**Question 11 :**

In a diagram, each small box is a square whose side is 3. What is the area of the shaded figure ?

**(A) 108 (B) 54 (C) 36 (D) 18 (E) 6**

**Solution : **

Base of the triangle = 3

height = 4

Area of triangle = (1/2) ⋅ base ⋅ height

= (1/2) ⋅ 3 ⋅ 4

= 6 square units

**Question 12 :**

When expressed in scientific notation, the number

1,230,000,000 is 1.23 x 10^{B}.

The value of B is

(A) 2 (B) 7 (C) 8 (D) 9 (E) 10

**Solution :**

Scientific notation of the given number

1,230,000,000 = 1.23 x 10^{9}

Since we move the decimal 9 digits to the left side, we use positive sign.

Hence the value of B is 9.

**Question 13 :**

In a diagram, lines m and n are parallel. What is the value of x ?

**(A) 20 (B) 40 (C) 45 (D) 60 (E) 70**

**Solution :**

Here l and m are parallel lines.

In a triangle, sum of angles = 180

<ABC + <BAC + <BCA = 180

<ABC + 90 + 70 = 180

<ABC + 160 = 180

<ABC = 180 - 160

<ABC = 20 = x (alternate interior angles)

Hence the value of x is 20.

**Question 14 :**

If p = √(2 + √10), Q = √(10 + √2) and R = √(5 + √5)

(A) P < Q < R (B) P < R < Q (C) Q < R < P

(D) R < Q < P (E) P = Q

**Solution :**

**Approximate value of P :**

The approximate value of √10 is 3.....

By adding 3.... and 2, we get 5......... By taking √5......, we get 2.......

**Approximate value of Q :**

The approximate value of √2 is 1.....

By adding 1.... and 10, we get 11......... By taking √11......, we get 3.......

**Approximate value of R :**

The approximate value of √5 is 2......

By adding 2.... and 5, we get 7......... By taking √7......, we get 2.......

P = √5......, Q = √11...... and R = √7......

Hence the answer is P < R < Q.

**Question 15 :**

The sides of a triangle all have integer lengths. Two side have lengths 7 and 10. If the largest and smallest possible perimeters for the triangle are L and S, the value of L + S.

(A) is 20 (B) is 51 (C) is 52 (D) is 54

(E) cannot be determined from the information given

**Solution :**

Any side of a triangle has to be greater than the difference of the other 2, and less than the sum of the other 2

c > 10 - 7

c > 3

c < 10 + 7

c < 17

The smallest integer value is 4, and the largest is 16.

S = 7 + 10 + 4 = 21

L = 7 + 10 + 16 = 33

L + S = 54

**Question 16 :**

Evaluate (1/2) + (1/3) - (1/4) =

(A) 1/20 (B) 7/12 (C) 3/4 (D) 1 (E) 13/12

**Solution :**

L.C.M (2, 3 and 4) = 12

To convert the denominator of first fraction as 12, we have to multiply both numerator and denominator by 6.

(1/2) ⋅ (6/6) = 6/12 ----(1)

The second fraction by 4

(1/3) ⋅ (4/4) = 4/12 ----(2)

The third fraction by 3

(1/4) ⋅ (3/3) = 3/12 ----(3)

(1) + (2) - (3)

= (6/12) + (4/12) - (3/12)

= (6 + 4 - 3)/12

= 7/12

**Question 17 :**

In the diagram, AC = BD = 17 and BC = 3. The length of segment AD is

**(A) 20 (B) 24 (C) 28 (D) 31 (E) 34**

**Solution :**

To find the length of AD, we have to add the lengths of AB, BC and CD.

AC = 17 AB = AC - BC = 17 - 3 AB = 14 |
BD = 17 CD = BD - BC = 17 - 3 CD = 14 |

AD = AB + BC + CD

= 14 + 3 + 14

= 31

Hence the answer is 31.

**Question 18 :**

What is the value of |x - y| + |y - x| if x = -3 and y = -7 ?

(A) -14 (B) -6 (C) 0 (D) 8 (E) 20

**Solution :**

|x - y| = |-3 - (-7)| = |-3 + 7| = 4 |
|y - x| = |-7 - (-3)| = |-7 + 3| = 4 |

|x - y| + |y - x| = 4 + 4 = 8

Hence the answer is 8.

**Question 19 :**

The sum 2^{10} + 1^{10} + (1/2)^{10} + (1/3)^{10} + (1/4)^{10 }is closest to

(A) 21 (B) 32 (C) 513 (D) 1025 (E) 2000

**Solution :**

2^{10 }= 1024

2^{10 } = 1

Other than the above two, the values of other terms will be too small.

Hence the sum is closest to 1025.

**Question 20 :**

4^{3} + 4^{3} + 4^{3} + 4^{3 }=

(A) 4^{4 }(B) 4^{9 }(C) 4^{12 }(D) 16^{3 }(E) 16^{12}

**Solution :**

4^{3} + 4^{3} + 4^{3} + 4^{3 }= 4(4^{3})

= 4^{(1 + 3)}

= 4^{4}

**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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