**SHSAT Math Practice Questions and Answers :**

Here we are going to see some practice questions questions for SHSAT exams.

**Question 1 :**

Phone Company A charges 50 + 3x dollars for an international phone plan, where x is the number of minutes spent talking. Phone Company B charges 60 + 2x dollars for an international phone plan, where x is the number of minutes spent talking. What is the price at which both companies charges the same amount?

**Solution :**

Charge of company A = 50 + 3x

Charge of company B = 60 + 2x

50 + 3x = 60 + 2x

3x - 2x = 60 - 50

x = 10

Hence the answer is $10.

**Question 2:**

William, Xing Mei, Yuki, and Zack run a race. In how many different ways can they finish?

**Solution :**

There are 4! ways to finish the race.

4! = 4 ⋅ 3 ⋅ 2 ⋅ 1

= 24

Hence they may finish the race is 24 ways.

**Question 3 :**

What is the solution set for -1 ≤ -2f + 1 ≤ 9?

**Solution :**

-1 ≤ -2f + 1 ≤ 9

= -1 + 1 ≤ -2f + 1 + 1 ≤ 9 + 1

= 0 ≤ -2f + 2 ≤ 10

= 0 - 2 ≤ -2f + 2 - 2 ≤ 10 - 2

= -2 ≤ -2f ≤ 8

Divide by (-2)

= 1 ≥ f ≥ -4

= -4 ≤ f ≤ 1

Hence option A is correct.

**Question 4 :**

On a blueprint of a school 1/4 inch represents 24 feet. If the cafeteria is 60 feet long, what is its length,in inches, on the blue print?

**Solution :**

24 feet = 1/4 inch

1 feet = 1/4(24) inch

= 1/96 inch

60 feet = 60(1/96) inch

= (60/96) inch

= (5/8) inch

**Question 5 :**

In the above figure, the two circles are tangent at point R. The length of PR = 8. The area of the circle with center Q is 4 times larger than the area of the circle with center S.What is the length of QS?

**Solution :**

Length of PR = 8

PQ = QR = 4 (radius)

Area of the circle with center Q = 4 (Area of circle with center S)

Area of circle with center Q = πr^{2}

= π(4^{2}) = 16π

16π = 4 π(RS)^{2}

4 = (RS)^{2}

RS = 2

QS = QR + RS

QS = 4 + 2

QS = 6

**Question 6 :**

Given that 0 < x < 1, and set A = {x, x^{2}, x^{3}, x^{4}}, what is the smallest value in set A ?

**Solution :**

Let x = 0.5

x^{2} = 0.25

x^{3} = 0.125

x^{4} = 0.0625

When the power is being increased, the answer get decreased. Hence the smallest value of the given set is x^{4}

**Question 7 :**

Darius ran 1/6 as many times around the track as Ezekiel. Darius ran around the track 2 ⅔ times. How many times did Ezekiel run around the track?

**Solution :**

Let "x" be the number of times that Ezekiel around the track, then

Darius ran around the track = (1/6)x = x/6

Now, Darius ran around the track = 2 ⅔ times

= 8/3

We need to show 8/3 is terms of 1/6.

For that, let us multiply the numerator and denominator by 2.

So, we get

= (8/3) ⋅ (2/2)

= 16/6

= (1/6) ⋅ 16

Hence Ezekiel run around the track 16 times.

**Question 8 :**

A decagon has 10 sides and 10 angles. What is the average number of degrees in each interior angle of a decagon?

**Solution :**

All sides are the same length (congruent) and all interior angles are the same size (congruent).

To find the measure of the angles, we know that the sum of all the angles is 1440 degrees

Average = 1440/10 = 144

**Question 9 :**

The table below show a relationship between x and y values.

**Solution :**

If x = 0, y = 1

If x = 2, y = 5

In the given options, option C satisfies the above conditions.

y = 2x + 1 x = 0 and y = 1 1 = 2(0) + 1 1 = 1 |
y = 2x + 1 x = 2 and y = 5 5 = 2(2) + 1 5 = 5 |

Hence option C is correct.

**Question 10 :**

|x - 3 x 5| = 6 + y, |9 – y + 6| = 21

In the equations above, y < 0. What is the value of x?

**Solution :**

**|x - 3 x 5| = 6 + y**

**|x - 15| = 6 + y**

**x - 15 = 6 + y (or) -x + 15 = 6 + y**

**x - y = 6 + 15 (or) -x - y = 6 - 15**

**x - y = 21------(1) (or) -x - y = -9****-----(2)**

**(1) + (2)**

**-2y = 12**

**y = -6 < 0**

**x = 21 + y ==> x = 21-6 = 15**

**Hence the value of x is 15.**

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