Problem 1 :
Which expression is a factor of 10x^{2} - 19x + 6 ?
A) 10x - 3 B) 10x - 1 C) 5x - 3 D) 5x - 2
Solution :
10x^{2} - 19x + 6
10x^{2} - 15x - 4x + 6
5x(2x - 3) - 2(2x - 3)
(5x - 2) (2x - 3)
So, option D) is correct.
Problem 2 :
The table shows the linear relationship between the distance in feet below sea level and the time in seconds traveled by a submarine.
Submarine
What is the rate of change of the distance in feet below sea level with respect to time that the submarine traveled ?
Record your answer and fill in the bubbles on your answer document.
Solution :
The rate of change of distance with respect to time
difference between two consecutive observed distances/time taken
= (604 - 460)/(18 - 0)
= 144/18
= 8 feet/second
Problem 3 :
Which equation best represents the line shown on the grid ?
A) y = 0 B) y = -6 C) x = 0 D) x = -6
Solution :
By observing the figure,
The equation of the line is y = -6
So, option B) is correct.
Problem 4 :
An insect population after x months can be modeled by the function g(x) = 18(1.3)^{x}. Which statement is the best interpretation of one of the values in this function ?
F) The inspect population increased by 13 insects each month.
G) The inspect population decreased by 13 insects each month.
H) The inspect population increased at a rate of 30% each month.
J) The inspect population decreased at a rate of 30% each month.
Solution :
g(x) = 18(1.3)^{x}
Let x = 1 and x = 2
g(1) = 18(1.3)^{1}
g(1) = 23.4 --- (1)
g(2) = 18(1.3)^{2}
= 18 × 1.69
g(2)= 30.42 --- (2)
Subtract (2) and (1), we get
30.42 - 23.4 = 7.02
= 7.02 --- (3)
Statement F) and G) are false.
Let check the statement H) and J).
Dividing (3) and (1) we get,
= 7.02/23.4
= 0.3
= 0.3 × 100
= 30%
The inspect population increased at a rate of 30% each month.
So, option H) is correct.
Problem 5 :
The graph of y = -(1/6)x - 4 is shown on the grid.
Which ordered pair is in the solution set of y > -(1/6)x - 4 ?
A) (-8, 8) B) (6, -5) C) (4, -6) D) (-2, -7)
Solution :
y > -(1/6)x - 4
Check the ordered pair that satisfy the inequality.
Point (-8, 8) ==> x = -8, y = 8
8 > -(1/6) × (-8) - 4
8 > 8/6 - 4
8 > 4/3 - 4
8 > (4 - 12)/3
8 > -8/3
(-8, 8) is a solution of y > -(1/6)x - 4.
y > -(1/6)x - 4
Check the ordered pair that satisfy the inequality.
Point (6, -5) ==> x = 6, y = -5
-5 > -(1/6) × 6 - 4
-5 > -1 - 4
-5 > -5
(6, -5) is not a solution of y > -(1/6)x - 4.
y > -(1/6)x - 4
Check the ordered pair that satisfy the inequality.
Point (4, -6) ==> x = 4, y = -6
-6 > -(1/6) × 4 - 4
-6 > -4/6 - 4
-6 > -2/3 - 4
-6 > (-2 - 12)/3
-6 > -14/3
(4, -6) is not a solution of y > -(1/6)x - 4.
y > -(1/6)x - 4
Check the ordered pair that satisfy the inequality.
Point (-2, -7) ==> x = -2, y = -7
-7 > -(1/6) × (-2) - 4
-7 > 2/6 - 4
-7 > 1/3 - 4
-7 > (1 - 12)/3
-7 > -11/3
(-2, -7) is not a solution of y > -(1/6)x - 4.
Then, the required solution is (-8, 8).
So, option A) is correct.
Problem 6 :
The conversion of degrees Celsius to degrees Fahrenheit can be represented by a linear relationship. The graph shows the linear relationship between y, the temperature in degrees Fahrenheit, and x, the temperature in degrees Celsius from the freezing point of water.
Which equation best represents this situation ?
F) y = 5/9 x H) y = (5/9)x + 32 |
G) y = 9/5 x J) y = (9/5)x + 32 |
Solution :
Slope (m) = (y_{2} - y_{1})/(x_{2} - x_{1})
Two points (x_{1}, y_{1}) (x_{2}, y_{2}) = (0, 32) (40, 104)
= (104 - 32)/(40 - 0)
= 72/40
= 36/20
(m) = 9/5
y = mx + b
y = (9/5)x + 32
So, option J) is correct.
Problem 7 :
Which graph best represents the solution set for this system of inequalities ?
x + 2y < -2
y - x < 3
Solution :
In the given options , only option B and C will have dotted lines.
x + 2y < -2
y - x < 3
Select one of the points from the shaded region from B,
(2, 2)
2 + 2(2) < -2
8 < -2 (False)
So, option B is not correct.
Select one of the points from the shaded region from C,
(-2, -2)
-2 + 2(-2) < -2
-8 < -2 (True)
y - x < 3
-2 - (-2) < 3
-2 + 2 < 3
0 < 3 (True)
So, option C is correct.
Problem 8 :
Which graph best represents h(x) = (x + 1) (x - 3) ?
Solution :
h(x) = (x + 1) (x - 3)
When h(x) = 0, x-intercepts are -1 and 3. Both options F and H are having the same x-intercepts.
Finding vertex :
h(x) = (x + 1) (x - 3)
h(x) = x^{2} - 2x - 3
h(x) = x^{2} - 2x(1) + 1^{2} - 1^{2} - 3
h(x) = (x - 1)^{2} - 4
Vertex is at (1, -4). So, option F is correct.
Problem 9 :
The first six terms in a geometric sequence are shown, where a_{1} = -4.
-4
-16
-64
-256
-1,024
-4,096
…
Based on this information, which equation can be used to find the n^{th} term in the sequence, a_{n} ?
A) a_{n} = -4n B) a_{n} = -(4)^{n }C) a_{n} = -n^{2 }D) a_{n} = (-4)^{n}
Solution :
By observing all six terms are having negative signs, and it is geometric sequence,
Given, a_{1} = -4
a_{2} = -(4)^{2} = -16
a_{3} = -(4)^{3} = -64
⁞
a_{n} = -(4)^{n}
So, option B) is correct.
Problem 10 :
What is the solution to 4(q + 56.5) = 30q - 112 ?
Record your answer and fill in the bubbles on your answer document.
Solution :
4(q + 56.5) = 30q - 112
4q + 226 = 30q - 112
4q - 30q = -226 - 112
-26q = -338
q = 338/26
q = 13
Problem 11 :
Which expression is equivalent to 36m^{2} - 100 ?
A) (9m - 20) (4m + 5) B) 4(3m - 5) (3m + 5)
C) 2(2m - 5) (9m + 10) D) 4(3m - 5)^{2}
Solution :
36m^{2} - 100 = 4(9m^{2} - 25)
= 4((3m)^{2} - 5^{2})
= 4(3m + 5) (3m - 5)
So, option B) is correct.
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