SHSAT PRACTICE TEST

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

SHSAT Practice Test - Questions ans Solution

Question 1 :

Find the next term in the series :

0, 1, 1, 2, 4, 7, 13, 24,.......

(A)  28  (B)  37  (C)  44  (D)  48  (E)  81

Solution :

By adding the preceding three terms, we get the next term.

4^th term  =  0 + 1 + 1  ==>  2

5^th term  =  1 + 1 + 2  =  4

6^th term  =  1 + 2 + 4  =  7

In this way, we will get the 

9th term  =  7 + 13 + 24  ==>  44

Hence the required term is 44.

Question 2 :

Which is true about A and B ?

A  =  √65 - 9

B  =  √50 - 8

(A)  A = B   (B)  A > B  (C)  A > 1  (D)  B > A  (E)  A + B > 0

Solution :

√65  =  8.07

√65 - 9  = 8.06 - 9  =  -0.9377

√50  =  7.07

√50 - 8  =  7.07 - 8     =   -0.9289

Hence B > A is the true statement.

Question 3 :

Which is the solution of the following equation ?

(x² + x - 6)/(x - 2)  =  0

(A)  -2  (B)  -3  (C)  0  (D)  2  (E)  3

Solution :

By factoring the numerator, we get

(x - 2)(x + 3)/(x - 2)  =  0

x + 3  =  0

x  =  -3

Hence the solution is -3.

Question 4 :

John is stacking boxes directly upon each other. He stacks as 1 box per minute initially and every minute after that, his staking rate increases by 1 box per minute. If each box is 5 inches tall, in how many minutes will the stack be 30 inches tall.

(A)  2 min  (B)  3 min  (C)  5 min  (D)  6 min  (E)  30 min

Solution :

If we place the second box over the first box, the height will become 10 inches.

In the same way, by placing the third over the first two boxes the height of the stack will become 15 inches.

Total height of the stack  =  30 inches

Number of minutes taken  =  30/5

  =  6 minutes

So we need 6 minutes to build a stack of height 30 inches.

Question 5 :

A Dilob has a mass of 20.2 milligrams. What is the Dilob's mass in grams ?

(A)  0.0202 g  (B)  0.202 g  (C)  2.02 g 

(D)  20.2 g  (E)  202 g

Solution :

1000 milligrams  =  1 gram

To convert milligram to gram, we have to divide 20.2 by 1000

20.2 milligrams  =  20.2/1000

  =  0.0202 g

Hence Dilob's mass in grams is 0.0202 g.

Question 6 :

Jesse goes to store. He buys a magazine for $8. The he sells it for $10 and buys it back again for $11. He finally sells it for $12. What was his profit ?

(A)  -$1    (B)  $0  (C)  $2  (D)  $3  (E)  $5

Solution :

Cost price of magazine  =  8 + 11

  =  $19

Selling price  =  10 + 12

  =  $22

Profit  =  Selling price - Cost price

=  22 - 19

=  $3

Hence his profit is $3.

Question 7 :

After a 10% increase, a population was 55. What was the population before the increase ?

(A)  54.45  (B)  55.45  (C)  50  (D)  56  (E)  10

Solution :

Let x be the original population

x + 10% of x  =  55

x + 0.10x  =  55

1.01 x  =  55

x  =  55 / 1.01

x  =  54.45

Question 8 :

A substance's length doubles every hour. At 2 PM it was 3 meters. What was the length at 12 PM that same day?

(A)  0.375 meters  (B)  0.5 meters  (C)  0.75 meters

(D)  1 meter  (E)  1.5 meters

Solution :

By writing the length of substance from 2 PM as sequence, we get

At 1 PM, the length of substance  =  (1/2)(3)

At 12 PM, the length of substance  =  (1/2)²3

3/4  =  0.75 meters 

Question 9 :

Which is true of these three functions ?

f  =  x ^{x^4}

g  =  (x^x)⁴

h  =  x ^{4^x3}

(A)  f = g = h  (B)  f = g  (C)  h = g 

(D)  f  =  g + h  (E)  f ≠  g

Solution :

f  =  x ^{x^4}

g  =  x^4x

h  =  x ^{4^x}

Hence we can say f ≠ g.

Question 10 :

Linda scored  66, 82, 81 and 92 on her English exams. What score must Linda obtain on the next math test, to have an average of exactly 84 ?

(A)  84  (B)  87  (C)  95  (D)  99  (E)  100

Solution :

Linda's marks are 66, 82, 81 and 92.

Average of 5 marks  =  84

Let "x" be the unknown score in English

(66 + 82 + 81 + 92 + x)/5  =  84

  321 + x  =  84 (5)

  321 + x  =  420

x  =  420 - 321 

x  =  99

Hence Linda has to score 99 marks in the next test to get the the average 84.

Question 11 :

If today is Saturday, what day of the week will it be in 365 days from now?

(A)  Monday  (B)  Tuesday  (C)  Thursday 

(D)  Friday   (E)  Sunday

Solution :

The problem starts with Saturday, every 7 days from Saturday, it will be Saturday.

By dividing 365 by 7, we get 1 as remainder.So the answer will be 1 day after Saturday. 

Hence the answer is Sunday. 

Question 12 :

What is the remainder of 7, 700, 000, 000, 202 divided by 9 ?

(A)  0  (B)  1  (C)  2  (D)  3  (E)  8

Solution :

If the sum of digits is divisible by 9, then the given number is divisible by 9.

7 + 7 + 2 + 2  =  18

Since the sum of the digits is divisible 9, the given number is divisible by 9.

Hence the remainder is 0.

Question 13 :

In the figure above AB  =  BC  =  DE  =  EF  and the side of the square is 12. Point B and E are the midpoints of the square. Find the area of the shaded region.

(A)  12π (B)  24π  (C)  36π  (D)  72π  (E)  144π

Solution :

AC  =  12, AE  =  6

There are four semicircles.

Area of 4 semicircles with radius 6  =  πr²/2

   = 4(πr²/2)  =  2 πr²

  =  2π(6)²

  =  2π(36)

  =  72π

Hence the answer is 72π.

Question 14 :

8 ^{x + 3}  =  64 ^3x, what is the value of x ?

(A)  1/2  (B)  3/5  (C)  5/3  (D)  2  (E)  3

Solution :

8 ^{x + 3}  =  64 ^3x

In order to compare the two terms, we have to convert with them having same base.

8 ^{x + 3}  =  (8²) ^3x

8 ^{x + 3}  =  8 ^6x

6x  =  x + 3 

6x - x  =  3

5x  =  3

x  =  3/5

Question 15 :

If A ⊏ ⊐ B  =  AB (A/B) - 2³, then what is the value of 3 ⊏ ⊐ (6 ⊏ ⊐ 2)

(A)  1   (B)  3   (C)  5   (D)  2   (E)  7

Solution :

First let us calculate the value of (6 ⊏ ⊐ 2), here instead of "A" we have "6" and instead of "B" we have 2.

(6 ⊏ ⊐ 2)  =  6(2) (6/2) - 2³

  =  12(3) - 8

  =  36 - 8

(6 ⊏ ⊐ 2)  =  28

3 ⊏ ⊐ 28  =  3(28) (3/28) - 2³

=  84(3/28) - 8

=  3(3) - 8

  =  9 - 8 

 =  1

Hence the answer is 1.

Question 16 :

If the average of 11 numbers is 15, then what is the sum of these 11 numbers ?

(A)  324   (B)  350   (C)  155   (D)  165   (E)  174

Solution :

Average of 11 numbers  =  15

Sum of 11 numbers/11  =  15

Sum of 11 numbers  =  15(11)  =  165.

Hence the required answer is 165.

Question 17 :

What is the average of (9b - 7) + (7 - 3b) - (-3 -3b) + (6 + 3b)

(A)   3b + 9/4   (B)   9b/4 + 3   (C)  3b + 2

(D)  2b + 3  (E)  3b + (4/9)

Solution :

  =   (9b - 7) + (7 - 3b) - (-3 -3b) + (6 + 3b)

  =  9b - 7 + 7 - 3b + 3 + 3b + 6 + 3b

  =  9b + 3b + 9 

  =  12 b + 9 

Average of four terms  =  (12b + 9)/4

  =  3b + 9/4

Question 18 :

(y^-1⋅y³⋅y⁴⋅y⁵⋅y⁶) / (y⁶⋅y⁵⋅y⁴)

(A)   y²  (B)   y¹  (C)  1  (D)   y⁵   (E)   y^-3

Solution :

  =  y^-1 ⋅y³

  =  y ^{(-1 + 3)}

  =  y²

Hence the answer is y^2.

Question 19 :

If the pattern continues, what will be the 50th symbol ?

Solution :

Each group consists of 6 different symbols. A group ends with the symbol upside, then the new starts with triangle.

Let us divide 50 by 6, we get the remainder 2. The symbol triangle must be filled in the 49th place and 50^th place should be heart.

Question 20 :

A trapezoid has base length in the ratio of 2 : 6. If the area of a trapezoid is 260 and altitude is 5, then what is the length of longer side ?

(A)  13  (B)  20  (C)  26  (D)  65  (E)  78

Solution :

Area of trapezoid  =  (1/2) h (a + b)

a  =  2x, b = 6x

 (1/2) 5 (2x + 6x)  =  260

(5/2)(8x)  =  260

x  =  260/20

x  =  13

2x  =  2(13)  =  26 and 6x  =  6(13)  =  78

Hence the longer side is 78.

MORE SHSAT QUESTION 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

After having gone through the stuff given above, we hope that the students would have understood, how to solve problems in SHSAT exams.

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You can also visit the following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6