MPM 1D1 – Unit #5 Test – More AlgebraName: ______
Short Answer – Write an equation to represent each sentence.
______1. Five more than a number is 21.
______2. A number decreased by 11 is 15.
______3. Four times a number, added to 6, is 14.
______4. A number divided by 3 is 18
______5.The sum of two consecutive numbers is 303.
Multiple Choice - Identify the best answer by circling the letter.
1. The total cost, C, in dollars, of running an advertisement in a newspaper is $12, plus a charge of $5.00 per day: where n represents the number of days. Which equation represents the cost of running an ad?
a) C = 12n + 5b) C = 12 + 5nc) C = (12 + 5)nd) C = 12 + 5 + n
2. The equation 7 = 4y + 2(y – 1) is the same as:
a) 7 = 6y – 1b) 7 = 8y2 – 4yc) 7 = 6y – 2d) 6 = 6y
3. Darrick and Sabrina are each asked to solve an equation.
Who correctly solved his or her equation?
a) Darrick only
b) Sabrina only
c) Both Darrick and Sabrina
d) Neither of them
4. What equation represents the area of the garden below if the total area of the garden is 375 m2. Remember area of a rectangle is equal to the length times the width.
a) 25(10 + x) = 375 b) 2(25) + 2(10 + x) = 375c) 25(10) + 10x = 375 d) 25(10) + x = 375
5. The perimeter of an equilateral triangle is 45 cm. Which equation gives the length of one side?
a)b)
c) d)
6. By what number would you divide both sides to solve the equation?
a) 2b) 3c) 6d) 12
7. Which is the correct solution for ?
a) x = 5b) x = 15c) x = 10d) x = 20
8. By what number would you multiply both sides to solve the equation?
a) 2b) 4c) -2d) - 4
9. is the correct solution for which equation?
a) b) c) d)
10. The perimeter of a rectangle is 36m. If the length is three times the width, what is the length?
a) 4.5 mb) 18 mc) 13.5 md) 9 m
11. The expression is also equal to:
a) 6x + 10b) 4x c) d)
Modified True / False
Indicate whether the statement is true or false. If false, change the identified word or phrase to make the statement true.
____12.To solve an equation means to find a number for the variable that makes both sides of the equation have the same value. ______
____13.The algebraic expression represents two more than a number
______
____14. represents the statement two less than five times a number
______
____15.x = 2 is the solution for x – 2 = 4. ______
___16.a = 3 is the solution for 2a + 3 = 9. ______
Short Answer–Place your answer in the space provided.
1. Solve each equation using the algebraic rules studied in class. You must show your algebraic thinking.
a) 4x – 7 = 9 b) 2(4y – 1) = -10 c) - x = -5 d) 0 = 20 – 5x – 5 + 8x
e) f) 5(m – 2) = 2(m - 2) – 9 g) (x – 2) = 5
2. The solution to the equation 7x – 2(x + 5) = 1 – 2(4 – 3x) is x = -3.
Using LS = RS and substitution, verify that this answer is correct.
7x – 2(x + 5) = 1 – 2(4 – 3x) ; where x = -3
3. Rearrange each formula to isolate for the indicated variable.
a) y = mx + b (for m)b) P = 2(l + w) (for w)c) V = lwh(for h)
4. The sum of two consecutive numbers is -167. What are the numbers?
5. Rebecca is 7 years older than Jessica. The sum of their ages is 39.
How old are they?
6. The side length or a rectangle is 6 cm longer than the width. If the perimeter of the rectangle is 48 cm, how long is each side?
7.The formula relates temperature in degrees Fahrenheit to temperature in degrees Celsius.
a) Rearrange the formula to isolate C.
b) When the temperature is , what is it in Celsius, to the nearest tenth of a degree?
c) On the warmest summer day, the temperature was 100̊F. What was the equivalenttemperature in Celsius, to the nearest tenth of a degree?
Bonus:Find the perimeter of the shape below.
MPM 1D Unit #5 – EquationsAssessment RubricName:______Date:______
Know./
Underst. / Demonstrates a solid and thorough understanding of Equations(opposite operations, simple equations, equations with variables on both sides, equations involving fractions, rearranging formulas, word problems and equations). Able to solve problems with no errors. / Demonstrates good understanding of Equations. Able to solve the problem with a minor error(s) / Demonstrates moderate understanding of Equations. Able to solve the problem with someerrors. / Demonstrates a limited or inaccurate understanding of Equations needed to solve the problems. / Needs to demonstrate an understanding of Equations. No attempt made at solving the problem, or the attempt has little or no validity.
Application /
Has a thorough understanding of how to use the concepts (Equations) to form a solution.
Demonstrates a solid understanding of the connection between the questions required solution and its interpretation. /
Has good understanding of how to use the concepts (above) to form a solution.
Demonstrates good understanding of the connection between the questions required solution and its interpretation. /
Has some understanding of how to use the concepts (above) to form a solution.
Demonstrates a moderate understanding of the connection between the questions required solution and its interpretation. /
Has limited understanding of how to use the concepts (above) to form a solution.
Demonstrates little understanding of the connection between the questions required solution and its interpretation. /
Needs to show understanding of how to use the concepts answer question.
Demonstrates an insufficient connection between the questions required solution and its interpretation.
Commun-ication / Provides a thorough, clear and insightful explanation/justification.Solutions are well formed, with completeness, accuracy and proper mathematical form / Provides a complete, clear, and logical explanation, missing small details.Solutions are complete but some proper form is missing /
Provides a partial explanation/justification that shows some clarity and logical thought.Solutions are somewhat complete, but disorganized. /
Provides a limited or inaccurate explanation/justification that lacks clarity or logical thought.Solutions are incomplete, scattered and disorganized. /
Needs to provide some explanation/justification.
Thinking /
Shows flexibility and insight when carrying out the plan, by trying and adapting one or more strategies to solve the problem. (when necessary) /
Carries out a plan effectively by using an appropriate strategy and solving the problem. /
Carries out the plan to some extent using a strategy, and develops a limited and/or incorrect solution /
Uses a strategy and attempts to solve the problem but does not arrive at a solution. /
Needs to demonstrate a strategy that could be used to solve this problem.