segment MA = 42 cm?
42
21 units
42 cm
21
Which of the following is not example of similar fractions?
31 and 32
82 and 84
22 and 99
53 and 59
x - 4 is the?
Radicand
index
Radical symbol
Exponent
3 is the?
Radicand
index
Radical symbol
Exponent
The base angles of an isosceles trapezoid are congruent.
TRUE
FALSE
SOMETIMES TRUE
ALWAYS TRUE
The diagonals of a kite are supplementary.
TRUE
FALSE
SOMETIMES TRUE
ALWAYS TRUE
Median of a triangle is a segment joining the midpoints of the two sides of a triangle.
TRUE
FALSE
SOMETIMES TRUE
ALWAYS TRUE
Square has all of the properties of the parallelogram and the rectangle and the rhombus.
TRUE
FALSE
SOMETIMES TRUE
ALWAYS TRUE
The diagonals of rectangle are congruent.
TRUE
FALSE
SOMETIMES TRUE
ALWAYS TRUE
Each diagonal of a rhombus bisects (a) .
The base angles of an isosceles trapezoid are (a) .
A quadrilateral is a parallelogram if both pairs of (a) sides are congruent.
(a) are referred to as the angles created by a base and a leg of a trapezoid.
If a parallelogram has four right angles, it is (a) .
if the measurement of angle J = 14 degrees, what is the measurement of angle E?
14 degrees
7 degrees
4 degrees
10 degrees
if the diagonal LF = 18 cm, what is the measurement of the diagonal ET?
18 cm
9 cm
8 cm
10 cm
if angle R = 5 degrees and angle M = 8 degrees, what is the measurement of angle Y?
18 cm
9 cm
8 cm
10 cm
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
If angle Y = 34 degrees, what is the measurement of angle 1?
45 degrees
34 degrees
90 degrees
17 degrees
if segment MZ = 128 cm, what is the measurement of segment LV?
128 cm
256 cm
64 cm
64
2y + 5 = 25
y = 15
y = 10
y = 7.5
y = 60
Solve for b 42b = 8
b = 32
b = 6
b = 16
b = 4
Solve for k 16 − 2k = 20
k = 2
k = 18
k = −18
k = −2
k −12 = 6 Solve for k
k = 72
k = 2
k = −2
k = −18
-5x = 25
4x + 1 = 7x - 5
6(2x + 1) = 18
7x + 19 = -2x + 55
2(2x + 3) = -6(x + 9)
19 - 2k = 3k - 1
+3k +3k
19 + 1k = -1
-19 -19
k = -20
solve for m:
32(9m−6)=20m=4
m=3
m=2
m=8
Solve for x:
50=45(3x−8)x=316
x=16
x=4
x = 415
Solve the following for x: 0.4x + 1.6 = -1.6x + 53.2
25.8
-25.8
27.4
54.8
Solve: x - 24.1 = -18.4
-5.7
42.5
-42.5
5.7
Solve the following for x: 0.4x + 1.6 = -1.6x + 53.2
25.8
-25.8
27.4
54.8
The definition of a circle is
set of all points in a plane that are the same distance from a point called the center
the distance around a share
a large figure
a pizza, orange, plum, or watermelon
Identify the region of PAQ
radius
minor arc
minor sector
minor segment
