# 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.

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

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

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 $180(n - 2)$.

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

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,
$3x = 135$.