Grade 7 MTAP 2015 Questions with Solutions Part 1

Below are actual MTAP Questions that has been released. I have created a detailed solution for each question. In this post, we answer 1-10. You can also read the solutions of problems 2-20.  The file can be downloaded here.

1.) Simplify: 2(3)^2 - 3(2)^3 + (1 - 4)^3

Solution
2(3)^2 - 3(2)^3 + (1-4)^3
= 2(9)- 3(8) + (-3)^3
= 18 - 24 + (-27)
= -33

Answer: -33

2.)  By how much is 3 – 1/3 greater than 2 and 1/2?

Solution

3 - \frac{1}{3} = 2 \frac{2}{3}
2 - \frac{1}{2} = 1 \frac{1}{2}

Subtracting the two results, we have 
2 \frac{2}{3} - 1 \frac{1}{2} = 2 \frac{4}{6} - 1 \frac{3}{6} = 1 \frac{1}{6}.

Answer: 1 \frac{1}{6}

3.) Write 9/20000 in scientific notation.

Solution

\dfrac{9}{20000} can be written as \dfrac{9}{2} \times \dfrac{1}{10000}.
Since \dfrac{9}{2} = 4.5 and \dfrac{1}{10000} = 10^{-4},
\dfrac{9}{2000} = 4.5 \times 10^{-4}

Answer: 4.5 \times 10^{-4}

4.) What is the product of three consecutive multiples of 5 if the middle number is n?

Solution

If n is a multiple of 5 and the middle number of the three numbers, then the other numbers are n + 5 and n - 5.

So, the product is (n - 5)(n)(n + 5) = n(n^2 -25) = n^3 - 25n.

Answer: n^3 - 25n.

5.) If water pours into a tank at a rate of 100 liters per minute, at what rate is the tank being filled in kiloliters per hour?

Solution

100 liters/minute \times 60 minutes per hour = 6000 liters per hour

6000 liters per hour = 6 kiloliters per hour.

Answer: 6 kiloliters per hour

6.) Subtract the sum of a + 2b + c and 3a - b - c from 6a + b - 2c.

Solution

(a + 2b + c) + (3a - b - 2c) = 4a + b - c.
(6a + b - 2c) - (4a + b - c) = 6a + b - 2c - 4a - b + c = 2a - c

Answer: 2a - c

7.) Simplify (3-8) \times \left ( - \dfrac{7}{2} \right ) - \dfrac{5}{2} (-2).

Solution

Simplifying we have,

(3-8) \times \left ( - \dfrac{7}{2} \right ) - \dfrac{5}{2} (-2) = (-5) \times \left ( - \dfrac{7}{2} \right ) + \dfrac{10}{2}.

The expression further simplifies to

\dfrac{35}{2} + \dfrac{10}{2} = \dfrac{45}{2} = 22.5.

Answer: 22.5

8.) The sum of the interior angles of a polygon is 1620 degrees. How many sides has the polygon?

Solution

The sum of the interior angles of a polygon with n angles is 180(n - 2).

180(n - 2) = 1620
180n - 360 = 1620
180n = 1980
n = 11

Answer: 11

9.) Simplify: \left (3 - \dfrac{1}{4} \right )^2 - \left (3 + \dfrac{1}{4} \right )^2.

Solution

\left (3 - \dfrac{1}{4} \right )^2 - \left (3 + \dfrac{1}{4} \right )^2 = \left ( \frac{11}{4} \right )^2 - \left ( \frac{13}{4} \right )^2 = \dfrac{121}{16} - \dfrac{169}{16} = \dfrac{-48}{16} = -3.

10.) The sum of the two angles of a triangle is three times the third angle. What is the sum of the first two angles?

3x + x = 180
4x = 180
x = 45

Therefore,
3x = 135.

Answer: 135

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