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MATC 1200 Readiness Self-Exam
Look over the following questions. These cover concepts that I assume you already know. If you
have trouble with any of these, don’t hesitate to come see me or a TA.
1. Numbers and absolute values:
a. Put the following numbers in order from smallest to largest:
80, 0. 235, −6, 72 , 1, 2, 5. 25 × 10 −3 , −0. 001
b. If ab = 0, which one of the following is certainly true? (only one is correct)
● a > 0
● b > 0
● b = 0
● a = 0
● b = 1
● b < 0
c. What is |−2| − |−3|?
d. If x + 3x − 1 = 0, then what is true?
● x + 3 = 0 and x − 1 = 0
● x + 3 = 0 or x − 1 = 0
● x = 0
● x = −3
2. Each of these statements is false. Figure out why.
a. 3x + y = 3x + y
b. 5 − 32 = 5 − 3
2
c. 3x 2 = 3x 2
d. 4 − −4 = 0
8 =0
e.
0
f. 2 − 13 + 4 = 6 − 4
3. Perform the following calculation: start with the number x. Now subtract 3. Then add 5.
Then divide by 4. Then multiply by 7. Now square it. What do you get?
4. Functions and lines
a. Find the x −intercept for the line with equation y = 2x − 5.
b. Find the y −intercept for the line with equation y = 2x − 5
c. Find the y coordinate to the point on the line y = − 23 x + 7 when x = 6.
d. What is the slope of a horizontal line?
e. What is the slope of the line passing through the points 1, 4 and 3, 10?
f. Let fx = 3x 2 − 4. What is f0?
g. Let gx = 3
x . What is g−2?
h. Look at the graph below of a function Ax. Determine the value of A0 and
A3, and find the x −values where Ax = 0 and Ax = −4.
1
y
8
6
4
2
-2.0 -1.5 -1.0 -0.5
-2
0.5 1.0 1.5 2.0 2.5 3.0 3.5
x
-4
-6
-8
-10
-12
i.
j.
If the point 3, 8 is on the graph of a function hx, then which one of the
following statements is true?
● h8 = 3
● h3 = 8
● The line y = 3x + 8 intersects the graph of hx.
● hx is not a line.
Which of the following 3 pictures is the graph of y = 2x − 5?
y
10
-2
y
2
-10
x
10
-2
y
2
-10
x
10
-2
2
x
-10
Solutions
1.a. − 6 < −0. 001 < 5. 25 × 10 −3 < 0. 235 < 1 < 2 < 72 < 80
1.b. a = 0. 1.c. |−2| − |−3| = 2 − 3 = −1 1.d. x + 3 = 0 or x − 1 = 0
2.a. The distributive law of multiplication tells us that 3x + y = 3x + 3y, not 3x + y.
2.b. 5 − 32 = 102 − 32 = 72 . while 5 − 3 = 22 = 1.
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2.c.3x 2 = 3x3x = 3 ⋅ 3 ⋅ x ⋅ x = 9x 2 the rule here is to square everything in the parentheses,
not just x. 2.d.4 − −4 = 4 + 4 = 8, since subtracting a negative number is the same thing as
adding a positive one.
2.e. You can’t divide by 0. It makes no sense to take something and
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divide it into zero parts. 0 is an undefined expression, not zero.
2.f. It’s probably obvious to you that 1 ⋅ 7 = 7 ≠ 6 − 4 = 2 but if I had written this problem with
variables, x − ya + b = xa − yb, you might not have noticed the error. The point here is that the
addition inside the parentheses "comes first," so to multiply these two numbers properly you have
to account for this by distributing your multipliers.
x − ya + b = x − ya + x − yb = xa − ya + xb − yb, not xa − yb.
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x − 3 + 5
3. 7
4.a. x intercept is 52 4.b.y intercept is −5 4.c.− 23 6 + 7 = 3 4.d.0
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4.e. 10−4
= 3 4.f.f0 = −4 4.g. g−2 = − 32 4.h.A0 ≈ −0. 5, A3 = 4, Ax = 0 when x = 1,
3−1
Ax = −4 when x = −1 4.i.h3 = 8 4.j. The center picture is the correct graph because the y
intercept is −5 and the slope is 2.
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