# HiSET Math Practice Quiz 2

#### One third of the candidates for a job were 25 years old or younger. Two sevenths of the candidates were at least 50 years old. If 84 people applied for the job, how many were between 25 and 50?

One third of 84 is 84 × 1/3 = 84÷3 = 28. 28 people 25 years old or younger applied for the job. Two seventh of 84 is 84 × 2/7= 2×84÷7 = 24. 24 people who were at least 50 years old applied for the job. 84 - 28 - 24 = 32. 32 people applied for the job who were between 25 and 50.

#### Which of the following is a factor of 450 and multiple of 25?

It can be confirmed by division that (a), (b) and (c) are factors of 450, while 100 is not. The multiples of 25 are 25, 50, 75,.... 75 is both a factor of 450 and multiple of 25

#### The formula h -15 = 3.2t gives the height h in inches of a plant t weeks after planting. How high was the initial height of the shrub?

Initial means at the beginning. At the beginning t is 0. h =15 + 3.2t gives the height of a shrub in inches after t weeks. When planting occurs the height is 15 + 3.2× 0 = 15 inches

#### A graph of the temperature T (degrees Fahrenheit) in a refrigerator t hours after midday. What is the equation of the axis of symmetry of this graph?

It is clear from the diagram that the T -axis is the mirror line or axis of symmetry of this diagram. The equation of the T- axis is t = 0. The equation of the axis of symmetry of this graph is t = 0

#### If the radius of the sphere were doubled by what factor would the surface area be enlarged? Note: The formula for the surface area S of the sphere = 4 x (pi) x r2

If r = 1 then the surface area of the smaller sphere is 12.56...... If the radius is doubled the surface area is 50.26...... The factor is 50.26... ÷ 12.56.... = 4. The surface area is enlarged by a factor of 4.

#### It is necessary to find the times when the temperature is 8o F. Which of the following is the correct equation to do this.

It is apparent from the graph that it is not linear hence the answer cannot be (A) If an attempt is made to solve (B) it will be found there is no real solution. One of the solutions to (D) is 8, which gives a negative value. (C) is the only possible solution.

#### The formula for the volume V of the sphere = 4(pi)r3 / 3. Which of the following is the closest approximation to the volume when r, the radius, is 11 inches?

It is necessary to substitute 11 for r in the formula. The calculation is V = 4/3 x (pi=3.14) x 113 = 5572.45....... Clearly the closest approximation to this is (c)

#### Which of the following is the equation of the straight line joining the points on the graph corresponding to t = 2 and t = 1?

The point on the graph corresponding to t = 1 is (1,8). The point on the graph corresponding to t = 2 is (2,5). The slope of the straight line joining them is (5 - 8)÷(2 - 1) = -3. The equation is T = -3t + c As (2,5) lies the line we can substitute for t and T. 5 = -3×2 + c c = 11 Equation is T = -3t + 11 which is the same as (a)

#### The formula h - 15 = 3.2t gives the height h in inches of a plant t weeks after planting. Which is the rate at which the plant's height is increasing?

h =15 + 3.2t gives the height of a shrub in inches after t weeks. When planting occurs the height is 15 + 3.2× 0 = 15 inches After one week the height is 15 + 3.2× 1 = 18.2 inches The rate at which the height increases is 18.2 - 15 = 3.2 inches

#### The formula h -15 = 3.2t gives the height h in inches of a plant t weeks after planting. When was the height 31 inches?

h =15 + 3.2t gives the height of a shrub in inches after t weeks. When the height is 31 inches 31 = 15 + 3.2t 3.2t = 16 t = 16÷3.2 t = 5 The height is 31 inches after 5 weeks