Grade 8 MTAP 2015 Elimination Questions with Solutions – Part 1

Below is the first part of the Grade 8 MTAP 2015 Elimination Questions with Solutions and answers. If you find any errors, please comment on the box below.

1.) Find the average of the numbers -1, 3/2, and 1/2.

Solution

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

2.) How much larger is 2/3 than 1/6?

Solution
2/3 – 1/6 = 4/6 – 1/6 = 3/6 = 1/2

3.) If one ream contains 500 sheets of paper and a sheet of paper is 0.3 mm thick, how thick is one ream in meters?

Solution

500 × 0.3mm = 150 mm = 0.15m

4.) What is the second largest number among numbers $\sqrt{2}$, 3/2 , 1.4, $\sqrt{3}$ and 1.6?

Solution

$\sqrt{2}$ is around 1.41 and $\sqrt{3}$ is around 1.7.

5.) If an inch is about 2.54 cm, what is 1 cm to the nearest hundredth of an inch?

Solution

$1:2.54 = x: 1, x = 0.39$

6.) If U = {1, a, 2, b, 3, c, 4, d} and A = {1, 2, c, d}, what is Ac ?

Solution

Ac is the complement of A, or the elements of the set that is not in A but in U. So,
Ac = {a, b, 3, 4 }
Answer: Ac = {a, b, 3, 4 }

7.) Using the same sets in Item 6 and B = {1, 2, 3, 4}, how many subsets does A ∩ Bc have?

Solution

A = {1, 2, c, d} and B = {1, 2, 3, 4}. The complement of B denoted by Bc are the elements of U not in B. So, Bc = {a, b, c, d}. Now, A ∩ Bc are the elements that are common to A and Bc. Therefore, A ∩ Bc = {c, d}. Now, the number of subsets of a set with n elements is 2n (this includes the empty set), so there are 22 = 4 subsets.

8.) If |P| = 10, |Q| = 12, and |P Q| = 15, what is |P ∩ Q |?

Solution 1

We know that the cardinality of the union of two sets is equal to the sum of the cardinality of these sets less the cardinality of their intersection. That is, if we have sets P and Q, |P ∪ Q| = |P| + |Q| – |P ∩ Q|.

Substituting, we have
15 = 10 + 22 – |P ∩ Q|
|P ∩ Q| = 7

Solution 2

x + y + z = 15 ()
x + y = 12 ()
y + z = 10 (
)
Adding the (**) and (***), we have x + 2y + z = 22 (#)

Subtracting (*) from (#),
x + 2y + z – (x + y + z) = 22 – 15
y = 7

9.) If |M ∩ N| = 24 and |M ∪ N| = 26, what is |M| + |N|?

Solution

From number 8, we know that |M ∪ N| = |M| + |N| – |M ∩ N|. Substituting, we have,
26 = |M| + |N| – 24
|M| + |N| = 50.