Question

shsat summer math workbook - lesson 1 homework

1. at 8 a.m. the temperature was \\(-4^{\circ}\\). if the temperature rose 7 degrees during the next hour, what was the thermometer reading at 9 a.m.?

(a) \\(-11^{\circ}\\)
(b) \\(+7^{\circ}\\)
(c) \\(+3^{\circ}\\)
(d) \\(-3^{\circ}\\)

1. in asia, the highest point is mount everest, with an altitude of 29,002 feet, while the lowest point is the dead sea, 1,286 feet below sea level. what is the difference in their elevations?

(a) 27,716 feet
(b) 30,288 feet
(c) 28,284 feet
(d) 30,198 feet

1. find the product of \\((-6)(-4)(-4)\\) and \\((-2)\\).

(a) \\(-16\\)
(b) \\(+16\\)
(c) \\(-192\\)
(d) \\(+192\\)

1. the temperature in maxs bedroom was \\(32^{\circ}\\) at 9:00 a.m. if the temperature then started decreasing by \\(5^{\circ}\\) every hour for 10 hours, what is the temperature at 5:00 p.m.?

(a) \\(-40^{\circ}\\)
(b) \\(-13^{\circ}\\)
(c) \\(-8^{\circ}\\)
(d) \\(8^{\circ}\\)

1. the temperatures reported at hour intervals on a winter evening were \\(+4^{\circ}\\), \\(0^{\circ}\\), \\(-1^{\circ}\\), \\(-5^{\circ}\\) and \\(-8^{\circ}\\). find the average temperature for these hours.

(a) \\(-10^{\circ}\\)
(b) \\(-2^{\circ}\\)
(c) \\(+2^{\circ}\\)
(d) \\(-2\frac{1}{2}^{\circ}\\)

1. \\((-8) - (-13) =\\)

(a) \\(-21\\)
(b) \\(-5\\)
(c) 5
(d) 21

1. for which value of \\(k\\) is the value of \\(k(k-2)(k+1)\\) negative?

(a) \\(-2\\)
(b) \\(-1\\)
(c) 0
(d) 2

1. \\(|-9| - |5| + |-4| =\\)

(a) \\(-18\\)
(b) \\(-10\\)
(c) 8
(d) 10

Explanation:

Solve Questions 1 to 4

1. Initial temperature is \(-4^\circ\). It rises by \(7^\circ\):

$$-4 + 7 = 3^\circ$$

Matches option (C).

1. Mount Everest is at \(29,002\) feet. Dead Sea is at \(-1,286\) feet. The difference is:

$$29,002 - (-1,286) = 29,002 + 1,286 = 30,288\text{ feet}$$

Matches option (B).

1. Product of four negative numbers:

$$(-6) \times (-4) \times (-4) \times (-2) = 24 \times 8 = 192$$

Since there are four negative signs, the product is positive.
Matches option (D).

1. Initial temperature is \(32^\circ\) at 9:00 A.M. From 9:00 A.M. to 5:00 P.M. is 8 hours.

The temperature decreases by \(5^\circ\) every hour:

$$32 - (5 \times 8) = 32 - 40 = -8^\circ$$

Matches option (C).

Solve Questions 5 to 8

1. The temperatures are \(+4^\circ, 0^\circ, -1^\circ, -5^\circ, -8^\circ\).

Sum of temperatures:

$$4 + 0 + (-1) + (-5) + (-8) = -10$$

Average temperature over these 5 hours:

$$\frac{-10}{5} = -2^\circ$$

Matches option (B).

1. Subtracting a negative number:

$$(-8) - (-13) = -8 + 13 = 5$$

Matches option (C).

1. Evaluate \(k(k-2)(k+1)\) for each option:

• For \(k = -2\): \((-2)(-2-2)(-2+1) = (-2)(-4)(-1) = -8\) (negative)
• For \(k = -1\): \((-1)(-1-2)(-1+1) = 0\)
• For \(k = 0\): \(0(0-2)(0+1) = 0\)
• For \(k = 2\): \(2(2-2)(2+1) = 0\)

Matches option (A).

1. Evaluate absolute values:

$$|-9| - |5| + |-4| = 9 - 5 + 4 = 8$$

Matches option (C).

Answer:

Question 1

• (A) \(-11^\circ\)
• (B) \(+7^\circ\)
• (C) \(+3^\circ\) (Correct answer)
• (D) \(-3^\circ\)

Question 2

• (A) 27,716 feet
• (B) 30,288 feet (Correct answer)
• (C) 28,284 feet
• (D) 30,198 feet

Question 3

• (A) \(-16\)
• (B) \(+16\)
• (C) \(-192\)
• (D) \(+192\) (Correct answer)

Question 4

• (A) \(-40^\circ\)
• (B) \(-13^\circ\)
• (C) \(-8^\circ\) (Correct answer)
• (D) \(8^\circ\)

Question 5

• (A) \(-10^\circ\)
• (B) \(-2^\circ\) (Correct answer)
• (C) \(+2^\circ\)
• (D) \(-2\frac{1}{2}^\circ\)

Question 6

• (A) \(-21\)
• (B) \(-5\)
• (C) \(5\) (Correct answer)
• (D) \(21\)

Question 7

• (A) \(-2\) (Correct answer)
• (B) \(-1\)
• (C) \(0\)
• (D) \(2\)

Question 8

• (A) \(-18\)
• (B) \(-10\)
• (C) \(8\) (Correct answer)
• (D) \(10\)