Question 11 :
Express 6.925 x 10^{5} in standard form.
Solution :
= 6.925 x 10^{5}
= 6.925 x 100000
= 692500
Question 12 :
On the number line above, X is located at -10, Y is at -2, and Z is at 8. M (not shown) is the midpoint of XY, and N (not shown) is the midpoint of YZ. What is the midpoint of MN?
Solution :
Y is located at -2 and X is located at -10.
Numbers between X and Y are
-2, -3, -4, -5, -6, -7, -8, -9, -10
The midpoint of these two numbers is -6.
So, M is located at -6.
Numbers between Y and Z are
-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8
So, N is located at 3.
Now, let us write the numbers between -6 and 3.
-6, -5, -4, -3, -2, -1, 0, 1, 2, 3
-1.5 is the midpoint of MN.
Question 13 :
If 0 < y < 1, which of the following statements must be true?
(A) y^{2} > y^{3} (B) y > 0.5y (C) y > y^{3}
(D) All of the above (E) None of the above
Solution :
Let x = 0.5
By applying the value of y in option A, we get
0.25 > 0.125 True
By applying the value of y in option B, we get
0.5 > 0.5 (0.5)
0.5 > 0.25 True
By applying the value of y in option C, we get
0.5 > (0.5)^{3}
0.5 > 0.125 True
Hence all of the above is true.
Question 14 :
The area of the square ABCD is 4 times larger than the area of square WXYZ. If the area of square WXYZ is 9, what is the difference between the length of a side of square ABCD and the length of a side of square WXYZ?
Solution :
Area of the square ABCD = 4 Area of the square WXYZ
Area of the square WXYZ = 9
a^{2} = 9
a = 3
Side length of square WXYZ = 3
Area of the square ABCD = 4(9) = 36
s^{2} = 36
s = 6
Difference between side length of ABCD and WXYZ
= 6 - 3
= 3
Question 15 :
Triangle GHI is similar to Triangle JKL.
What is the length of side JK?
Solution :
Since the above triangles are similar, the length of the sides are in the same ratio.
GI/JL = GH/JK = IH/ LK
(3x/4)/x = 12/JK = IH/LK
3/4 = 12/JK
JK = 12(4)/3
JK = 16
Question 16 :
Wesley and two of his friends are driving cross country nonstop and have agreed to take turns driving in 7-hours shifts. Each person will drive for one shift, and take two shifts off to rest. If Wesley’s first shift starts at 6:00 a.m., at what time will Wesley complete his third shift?
Solution :
1st shift 6 AM - 1 PM 1 PM - 8 PM 8 PM - 3 AM |
2nd shift 3 AM - 10 AM 10 AM - 5 PM 5 PM - 12 AM |
3rd shift 12 AM - 7 AM |
Hence the required answer is 7 : 00 AM.
Question 17 :
What is the difference between the largest and lowest integer in the sequence of consecutive odd integers whose sum is 15 ?
Solution :
Let us select three numbers 3, 5 and 7.
3 + 5 + 7 = 15
Difference between largest and lowest integer
= 7 - 3
= 4
Hence the answer is 4.
Question 18 :
The half life of a substance is the time it takes for a substance to decrease to half its initial amount. John has a pile of goo that decreases in amount at a constant rate. If John initially had 100 pounds of goo, and ten days later, he only had 25 pounds of goo, what is the half of the goo ?
Solution :
In 10 days, the goo decreased by 2 half lives. So each life is 5 days.
Question 19 :
What is the value of (9^{4} - 8^{4})/(9^{2} + 8^{2}) ?
Solution :
(9^{4} - 8^{4})/(9^{2} + 8^{2}) = [(9^{2})^{2} - (8^{2})^{2}] / (9^{2} + 8^{2})
= [(9^{2} + 8^{2}) (9^{2} - 8^{2})] / (9^{2} + 8^{2})
= 9^{2} - 8^{2}
= 81 - 64
= 17
Hence the answer is 17.
Question 20 :
Jackie fills a jug with water continuously. It takes her 2 minutes to fill up 50% of the empty space in the jug with water. After every 2 minutes, she puts a penny into a jar to celebrate. How many pennies will she have in the jar at the instant the jug has less than 30% empty space left ?
Solution :
Now Jackie starts to fill the jug. At the first round, he fills 50% of empty space in the jug in 2 minutes and drop a penny.
Now the jug contains 50% of empty space. If he fills half of the 50% of empty space at that instant, the quantity of water will become 75%. Hence the condition will not satisfy, by filling water in the second round.
So, there is only 1 penny in the jar at the instant the jug has lesser than 30% of empty space.
More Practice Test Papers
SHSAT math practice test - Paper 1
SHSAT math practice test - Paper 2
SHSAT math practice test - Paper 3
SHSAT math practice test - Paper 4
SHSAT math practice test - Paper 5
SHSAT math practice test - Paper 6
SHSAT math practice test - Paper 7
SHSAT math practice test - Paper 8
SHSAT math practice test - Paper 9
SHSAT math practice test - Paper 10
SHSAT math practice test - Paper 11
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