Problem 1 :
The box plot summarizes 15 data values. What is the median of this data set?
A) 2 B) 3 C) 5 D) 8
Solution :
Median is 5.
Problem 2 :
What is the x-intercept of the graph shown?
A) (−5, 0) B) (5, 0) C) (−4, 0) D) (4, 0)
Solution :
By observing the graph, the parabola touches the x-axis at 4.
So, the x-intercepts are (4, 0) and (4, 0).
Problem 3 :
Henry receives a $60.00 gift card to pay for movies online. He uses his gift card to buy 3 movies for $7.50 each. If he spends the rest of his gift card balance on renting movies for $1.50 each, how many movies can Henry rent?
A) 10 B) 25 C) 35 D) 40
Solution :
Number of movies he is busying = 3
Cost of each movie = $7.50
Cost spent for movies = 3(7.50)
= 22.5
Remaining money = 60 - 22.5
= 37.5
Number of movies renting = x
1.5x = 37.5
x = 37.5/1.5
x = 25
Problem 4 :
x = 49
y = √x+9
The graphs of the given equations intersect at the point (x, y) in the xy-plane. What is the value of y ?
A) 16 B) 40 C) 81 D) 130
Solution :
x = 49 ----(1)
y = √x+9 ----(2)
Applying the value of x in (2), we get
y = √49 + 9
= 7 + 9
= 16
So, the value of y is 16.
Problem 5 :
If 2x = 12, what is the value of 9x ?
Solution :
2x = 12
Dividing by 2 on both sides
x = 12/2
x = 6
Problem 6 :
Line k is defined by
y = (1/4)x + 1
Line j is parallel to line k in the xy-plane. What is the slope of j ?
Solution :
If two lines are parallel, then slopes will be equal.
y = (1/4)x + 1
Comparing with y = mx + b
Slope (m) = 1/4
Problem 7 :
6, 6, 8, 8, 8, 10, 21
Which of the following lists represents a data set that has the same median as the data set shown?
A) 4, 6, 6, 6, 8, 8 B) 6, 6, 8, 8, 10, 10
C) 6, 8, 10, 10, 10, 12 D) 8, 8, 10, 10, 21, 21
Solution :
6, 6, 8, 8, 8, 10, 21
The given data is arranged in ascending order.
Number of elements = 7
median = 8
So, option B is correct.
Problem 8 :
The length of the base of a certain parallelogram is 89% of the height of the parallelogram. Which expression represents the length of the base of the parallelogram, where h is the height of the parallelogram?
A) 89h B) 0.089h C) 8.9h D) 0.89h
Solution :
Let b be the base of the parallelogram and h be the height.
base = 89% of h
= 0.89 h
So, option D is correct.
Problem 9 :
For a camping trip a group bought x one-liter bottles of water and y three-liter bottles of water, for a total of 240 liters of water. Which equation represents this situation?
A) x + 3y = 240 B) x + y = 240
C) 3x + 3y = 240 D) 3x + y = 240
Solution :
x be the number of 1 liter bottle and y be the number of 3 liter bottle.
Quantity of water bottle = 240
1x + 3y = 240
So, option A is correct.
Problem 10 :
y = −4x + 40
Which table gives three values of x and their corresponding values of y for the given equation?
Solution :
When x = 0 y = −4x + 40 y = -4(0) + 40 y = 40 |
When x = 1 y = −4x + 40 y = -4(1) + 40 y = 36 |
When x = 2 y = −4x + 40 y = -4(2) + 40 y = 32 |
So, option B is correct.
Problem 11 :
The shaded region shown represents solutions to an inequality. Which ordered pair (x, y) is a solution to this inequality?
A) (0, −4) B) (0, 4) C) (−4, 0) D) (4, 0)
Solution :
(4, 0) is one of the point on the shaded region. So, option D is correct.
Problem 12 :
In triangle JKL , the measures of ∠K and ∠L are each 48°. What is the measure of ∠J, in degrees? (Disregard the degree symbol when entering your answer.)
Solution :
Sum of interior angles of triangle = 180°
∠J + ∠K + ∠L = 180°
∠J + 48 + 48 = 180°
∠J + 96 = 180°
∠J = 180° - 96°
∠J = 84°
Problem 13 :
y = x^{2} + 14x + 48
x + 8 = 11
The solution to the given system of equations is (x, y). What is the value of y ?
Solution :
y = x^{2} + 14x + 48 -----(1)
x + 8 = 11-----(2)
x = 11 - 8
x = 3
Applying the value of x in (1), we get
y = 3^{2} + 14(3) + 48
y = 9 + 42 + 48
y = 99
So, the value of y is 99.
Problem 14 :
A cleaning service that cleans both offices and homes can clean at most 14 places per day. Which inequality represents this situation, where f is the number of offices and h is the number of homes?
A) f + h ≤ 14 B) f + h ≥ 14 C) f - h ≤ 14 D) f - h ≥ 14
Solution :
At most 14 places, which means ≤ 14.
f is the number of offices and h is the number of homes
f + h ≤ 14.
Problem 15 :
Which expression is a factor of
2x^{2} + 38x + 10 ?
A) 2 B) 5x C) 38x D) 2x^{2}
Solution :
= 2x^{2} + 38x + 10
= 2(x^{2} + 19x + 5)
So, the common factor is 2.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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