Topic Quiz A.5: Graphs, slope and functions

Question 1 of 10 · Unit rate as slope

A store sells cereal in two sizes:

  • an 18-ounce box for $4.32
  • a 24-ounce box for $5.52

Which box is the better buy, and what is its price per ounce?

Answer choices
Hint

Find the price of 1 ounce for each box by dividing price by ounces.

Question 2 of 10 · Graph linear equations

No calculatorFill in

The table lists points on the graph of y = 4x - 3. Complete the table.

x-2-102
y-7-35

Type your answer in the box. Fractions like 3/4 are fine.

Hint

Substitute the x-value at the top of the empty column into the equation. Be careful with the negative.

Question 3 of 10 · Points in the coordinate plane

Hot spot

A point has a y-coordinate of 4, and its x-coordinate is the opposite of 2.

Click the point on the coordinate plane.

Click on the figure to mark your answer (or focus it and use the arrow keys).

Coordinate plane from -5 to 5 on both axes-5-5-4-4-3-3-2-2-1-11122334455xy
Hint

First write the point as an ordered pair. What number is the opposite of 2?

Question 4 of 10 · Slope from a graph, equation or table

No calculatorDrag and drop

Drag each line to the box that describes its slope.

Positive slopeNegative slopeZero slopeUndefined slope

Tap a tile, then tap a box to place it.

Hint

Think about the picture of each line. Rising, falling, flat, or straight up and down?

Question 5 of 10 · Slope from a graph, equation or table

Two points on the line below are marked. Use them to find the slope of the line.

Coordinate plane from -6 to 6 on both axes. A straight line rises from left to right and passes through the marked points (-4, -1) and (4, 5).xy−6−6−5−5−4−4−3−3−2−2−1−11122334455660(−4, −1)(4, 5)
Answer choices
Hint

Use the two marked points. Count how far up and how far right you go from one to the other.

Question 6 of 10 · Graph linear equations

Dana makes the same deposit into her savings account every week. The graph shows her balance.

Graph of savings account balance in dollars (vertical axis, 0 to 1,000, grid every 100) versus weeks (horizontal axis, 0 to 10). A straight line starts at the marked point (0, 300) and passes through the marked point (8, 900).01234567891002004006008001000WeeksBalance (dollars)(0, 300)(8, 900)

What does the slope of the line represent?

Answer choices
Hint

Slope = change in balance ÷ change in weeks. Use the two marked points.

Question 7 of 10 · Key features of graphs and tables

No calculator

The graph of f is shown. Assume the graph keeps going in the same way beyond the grid.

Graph of a function f on a coordinate plane with x from −6 to 4 and y from −4 to 10, grid every 1 unit. The curve is an upside-down U (parabola opening downward). It crosses the x-axis at (−4, 0) and (2, 0), crosses the y-axis at (0, 8), and its highest point is (−1, 9). Both ends of the curve point downward.−6−5−4−3−2−11234−4−2246810xy

As x increases without bound, what happens to f(x)?

Answer choices
Hint

Follow the right end of the curve. Is it heading up, heading down, or levelling off?

Question 8 of 10 · Points in the coordinate plane

A parking lot is a rectangle. On a site plan measured in meters, its corners are at (-5,\ 3), (2,\ 3), (2,\ -1) and (-5,\ -1). A fence will go all the way around the lot.

How many meters of fence are needed?

Answer choices
Hint

Find the length of a horizontal side and of a vertical side. Then add all four sides.

Question 9 of 10 · Unit rate as slope

Fill in

The graph compares the distance two cars can travel on a given amount of gasoline.

Graph of distance in miles (vertical axis, 0 to 320) versus gasoline used in gallons (horizontal axis, 0 to 10) for two cars. Both lines start at the origin. Car A's line passes through the marked point (4, 120). Car B's line passes through the marked point (5, 110).01234567891004080120160200240280320Gasoline used (gallons)Distance (miles)Car A (4, 120)Car B (5, 110)

On 12 gallons of gasoline, how many more miles can Car A travel than Car B?

miles

Type your answer in the box. Fractions like 3/4 are fine.

Hint

Find each car's miles per gallon from its marked point. Then use 12 gallons for both.

Question 10 of 10 · Key features of graphs and tables

No calculator

Use the theater profit graph again.

Graph of a theater's daily profit in dollars (vertical axis, −800 to 1,000, grid every 100) versus ticket price in dollars (horizontal axis, 0 to 40, grid every 5). The curve is an upside-down U. It starts at the marked point (0, −700), crosses the horizontal axis at the marked points (5, 0) and (35, 0), and its highest point is the marked point (20, 900).0510152025303540−800−600−400−20002004006008001000Ticket price (dollars)Daily profit (dollars)(0, −700)(5, 0)(20, 900)(35, 0)

What does the point (0,\ -700) tell you?

Answer choices
Hint

Translate each coordinate: the first number is a ticket price, the second is a daily profit. What does a negative profit mean?

Formula sheet

Area

Area of a square s = length of a side
A = s^2
Area of a rectangle l = length, w = width
A = lw
Area of a parallelogram b = base, h = height (straight up from the base, not the slanted side)
A = bh
Area of a triangle b = base, h = height
A = \tfrac{1}{2}bh
Area of a trapezoid b_1 and b_2 = the two parallel sides, h = height
A = \tfrac{1}{2}h(b_1 + b_2)
Area of a circle r = radius (half of the diameter); \pi \approx 3.14
A = \pi r^2

Perimeter and circumference

Perimeter of a square s = length of a side
P = 4s
Perimeter of a rectangle l = length, w = width
P = 2l + 2w
Perimeter of a triangle s_1, s_2, s_3 = the three side lengths
P = s_1 + s_2 + s_3
Circumference of a circle the distance around a circle; r = radius, d = diameter, \pi \approx 3.14
C = 2\pi r = \pi d

Surface area (SA) and volume (V)

p = perimeter of the base with area B; \pi \approx 3.14

Rectangular prism l = length, w = width, h = height
SA = 2lw + 2lh + 2wh \qquad V = lwh
Right prism B = area of the base, p = perimeter of the base, h = height
SA = ph + 2B \qquad V = Bh
Cylinder r = radius of the base, h = height
SA = 2\pi rh + 2\pi r^2 \qquad V = \pi r^2 h
Pyramid B = area of the base, p = perimeter of the base, s = slant height, h = height
SA = \tfrac{1}{2}ps + B \qquad V = \tfrac{1}{3}Bh
Cone r = radius of the base, s = slant height, h = height
SA = \pi rs + \pi r^2 \qquad V = \tfrac{1}{3}\pi r^2 h
Sphere r = radius
SA = 4\pi r^2 \qquad V = \tfrac{4}{3}\pi r^3

Data

Mean (average) add all the values of the data set, then divide by how many values there are
\text{mean} = \dfrac{\text{total of the values}}{\text{number of values}}
Median
the middle value when the data are in order; with an even number of values, it is the mean of the two middle values

Algebra

Slope of a line (x_1, y_1) and (x_2, y_2) = two points on the line
m = \dfrac{y_2 - y_1}{x_2 - x_1}
Slope-intercept form of a line m = slope, b = y-intercept (where the line crosses the y-axis)
y = mx + b
Point-slope form of a line m = slope, (x_1, y_1) = a point on the line
y - y_1 = m(x - x_1)
Standard form of a quadratic equation a, b, c are numbers and a \ne 0
y = ax^2 + bx + c
Quadratic formula solves ax^2 + bx + c = 0
x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}
Pythagorean theorem in a right triangle: a, b = the two legs, c = the hypotenuse (the longest side, across from the right angle)
a^2 + b^2 = c^2
Simple interest I = interest, P = principal (the amount saved or borrowed), r = rate per year as a decimal, t = time in years
I = Prt
Distance = rate × time d = distance, r = rate (speed), t = time
d = rt
Total cost
\text{total cost} = (\text{number of units}) \times (\text{price per unit})