The document outlines grade 2 math goals related to operations and computation, number and numeration, data and chance, and using repeated addition, arrays, and skip counting to model multiplication and equal sharing to model division. It provides examples of tasks for students including writing addition facts, counting by 5s, interpreting a bar graph, and solving an addition word problem. The goals and examples are for helping students learn skills like adding and subtracting 2-digit numbers, counting on and back, using graphs, and modeling multiplication and division.
memperkenalkan konsep perkalian kepada anak kelas 2 merupakan perjuangan yang sangat sulit. Ini merupakan pondasi pertama untuk menuju level berikutnya...
memperkenalkan konsep perkalian kepada anak kelas 2 merupakan perjuangan yang sangat sulit. Ini merupakan pondasi pertama untuk menuju level berikutnya...
Pre-Calculus Quarter 4 Exam
Name: _________________________
Score: ______ / ______
1.
Find the indicated sum. Show your work.
2.
Locate the foci of the ellipse. Show your work.
3.
Solve the system by the substitution method. Show your work.
2y - x = 5
x2 + y2 - 25 = 0
4.
Graph the function. Then use your graph to find the indicated limit. You do not have to provide the graph
f(x) = 5x - 3, f(x)
5.
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work.
4x - y + 3z = 12
x + 4y + 6z = -32
5x + 3y + 9z = 20
6.
Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.
x + y + z = -5
x - y + 3z = -1
4x + y + z = -2
7. A woman works out by running and swimming. When she runs, she burns 7 calories per minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336 calories in her workout. Write an inequality that describes the situation. Let x represent the number of minutes running and y the number of minutes swimming. Because x and y must be positive, limit the boarders to quadrant I only.
Short Answer Questions: Type your answer below each question. Show your work.
8.
A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work.
Sn: 12 + 42 + 72 + . . . + (3n - 2)2 =
9.
A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying Sk+1 completely. Show your work.
Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3
10.
Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and 70 pounds of B grade tea. These will be blended into 1 pound packages as follows: A breakfast blend that contains one third of a pound of A grade tea and two thirds of a pound of B grade tea and an afternoon tea that contains one half pound of A grade tea and one half pound of B grade tea. If Joely makes a profit of $1.50 on each pound of the breakfast blend and $2.00 profit on each pound of the afternoon blend, how many pounds of each blend should she make to maximize profits? What is the maximum profit?
11
Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and you need to make at least $3850 profit on them. How many of what type of printer should you order if you want to minimize your cost?
12
A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work.
Sn: 2 + 5 + .
1. Grade 2 Operations and Computation Goal: Use manipulatives, number grids, tally marks,
mental arithmetic, paper & pencil, and calculators to solve problems involving the addition
and subtraction of 2-digit whole numbers; describe the strategies used; calculate and
compare values of coin and bill combinations.
Unit 3: Show coins
for a given amount.
2. Grade 2 Operations and Computation Goal: Demonstrate automaticity with +/- 0, +/– 1, doubles, and sum-
equals-ten facts, and proficiency with all addition and subtraction facts through 10 + 10.
Unit 3: Know addition facts.
Write down as many facts as you can that
have a sum of 10.
_____ + _____ = 10
_____ + _____ = 10
_____ + _____ = 10
Write down all the double facts. _____ + _____ = 10
_____ + _____ = 10
_____ + _____ = 10
_____ + _____ = 10
_____ + _____ = 10
_____ + _____ = 10
_____ + _____ = 10
Connect the turn around facts with a line.
3. Grade 2 Number and Numeration Goal: Count on by 1s, 2s, 5s, 10s, 25s, and 100s past 1,000 and back by 1s
from any number less than 1,000 with and without number grids, number lines, and calculators.
Unit 3: Count by 5s.
Count by 5s. Start at 0.
0, _____, _____, _____, _____, _____, _____, _____, _____, _____,
_____, _____, _____, _____, _____, _____, _____, _____,_____, _____,
How much? _______
4. Grade 2 Data and Chance Goal: Use graphs to ask and answer simple questions and draw conclusions; find the maximum, minimum,
mode, and median of a data set.
Unit 3: Interpret a bar graph.
A class of 25 students was asked to name their favorite color: 5 chose
red, 8 chose green, 11 chose yellow and 1 chose blue. Which graph
shows this information?
5. Grade 2 Operations and Computation Goal: Identify and describe change, comparison, and
part-and-total situations; use repeated addition, arrays, and skip counting to model
multiplication; use equal sharing and equal grouping to model division.
Unit 3: Solve an
addition number-
story problem.
Ed and Karen each have 15 lion
stickers. Ashley has 20. How could they
find out how many stickers they
have all together?
A. Add 15 and 20.
B. Subtract 20 and 15.
C. Add 15 and 15 and 20.