Problem 41 :
Which expression represents the perimeter of the triangle?
A) 9k + 36 B) 10k + 25 C) 20k + 25 D) 24k + 36
Solution :
Perimeter = 3k + 5 + 2k + 16 + 15 + 4k
= 3k + 2k + 4k + 5 + 16 + 15
= 9k + 36
So, option A is correct.
Problem 42 :
The length of a rectangle is 6 units longer than the width, w. Which choice is a correct expression for the perimeter of the rectangle?
A) 2w + 6 B) 2w + 12 C) 4w + 6 D) 4w + 12
Solution :
Perimeter of the rectangle = 2(length + width)
Width be w, length = w + 6
Perimeter = 2(w + 6 + w)
= 2(2w + 6)
= 4w + 12
So, option D is correct.
Problem 43 :
Jane wants to visit her sister.
Which expression shows how much Jane will spend for gas on the trip to her sister’s house?
Solution :
Distance covered = x miles
Cost of gas = 3.50 per gallon
Money spent = distance covered x cost per gallon
= 3.50
In the total distance of 1000 miles, he covered x miles.
= (x/1000)
Jane will spend = 3.50(x/1000)
So, option B is correct.
Problem 44 :
Suppose that a stove and a freezer together weigh at least 370 pounds. The weight of the stove is 170 pounds. Which inequality correctly describes these conditions for the weight of the freezer, f ?
A) f ≥ 200 B) f > 200 C) f ≤ 200 D) f < 200
Solution :
Let s be the weight of stove
s + f ≥ 370
Wight of stove = 170
f ≥ 370 - s
f ≥ 370 - 170
f ≥ 200
So, option A is correct.
Problem 45 :
The Wilsons want to put outdoor carpet on their porch
How much carpet will be needed for their porch?
A) 42 ft^{2} B) 72 ft^{2} C) 108 ft^{2} D) 144 ft^{2}
Solution :
The top part is rectangle and bottom part is square.
Area of the given shape = Area of square + area of rectangle
= 6 x 6 + 12 x 6
= 36 + 72
= 108
= 108 ft^{2}
So, option C is correct.
Problem 46 :
What is the volume of the right rectangular prism below?
Solution :
Volume of rectangular prism = 2 x 1 1/4 x 1 1/2
= 2 x 5/4 x 3/2
= 15/4
= 3 3/4
So, option C is correct.
Problem 47 :
In the graph below, each grid square represents one square yard.
What is the area of the shaded figure?
A) 20 yd^{2} B) 30 yd^{2} C) 36 yd^{2} D) 40 yd^{2}
Solution :
Area of triangle + are of parallelogram
= ( 1/2) x base x height + base x height
= (1/2) x 5 x 4 + (5 x 4)
= 10 + 20
= 30 yd^{2}
So, option B is correct.
Problem 48 :
Abby is making a decoration. When folded, the decoration is a triangular pyramid made of four congruent equilateral triangles. Approximately, what is the surface area of Abby’s decoration?
A) 64 in^{2} B) 85 in^{2} C) 97 in^{2} D) 170 in^{2}
Solution :
From the figure, height of the triangle = 6.06, base = 7
Area of 1 triangle = (1/2) x 7 x 6.06
= 21.21
Area of 4 triangles = 4 (21.21)
= 84.84
= 85 in^{2}
So, option B is correct.
Problem 49 :
Katherine earned 84, 92, 84, 75, and 70 on her first 5 tests. What is the minimum grade Katherine needs to earn on the next test to have a mean of 84?
A) 81 B) 84 C) 95 D) 99
Solution :
Let x be the unknown score.
(84 + 92 + 84 + 75 + 70 + x)/6 = 84
405 + x = 84(6)
x = 504 - 405
x = 99
So, the answer is option D.
Problem 50 :
The weather station recorded the high temperature each day for 30 days. The graph of the temperature data is shown below.
In which interval is the median temperature?
A) 41–50 B) 51–60 C) 61–70 D) 71–80
Solution :
= (3 + 8 + 6 + 7 + 4 + 2)
= 30 (even)
then average of 15th and 16th term will be median.
So, median is 51-60.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM