Whittier Tech
Grade 10:
Honors Alge
a II/Geometry
Summer Project
Grade 10 Honors Alge
a II/Geometry
Name: Date:
1. Right triangles ABC and AED are shownon the
coordinate grid below.
Which single transformation, with respect to the
line y = x, maps ^ABC → ^AED ?
A. dilation B. reflection
C. rotation D. translation
2. The distance along the walking trail behind
Jessica’s school is approximately 6,290 feet.
Jessica calculated the mean length of her walking
steps to be 2.9 feet.
Which of the following is closest to the number of
steps Jessica would take to walk the entire trail?
A. 200 steps B. 1,800 steps
C. 2,000 steps D. 18,000 steps
3. Sandra created the line plot shown below to
display data on the shoe sizes of her classmates.
Based on the data given in the line plot, what is
the median shoe size of Sandra’s classmates?
A. 7 B. 8 C. 10 D. 19
4. In the figure below, ^HIJ ∼= ^LKJ.
If m∠L = 50◦, what is m∠IJH ?
A. 35◦ B. 40◦ C. 45◦ D. 50◦
page 1
5. Which of the following best represents the graph
of a line with an undefined slope?
A.
B.
C.
D.
6. Andrew used a wooden stick to estimate the length
of a couch. Andrew, who is approximately 6 feet
tall, measured his height to be about 1 12 sticks
in length. He measured the couch to be about
2 sticks in length.
Based on Andrew’s measurements, which of the
following is closest to the length of the couch?
A. 8 feet B. 9 feet
C. 12 feet D. 18 feet
7. The following box-and-whisker plot shows the ages
of players on a neighborhood baseball team.
a) What is the range of the data set?
8. A landscape artist plans to create a garden on the
front lawn of an art museum. The garden will be
in the shape of a trapezoid. If the height of the
trapezoid is 15 feet, and its bases measure 14 feet
and 20 feet, what is the area, in square feet, of the
trapezoid?
9. Andy’s Housecleaning Service charges a fixed fee
of $40 per job, plus $15 per half-hour that a jo
equires.
a) If c represents Andy’s total charges, write an
equation that expresses c in terms of h, the
number of half-hours that a job requires.
) What is the total charge for Andy’s services
when a job requires 5 12 hours? Show all
your work.
Hannah’s Homemaids, another housecleaning
service, charges no fixed fee but charges $25
per half-hour that a job requires.
c) If c represents Hannah’s total charges, write
an equation that expresses c in terms of h,
the number of half-hours that a job requires.
d) The Jordans plan to have their house cleaned,
and they like Andy’s and Hannah’s services
equally well. For what number of half-hours
would the charges for the two services be
identical? Show or explain how you got you
answer.
page 2 Grade 10 Honors Alge
a II/Geometry
10. The value of all of the quarters and dimes in a
parking meter is $18. There are twice as many
quarters as dimes. What is the total number of
dimes in the parking meter?
11. Ms. Vargas is analyzing the scores her 10 chemistry
students earned on their last test. To make he
calculations easier, she reduced each score by
80 points and a
ived at the simplified data set
shown below.
{0, 4, 4, 5, 6, 7, 7, 7, 7, 9}
a) For the simplified data set, find each of the
measures listed below. Show or explain how
you got each answer.
• mean
• median
• mode
• range
) For the set of actual scores on the chemistry
test, find each of the measures listed below.
Show or explain how you got each answer.
• mean
• median
• mode
• range
12. Two real numbers have coordinates w and t as
shown on the number line below.
a) What are the two real numbers represented
y w and t on the number line?
) The coordinate of Point A on the numbe
line is w + t. Plot and label Point A on the
number line and explain how you decided
upon its location.
c) The coordinate of Point B on the numbe
line is w − t. Plot and label Point B on the
number line and explain how you decided
upon its location.
d) The coordinate of Point C on the numbe
line is w · t. Plot and label Point C on the
number line and explain how you decided
upon its location.
13. If 4 more than twice a number is 18, find the
number.
14. The cost of a long-distance telephone call is
determined by a flat fee for the first 5 minutes
and a fixed amount for each additional minute.
If a 15-minute telephone call costs $3.25 and
a 23-minute call costs $5.17, find the cost of a
30-minute call.
15. James is four years younger than Austin. If three
times James’ age is increased by the square of
Austin’s age, the result is 28. Find the ages of
James and Austin.
16. What is the slope of the line that passes through
the points (4, 5) and (7, 3)?
17. a) On the same set of coordinate axes, graph
the following system of inequalities:
y ≤ −3x + 2
y − x > 0
) Write the coordinates of a point not in the
solution set of the inequalities graphed in
part a.
18. Find an equation of the line passing through the
point (6, 5) and perpendicular to the line whose
equation is 2y + 3x = 6.
19. The expression (m − n) − (n − m) is equivalent to
A. 2m − 2n B. 2m
C. −2n D. m − n
20. A set of data consists of 3, 3, 6, 4, and 9. The
median for these data is
A. 6 B. 5 C. 3 D. 4
21. Pat’s grades on Course I tests were 90, 75, 98, 82,
90, and 87. The mode of her grades is
A. 90 B. 89 C. 87 D. 82
page 3 Grade 10 Honors Alge
a II/Geometry
22. The set of scores on a mathematics test is 72, 80,
80, 82, 87, 89, and 91. The mean score is
A. 84 B. 83 C. 82 D. 80
23. The accompanying histogram shows the distribution
of the number of children in the families of the
students in a ninth-grade class.
The mode of the set of data in the histogram is
A. 5 B. 2
C. 3 D. 7
24. A student’s four test scores were 88, 91, 93,
and 86. What score would be needed on a fifth
test to obtain a mean of 90 for all five tests?
A. 90 B. 92 C. 95 D. 96
25. What was the median high temperature in
Middletown during the 7-day period shown in the
accompanying table?
Daily High Temperature
in Middletown
Day Temperature
(F◦ )
Sunday 68
Monday 73
Tuesday 73
Wednesday 75
Thursday 69
Friday 67
Saturday 63
A. 69 B. 70 C. 73 D. 75
26. For a set of scores, 80 is the score for the 75th
percentile. Which statement is true?
A. Eighty scores are at or below 75.
B. Seventy-five scores are at or below 80.
C. Seventy-five percent of the scores are at o
elow 80.
D. Eighty percent of the scores are at o
elow 75.
27. Which measure is always the same as the 50th
percentile?
A. mean B. median
C. mode D. lower quartile
28. The freshman class held a canned food drive fo
12 weeks. The results are summarized in the table
elow.
Canned Food Drive Results
Week XXXXXXXXXX XXXXXXXXXX
Numbe
of Cans
XXXXXXXXXX XXXXXXXXXX
Which number represents the second quartile of
the number of cans of food collected?
A. 29.5 B. 30.5 C. 40 D. 60
29. The accompanying diagram shows a
ox-and-whisker plot of student test scores on last
year’s Mathematics A midterm examination. What
is the median score?
A. 62 B. 71 C. 81 D. 92
page 4 Grade 10 Honors Alge
a II/Geometry
30. Jorge made the accompanying stem-and-leaf plot
of the weights, in pounds, of each member of
the wrestling team he was coaching. What is the
mode of the weights?
A. 145 B. 150 C. 152 D. 168
31. The box-and-whisker plot below represents
students’ scores on a recent English test.
What is the value of the upper quartile?
A. 68 B. 76 C. 84 D. 94
32. Which pair of angles x and y are supplementary?
A. m∠x = 113
m∠y = 67
B. m∠x = 76
m∠y = 14
C. m∠x = 140
m∠y = 190
D. m∠x = 180
m∠y = 180
33. In the accompanying diagram,
−−→
BD ⊥ ←−→ABC at B and−→
BE ⊥ −→BF at B. If m∠FBC = 20, what is m∠EBD ?
A. 20 B. 70
C. 90 D. 110
34. In the accompanying diagram, line a intersects
line b.
What is the value of x?
A. −10 B. 5 C. 10 D. 90
35. The measures of two angles of a triangle are 70
and 55. This triangle is
A. a right triangle
B. a scalene triangle
C. an obtuse triangle
D. an isosceles triangle
36. In the diagram below, ^LMO is isosceles with
LO = MO.
If m∠L = 55 and m∠NOM = 28, what is m∠N?
A. 27 B. 28 C. 42 D. 70
37. In the accompanying diagram of isosceles
triangle ABC, −−−AB ∼= −−−BC, m∠BAC = x, and
m∠ABC = x + 30.
What is the value of x ?
A. 80 B. 75
C. 50 D. 30
page 5 Grade 10 Honors Alge
a II/Geometry
38. In the diagram below of ^ABC, −−−AB ∼= −−−AC,
m∠A = 3x, and m∠B = x + 20.
What is the value of x?
A. 10 B. 28 C. 32 D. 40
39. In the accompanying diagram, ∠ACD is