Practice Final MAT 101

(1) If the perimeter of a rectangle is 76 inches and the length of that rectangle is 4 inches longer than its width, find the dimensions

(2) In a given country there are text messages per day. How many are there in 360 days? (Give the answer in scientific notation).

(3) (a) Find the equation of the line passing through the points (-2,-4), and (1,2), and express it in slope-intercept form.

(b) Find the x-intercept and y-intercept of the line with equation:

(4) (a) Evaluate the polynomial:

(b) The height of an object t seconds after launch is given by the function . How high will the object be after 4 seconds?

(5) A computer tech charges $60 for a service call, plus 30 dollars for every hour h that he works on the job. Give an algebraic expression that represents the tech's fee.

(6) In 2009, a company's profits decreased by $30 million, and they lost $5 million over all. How much were their profits in 2008? (Give a linear equation which represents this problem, and solve it).

(7) Solve the linear equation:

(a) (b) 4x + 15 = 27 (c) 2x - 3 = 5 - 4x + 10x (d)

(8) An item costs a retailer $20. He sells it for $28. What percent of the original price is the markup on the item?

(9) Solve the linear inequality, and give the solution in interval notation:

(10) Simplify using exponent rules:

(a) (b) (c)

(11) (a) Subtract:

(b)

(d) Divide:

(12) Factor completely:

(a) (b)

(e)

(13) Solve the equation:

(a) (b)

Solutions:

(1) The unknowns are:

w = width

w + 4 = length. The perimeter formula must be used: P = 2l + 2w, and the info:

76 = 2w + 2(w + 4)

76 = 2w + 2w + 8,

-8 -8

68 = 4w, w= 17, w + 4 = 21.

(2) Use scientific notation to perform the calculation:

(3) (a) First, we need to find the slope: =3, and then we use point-slope form. You need to pick a point to use the formula i'm going to use (2,4):

(b)

To find the intercepts, set one variable equal to 0, and then solve for the other variable:

y = -5x – 3

(4) (a) plug in x = -3, be careful:

(b) This is easy – just plug in t = 4:

(5) h = # hours worked, 60 is the base cost, and

60 + 30h would give the total fee.

(6)unknownx = profits of company in 2008

translate 'dropped' => subtract, 'lost 5 million' => -5 million profits

x – 30 = - 5;

+30 +30

x = 25 million in profits in 2008

(7) (a) We need to multiply by the denominator to clear the fraction:

(b) 4x + 15 = 27 (Isolate x:)

-15 -15

4x = 12

4 4

x = 3.

2x - 3 = 5 - 6x (variable => one side)

+6x +3 +3 +6x

8x = 8,

(d)

(8) The markup is the difference between the original cost and the retail price:

28 – 20 = 8, so we want to know: What percent of 20 is 8?

n(20) = 8,

(9) The action is in the middle, where we have to isolate the variable:

In interval notation, that's [-1,4]

(10)(a)

(b)

(11) (a)

(b) Multiply every term of the first poly by ever term of the second:

(d) You don't have to use long division here, you can instead break up over the common denominator, and do monomial division term-by-term. You know, like this:

(12) (a)

Factor: . Trinomial with lead coefficient other than 1.

I'll do this one by grouping (you can use trial-and-error as well):

(b) Four terms, use grouping:

(c)

(d) Difference of squares:

(e) We can write this one as a sum of cubes:

(13) (a) It's quadratic – factor the left-hand side;

note: In such cases, we say the single solution x = 2 'repeats'.

(b) It's quadratic – factor the left-hand side, which is a trinomial with lead coefficient other than 1 – use grouping.