Ch 1-20 Review
Name:___________________________________________________ Period: _____
1.
Determine the midpoint of a line segment with each set of given endpoints: (8, 0) and (4, 6)
2.
Given the length of the long side of a 30-60-90 triangle, determine the length of
the hypotenuse. Write your answers as radicals in simplest form.
3. Determine the length of the hypotenuse of the
radical in simplest form.
triangle. Write your answer as a
4.
Use the Triangle Proportionality Theorem and the Proportional Segments
Theorem to determine the missing value.
5.Given:
bisects
, and
and
are right angles. Which theorem
would be used to show ⊿𝑅𝐺𝐹 ≅ ⊿𝑆𝐺𝐹?
6. Solve for x.
7. Determine the measure of the intercepted
8. Determine
arc
.
if
9. Calculate the volume. Use 3.14 for
.
10. Aiko is enclosing a new rectangular flower garden with a rabbit garden fence. She has 80 feet of fencing. Write
a quadratic function in standard form that represents the area as a function of the width. Remember to define
your variables.
11. Determine the x-intercepts of the quadratic function. f(x) = (x - 4)(x + 3)
12. Write a quadratic function that represents a catapult hurling a watermelon from a height of 36 feet at an initial
velocity of 82 feet per second.
13. Simplify the expression: (3x2 + 9) – (2x3 – 6).
14. Factor the trinomial completely using a multiplication table.
If possible, factor out the greatest common factor first: x2 + 3x – 28
15. Determine the root(s) of the quadratic equation. Check your answer(s): x2 + 2x – 48 = 0.
16. Determine the roots of each quadratic inequality. Use the interval method to determine the solution set of the
inequality. Round your answer to the nearest thousandth if necessary. 2x2 – 2x + 12 ≥ 36
17. Solve the system of equations to find the point of intersection.
𝑦 = 4𝑥 2 + 6𝑥 + 3
{
𝑦 = −6𝑥 − 6
Time
(Minutes)
18. Calculate i19
19. Write a piece-wise function to represent the data in the table.
–3
Number
of Blocks
9
–2
6
–1
3
0
0
1
3
2
6
3
9
20. Write a piece-wise function to represent the data.
21. An electronics store rewards customers with in-store reward vouchers. The value of the reward vouchers are
based on the total value of merchandise purchased. The rewards are calculated as follows:
4% for purchases more than $0 and up to and including $50,
8% for purchases more than $50 and up to and including $100,
14% for purchases more than $100 and up to and including $150,
16% for purchases more than $150 and up to and including $200, and
18% for purchases more than $200.
Sketch a graph to resemble the problem situation to the right.
22. Evaluate ⌈6.3⌉
23. Evaluate ⌊– 2.5⌋
24. Write a phrase to describe the inverse of “subtract 6 from a number and then divide by 9.”
25. What is the inverse of 𝑓(𝑥) = 3𝑥 + 7?
26. Given that (6, 3) is a point on the graph of 𝑓(𝑥), what is the corresponding point on the graph of𝑓 −1 (𝑥)?
27. Given 𝑓(𝑥) =
𝑥+8
3
and 𝑔(𝑥) = 3 𝑥 − 8, Determine if the functions f(x) and g(x) are inverses.
28. Is 𝑦 = 9 a one-to-one function?
29. Determine if the function and its inverse is one-to-one by examining the graph.
30. Determine the equation of the inverse for the quadratic function:
𝑓(𝑥) = 2𝑥 2 + 50.
31. Write an equation of a circle with center point (3, -8) when r = 7.
32. Determine whether the given point P lies on Circle A with a diameter of 10 in
figure to the right.
33. Determine the equation of the parabola shown
at the left.
34. A box contains 3 plain bagels, 3 blueberry bagels, 3 sesame seed bagel, and 3 cheese bagels. A bagel is chosen
at random from the box. Use a probability model to determine if the probability is uniform or non-uniform.
35. You write the letters A to J on separate index cards. Then you choose a card at random.
What is P(not a vowel)?
36. You spin the spinner to the right 2 times. What is the probability that it will land on a number
greater than 4 the first spin or a number less than 10 the second spin?
The two-way frequency table shows the current
inventory of hardwood that a lumberyard carries.
Suppose a board is selected at random from the
lumberyard’s inventory. Use the table to calculate each
probability. Round to the nearest percent if necessary.
37. P(oak)
38. P(maple or 1x2)
39. P(cherry, given 1x3)
40. 15 students are competing in the finals of a spelling bee. The top 3 finishers are awarded a gold, silver, and
bronze medal. In how many ways can the medals be won?
41. A committee of 5 students is to be formed from a homeroom of 30 students. How many different committees
are possible?
42. Calculate the number of ways the letters of each word can be arranged: MULTIPLY
43. 8 teachers seated around a circular table at a conference. Calculate the number of ways each arrangement can be
made.
44. According to a recent survey, 60% of high school students have their own tablets. Suppose 10 high school
students are selected at random. Determine the P(4 of the students have tablets.) Round your answers to the
nearest tenth of a percent.
45. Determine the probability that a dart that lands on a random part of each target will land in
the SHADED scoring section. Assume that all squares in a figure and all circles in a figure
are congruent unless otherwise marked. Round each answer to the nearest percent if
necessary
46. Calculate the expected value of spinning each spinner one time. Round to the nearest
hundredth if necessary.