8th GRADE MATH PRACTICE TEST WITH ANSWER KEY

Question 1 :

The quadratic equation n² - 6n - 55 is prime, then the largest value of n is

(A) 12       (B) 15       (C) 28

Solution

Question 2 :

A rectangle has been divided into congruent squares such that the sum of the perimeters of the squares is numerically equal to the area of the rectangle. What is the length of a side of one of the squares ?

(A) 2         (B) 4        (C) 10

Solution

Question 3 :

Paul and Mary are assigned a mathematics project to work on. If Paul works on it alone for 6 hours and let Mary take over, Mary needs another 12 hours to complete.

If Paul works on it for 8 hours then hands it over to Mary, she will need another 6 hours. How many hours does Mary alone to complete the project if Paul has already worked on it for 3 hours ?

(A) 21 hours   (B) 48 hours     (C) 30 hours

Solution

Question 4 :

In how many ways can a person go from the origin to the point (3, 3) if he can only move upwards and rightwards and his one step is one unit ?

(A) 10       (B) 20       (C) 30

Solution

Question 5 :

A company could choose any of the three builders (Anthony, Bob and Charles) to build a wall. Anthony would take A days to build the wall. Likewise, Bob and Charles would take B days and C days to build the wall respectively, The table shows the number of days needed to build the same wall if two of them worked together at the same time.

Find the value of A + B + C.

(A)  168      (B) 134        (C) 152

Solution

Question 6 :

ABC is a right angled triangle with <CAB  =  90. ADEF is a rectangle such that D lies on AB, E lies on BC and F lies on AC. IF BD  =  4 cm and CF  =  5 cm, find the area in cm² of the rectangle ADEF.

(A)  16 cm²      (B)  20 cm²         (C) 12 cm² 

Solution

Question 7 :

Find the total number of prime factors in the product

{(4)¹¹ ⋅ 7⁵ ⋅ (11)² }

(A) 25     (B)  4    (C) 29

Solution

Question 8 :

Rhodes, Watson, Rambo, Peter, Mark and Dwayne are standing in a line with their backs to a wall. How many different orders could they be standing in so that Rhodes and Dwayne are standing next to each other?

(A) 140       (B) 240        (C) 160

Solution

Question 9 :

If x  =  5 then find the value of x² - 5

(A) 20      (B) 30      (C) 5

Solution

Question 10 :

A group of seven students working on a project needs to choose two students to present the group's report. How many ways can they choose the two students ?

(A) 30        (B) 21       (C) 38

Solution

Answer Key

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