# ASVAB Mathematics Knowledge Test 1

#### Line l passes through the point (−1, 2). Which of the following CANNOT be the equation of line l?

The slope-intercept form of a line is y = mx + b. Since the line passes through (−1,2), there are three possibilities: the line will have a slope (the “m” in front of the “x” variable), it will be vertical (x = −1), or it will be horizontal (y = 2). Plug x = −1 into all four equations to see which equation is not satisfied. The only answer choice that doesn’t give us y = 2 is (B)

#### Given a circle with a radius of 0.85 meters, find the area of the circle.

The area of a circle is equal to π r^2. Putting in the variables we know, we find the area of the circle to be 2.27 pi.

#### If (3.2 + 3.3 + 3.5)w = w, then what is the value of w?

First add up the three numbers that are in parentheses: 10w = w 10w = w will only be true when w = 0.

#### A rectangle is cut in half to create two squares that each have an area of 25. What is the perimeter of the original rectangle?

The formula to find the area of a square is side x side. If each square has an area of 25, then the dimensions of the rectangle are 5 x 10. The perimeter is the sum of all the sides, and would therefore be 5 + 10 + 5 + 10 = 30.

#### Blair’s average (arithmetic mean) on two physics tests is 7. What should Blair’s score be on the next test to have an overall average of 8 for all the tests?

The arithmetic mean is defined as the sum of the terms divided by the number of terms. 7 = sum / 2 14 = sum Adding the next test’s score will change the average to an 8, and the total terms to 3. 8 = (14 + new score) / 3 24 = 14 + new score 10 = new score

#### 2 − 8 ÷ (2^{4} ÷ 2) =

Remember your order of operations:

- Complete operations within parentheses first.
- Calculate exponents.
- Then multiply and divide in order from left to right.
- Then add and subtract in order from left to right.

^{4}÷ 2) =

2 − 8 ÷ (16 ÷ 2) =

2 − 8 ÷ 8 =

2 − 1 =

1

#### If n is a positive integer divisible by 7, and if n < 70, what is the greatest possible value of n?

If you know one multiple of a number, you can find the other multiples by adding and subtracting that number. The number 70 is divisible by 7. The greatest multiple that is less than 70 will be 70 − 7 = 63.

#### If XY = YZ, and angle Y measures 90 degrees in the figure above, which of the following CANNOT be concluded?

Here we are looking for the choice that is NOT true. Since the triangle is isosceles (XY = YZ), then a = b = 45. This means that a + b = 90. (A) and (C) must be true. For all right triangles, the Pythagorean Theorem applies, so (D) is also true. (B) is the correct answer because it is not true that XZ < XY. In a right triangle, the hypotenuse is always the longest side.

#### Calculate the area of a parallelogram with a base of 3 feet and a height of 1.2 feet.

The area of a parallelogram is A = bh, and the area is 1.2 x 3, which is 3.6 feet squared.

#### 3(x − 4) = 18, what is the value of x?

Begin by dividing both sides by 3 to open the parenthesis: x − 4 = 6 Add 4 to both sides to find x: x = 10

#### The volume of this box is

The volume of a cubic rectangle is length x width x height: 3 x 4 x 5 = 60

#### What is the value of this expression:

You need to add the 25 and 144 first, and then take the square root. The square root of 169 is 13.

#### Which of these expressions is equivalent to: 3x^{3}y^{5} + 3x^{5}y^{3} − (4x^{5}y^{3} − 3x^{3}y^{5})

The key to this problem is distributing the negative sign. When distributing a negative sign, each term has a change of sign from negative to positive or from positive to negative. 3x^{3}y^{5} + 3x^{5}y^{3} − (4x^{5}y^{3} − 3x^{3}y^{5})

3x^{3}y^{5} + 3x^{5}y^{3} − 4x^{5}y^{3} + 3x^{3}y^{5}

6x^{3}y^{5} − x^{5}y^{3}

#### What is the area of this trapezoid?

The trapezoid consists of two smaller shapes: a triangle and a rectangle. Draw a line from point A across this figure to form the two shapes. Find the area of each shape and then add them together to find the area of the trapezoid.

Area of rectangle = length x width.

Therefore, the area of the rectangle is 18x20 = 360

Area of a triangle = 1/2(base)(height).

The base of the triangle is 20.

The height of the triangle is unknown.

Use the Pythagorean Theorem to find the triangle's height.
c^{2} = a^{2} + b^{2} where c is the triangle's hypotenuse.

29^{2} = 20^{2} + (height)^{2}

841 = 400 + (height)^{2}

441 = (height)^{2}

The square root of 441 is 21

height = 21.

Therefore, area of the triangle = (1/2)(20)(21) = 210. The total area of the trapezoid = 360+210 = 570.

#### (4x + 2) (x + 1) =

This is a multiplying binomials problem. Multiply the first term in the first binomial by both terms in the second binomial: 4x^{2} + 4x
Then multiply the second term in the first binomial by each term in the second binomial:
2x + 2
Adding them all together you get:
4x^{2} + 4x + 2x + 2
4x^{2} + 6x + 2

#### If 5^{11} = 5^{2} x 5^{m}, what is the value of *m*?

When multiplying two powers with the same base, you can always add the exponents. This means that 11 = 2 + m, so m = 9.

#### A scoutmaster is preparing his troop for their annual fishing expedition. He surveys each of his scouts to find out how many fishing poles they own. What is the mode of this data set?

The mode of the data is the number that appears the most often. In this case the largest number of scouts (7) own 0 fishing poles.

#### There are two pizza ovens in a restaurant. Oven 1 burns three times as many pizzas as oven 2. If the restaurant had a total of 12 burnt pizzas on Saturday, how many pizzas did oven 2 burn?

Begin by setting up a system of equations to represent the situation, letting x represent oven 1 and y represent oven 2. x = 3y and x + y = 12 Substituting the first equation into the second: 3y + y = 12 so y = 3.