**SHSAT Math Test Online :**

Here we are going to see some practice questions questions for SHSAT exams. Each question paper consists of 20 question. For each questions, you can find solution with detailed explanation.

SHSAT Math Test Online.

**Question 6 :**

A square of side 4 is topped by a semicircle, as shown. Point P is the center of the arc at the top. Then the shaded area is equal to

(A) π + 2 (B) (π/2) + 2 (C) 2π + 2

(D) 2π – 4 (E) 2π + 4

**Solution :**

Shaded region = Area of quadrant + Area of square semi square - Area of triangle Radius of circle = 2, side of square = 4 = (1/4) πr - (1/2) base (height) = (1/4) 4π + (1/2)4 - (1/2) 2 (4 + 2) = π + 8 - 6 = π + 2 Hence the answer is π + 2. |

**Question 7 :**

(4^{6}
x 3^{4} x 2^{2}) / (4^{2} x 3^{4} x 2^{6})
=

(A) 1 (B) 2 (C) 8 (D) 16 (E) 24

**Solution :**

= (4^{6} x 3^{4} x 2^{2}) / (4^{2} x 3^{4} x 2^{6})

= 4^{6-2 }x 3^{4-4} x 2^{2-6}

= 4^{4 }x 3^{0} x 2^{-4}

= 2^{8 }x 3^{0} x 2^{-4}

= 2^{8-4}

= 2^{4 }= 16

Hence the answer is 16.

**Question 8 :**

Which one of the following numbers is less than 1/3?

(A) 1111/3333
(B) 299/895 (C) **.**1 x 4

(D) **.**4 x 1 (E) 5! / 6!

**Solution :**

**5! / 6! = **5! / 6 ⋅ 5! = 1/6

= 0.1666

Hence the answer is 5! / 6!.

**Question 9 :**

The ratio of a to b is 3 to 4. The ratio of b to c is 5 to 6. The ratio of a to c is

(A) 9:10 (B) 5:8 (C) 1:2 (D) 2:5 (E) none of these

**Solution :**

a : b = 3 : 4

Multiply the ratio by 5

a : b = 15 : 20

b : c = 5 : 6

Multiply the ratio by 4

b : c = 20 : 24

a : b : c ==> 15 : 20 : 24

The ratio of a to c is 15 : 24

Hence the required ratio is 5 : 8.

**Question 10 : **

(All lines shown are either vertical or horizontal) If x and y are integers, and the shaded area is 52, then the perimeter of the figure is

(A) 20 (B) 24 (C) 52 (D) 56 (E) 196

**Solution :**

If we complete the square whose sides are length x, we see that the shaded are is x^{2} - y^{2. }

(x + y) (x - y) = 52

x + y = 2 ----(1) x - y = 26 ----(2)

(1) + (2)

2x = 28

x = 14 and y = 12

Perimeter of the shape = 2(x + y)

= 2(14 + 12)

= 2(26)

= 52

After having gone through the stuff given above, we hope that the students would have understood, "SHSAT Math Test Online".

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