NUMBER, RELATIONS & FUNCTIONS 10 EXAM REVIEW

FACTORS & PRODUCTS

PART A: Short ResponsePlace your answer to each of the following questions in the box provided.

1. Write the prime factorization of 2646.

2. Determine the greatest common factor of 126 and 144.

3. Determine the least common multiple of 84 and 90.

4. Determine the perimeter of the following

square.

5. Factor .

6. Expand and simplify

7. Factor

8. Expand and simplify

9. Factor

FHS

10. Factor

11. Factor .

Part B: Open Response

1. Two neon signs are turned on at the same time. Both signs blink as they are turned on. One sign blinks every 42 seconds and the other blinks every 70 seconds. In how many seconds will they blink together again?

2. Lisa is making activity baskets to donate to charity. She has 24 coloring books, 60 markers, and 84 crayons. What is the greatest number of baskets she can make if each type of toy is equally distributed among the baskets? How many of each supply will go into the baskets?

3. What is the side length of the smallest square that could be tiled with rectangles that measure 8 in. by 36 in.?

4. Use prime factorization to determine the square root of 1296.

5. Molly wants to paint a cube with volume . Each tub of paint covers . How many tubs of paint does Molly need to paint the cube?

6. Factor each of the following.

a.

b.

c.

d.

e.

f.

g.

7. Factor each of the following completely.

a.

b.

c.

d.

e.

f.

8. Determine the area of the shaded region in the diagram to the right.

9. Expand and simplify.

a.

b.

10. Expand and simplify.

a.

b.

ROOTS & POWERS

Part A: Short Response

Place your answers in the boxes provided.

1. Write an example of an irrational number.

2. Write an example of a rational number that is not an integer.

3. Write as a radical.

4. Write as a power.

5. Determine which of the following numbers is the smallest.

6. Write as an entire radical.

7. Write in simplest form.

8. Write in simplest form.

9. Evaluate .

10. Simplify . Write your exponents as positive exponents.

11. Evaluate

PART B: Open ResponseAll work must be shown to receive credit.

1. Simplify

a. b.

2. For each of the following questions,a. Write each power as a radical. Simplify.

b. Evaluate each power.

3. Evaluate each of the following powers without the aid of a calculator. All work must be shown to receive credit. Decimal answers will not be accepted.

4. For each of the following questions.a. Write each power as a radical. Simplify.b. Evaluate each power.

5. The height, h metres, of a certain species of fir tree can be estimated from the formula , where d metres is the diameter at the base. Use the formula to determine the approximate height of a fir tree with base diameter 3.2 m.

6. Simplify each of the following using the exponent laws. Write your answers with positive exponents.

7. Simplify each of the following using the exponent laws. Write your answers with positive exponents.

8. Simplify each of the following using the exponent laws. Write your answers with positive exponents.

RELATIONS & FUNCTIONS

PART A: Short Response.

Place your answer corresponding to each question in the box provided.

Questions 1 and 2 refer to the diagram below.

a b c

d e f

1. Which of the graphs illustrated above represent functions.

2. Justify your response.

3. Determine which of the ordered pairs listed below is NOT a function.a. {(-2,4), (-1,4), (0,4), (1,3), (5,5)}b. {(-3,-1), (-1, -3), (1,-3), (2,3), (-1, 5)}c. {(-1, 5), (0, 6), (1, 7), (2, 8), (3,9)}

4. State the domain and range of the relation illustrated below.

5. State the domain and range of the relation illustrated below.

DOMAIN:

RANGE:

6. State the domain and range of the relation illustrated below.

7. For the function , determine .

8. For the function , determine x when

9. The equation , represents the total cost, C(x), in dollars, for a sports banquet when x people attend. What does C (76) represent?

10. If , determine h(-3).

11. If , find x if g(x)=16.

12. The graph of the function, f(x), is illustrated below. Determine f(2).

Questions 13 & 14 refer to the set of ordered pairs listed below.a. b. c. d.

13. Which set(s) of ordered pairs represent linear relations?

14. Justify your answer.

Questions 15 and 16 refer to the graph to the right and the information presented below.

The graph represents a 150 –L hot-water tank being filled at a constant rate.

15. Determine the rate of change.

16. What does the rate of change mean in the context of this question?

Part B: Open Response

All work must be shown to receive credit.

1. Identify the independent and dependent variables in the situations described below. a. The size of grapes in a vineyard and the amount of rain.

b. On a game show, contestants win money for each question they answer correctly. The number of correct answers dictates the amount of prize money.

c. The manager of a restaurant uses the number of reservations made for a particular night to determine how many servers to schedule for that night.

d. The weather forecast for Fredericton has predicted that it will snow all afternoon. The more it snows, the longer it will take to plow all the streets.

2. The daily rental charge for renting a 1988 Buick at Wrenta-Wreck is $30 plus 25 cents per mile. The rental charge depends on the number of miles you drive. Let x represent the number of miles you drive. Let y represent the rental charge.

a. Complete the following table of values.

# Miles Cost0

255075

100

b. Label each axes.c. Sketch the graph.d. Determine the equation of the

relationship.

e. How much would a person be charged if they rented the car for 1 day and drove 85 miles?

f. How far would a person have driven the car in a day if the charge was $43.75

3. Construct a graph of the function .

x f(x)-2-1012

4. Your family is driving from Cincinnati to St. Louis. The graph relates your distance from St. Louis y (in miles) and travel time x (In hours).

a. State the x-intercept. What does the x-intercept represent in the context of this question?

b. State the y-intercept. What does the y-intercept represent in the context of this question?

c. Determine the slope. What does the slope represent in the context of this question?

d. Determine the equation of the line.

e. How far from St. Louis was your family after 3.5 hours?

f. When was your family 300 km from St. Louis?

5. The graph to the right describes Kate’s trip to the store. Answer each of the following questions based on the graph below.

a. What is happening between D and E?

b. Calculate the rate of change between C and D.

c. How long did it take Kate to reach the store?

d. How long did it take Kate to come home from the store?

e. What is the total distance Kate travelled?

6. Assume to have to draw the graphs for each of the situations described below. Would you join the data points? Justify your response.

a. the number of admissions in a hospital's accident and emergency unit each day over a period of two months.

b. the concentration of a pollutant in each of 20 samples or river water that were collected over a period of 1 week.

c. the number of bruised apples in each of 20 crates of 100 apples.d. the weights of blue cod caught by a fishing boat.

7. Matthew sells high-definition televisions. He is paid a weekly salary of 20% commission of his total weekly sales.a. Complete the table of values.

b. Graph the relationship.

c. Write an equation to model the relationship.d. Determine Matthew’s pay if his sales for the week total $8000.e. Matthew made $975. How much were his weekly sales?

8. Determine the equation for each of the following linear relations.a. The country club charges $270 for their facilities plus $30 per guest.b. As you hop into a taxicab in Las Vegas, the meter will immediately read $3.30; this is the “drop” charge

made when the taximeter is activated. After that initial fee, the taximeter will add $2.40 for each mile the taxi drives.

c.

LINEAR FUNCTIONS

PART A: Short Response.

Place your answer corresponding to each question in the box provided.

1. Determine the slope of the linear function illustrated below.

2. Determine the slope of a line passing through (-7, -1) and (-2, 9).

3. Draw a line segment passing through the point (4, -1) with a slope of .

4. Write the equation of a linear function that has a slope of and a y-intercept of -2.

5. Determine the slope of a line perpendicular to the linear function .

6. Write the equation of a linear function that has a slope of 0 passing through (3, -4).

7. Write the equation of a line parallel to that has a y-intercept of 5.

8. Write the equation of a linear relation perpendicular to with ay-intercept of -4.

9. Rewrite the equation in y = mx + b form.

10. Determine the equation of a line in point slope form that passes through

(-4, -3) and has a slope of .

11. Determine the equation of the function illustrated below. Express your answer in slope y-intercept form.

12. Draw a graph with an undefined slope.

13. A gym membership with two personal training sessions costs $125, while gym membership with five personal training sessions costs $260. What is the rate for personal training sessions?

14. Find the midpoint of the line segment connecting the points (6, -4) and (-2, -7).

15. Find the length of the line segment between (-1, 2) and (4, -3).

16. The midpoint of the line segment AB is M(-2,2). One endpoint, A, is located at (-5,7). Find the coordinates of the other endpoint, B.

Part B – Open Response Work must be shown to receive credit.

1.

a. Rewrite the equation in slope y-intercept form (y = mx + b)

b. State the slope and the y –intercept.m = ____________________ y-intercept= ______________________

c. Rewrite the equation in general form (Ax + By + C = 0)

2. Determine the slope and y –intercept of the linear function .

m = ________________________ y-intercept = ___________________________

3. If f(x) is a linear function, f(3) = -2 and f(8) = 1, find the equation for the function.

4. Sketch the graph of each of the following linear functions. All work must be shown.

a. b. (use intercepts)

5. A hot tub contains 1600 L of water when full. The tub can be emptied at a rate of 80L/min.a. Determine the equation of the linear function that represents the volume of water in the tank, V, as a

function of time, x.

b. Determine the amount of time it would take for the tank to empty to a volume of 875 L.

6. Working as an insurance salesman, Blair earns a base salary and a commission on each new policy, so Blair’s weekly income, I, depends on the number of new policies, n, he sells during the week. Last week he sold 3 new policies , and earned $720 for the week. The week before, he sold 5 new policies, and earned $920.

a. Write an equation for Blair’s weekly income in slope y-intercept form.Coordinates:

b. What does the slope represent? The y-intercept?

c. Use your equation to determine Blair’s salary if he sells 8 new policies in a week.

7. A clothing business finds there is a linear relationship between the number of shirts, n, it can sell and the price,

p, it can charge per shirt. In particular, historical data shows that 1000

shirts can be sold at a price of $30

,

while 3000

shirts can be sold at a price of $22

. Find a linear equation in the form p=mn+b

that gives the price p they can charge for n shirts.

8. Determine the equation of each linear function described below. Express your answer in slope y-intercept form.

a. Passes through the point with a slope of .

b. Passes through the points and .

c. Through the point and parallel to the line .

d. Perpendicular to the line and passing through the point .

e. Has the same x-intercept as and parallel to .

9. Prove that quadrilateral A (-3,3), B (4,5), C (6, -1) and D (-1, -3) is a parallelogram.

10. The coordinates of the vertices of are A(-3,1), B(6,-2) and C(3,4). Is a right angled triangle?

SYSTEMS OF LINEAR EQUATIONS

PART A: Short Response.

Place your answer corresponding to each question in the box provided.

1. Determine which of the following ordered pairs is a solution to the followingsystem of equations.

a. (3,-7) b. (-5,12) c. (-3,2) d. (1, 4)

2. Create a linear system to model the following situation.The perimeter of an isosceles triangle is 36 cm. The base of the triangle is 9 cm longer than each equal side.Let x represent each equal side.Let y represent the base.

3. At a skating rink, admission is $4.00 for a student and $8.00 for an adult.Tuesday evening, 20 people used the skating rink and a total of $132 in admission fees was collected. A linear system that models this situation is4s + 8a = 132s + a = 20where s represents the number of student admissions, and a represents the

number of adult admissions purchased.Use the graph to solve the following problem:How many students used the skating rink on Tuesday evening.

4. Draw a system of equations with an infinite number of solutions.

5. Draw a system of equations with no solutions.

Part B – Open Response

Work must be shown to receive credit.

1. Solve the following system of equations graphically.

2. Solve by substitution. Check your solution.

3. Solve by elimination. Check your solution.

a. b.

4. The receipts from 550 people attending a play were $9184. The tickets cost $20 for adults and $12 for students. Determine the number of adults that attended the play.

5. At Lisa’s Sub Shop, two ham subs and four roast-beef subs cost $34. Five ham subs and 6 roast beef subs cost $61. Determine the cost of each type of sub.

6. The length of a rectangle is 3 cm more than twice its width. If the perimeter of the rectangle is 36 cm, find the dimensions of the rectangle.

7. A stained glass design was made of triangles, each with area 14 square cm, and hexagons, each with area 84 square cm. the design used 81 shapes and covered an area of 5334 square cm. Determine the number of each shape used in the design.

8. To rent a car, a person is charged a daily rate and a fee for each kilometer driven. When Hannah rented a car for 15 days and drove 800 km, the charge was $715.00. When she rented the same car for 25 days and drove 2250 km, the charge was $1512.50. Determine the daily rate and the fee for each kilometer driven.