MCF3M1 – Exam Review Name:

Date:

You must show full solutions & show all your steps. Questions with only answers only will result in a zero marks. Exam Review: Basic Skills

1. Expand 3x(2x + 7).

a) 5x2 + 21x

b) 5x + 10 d) 6x + 7

e) None of the above

c) 6x2 + 21x

2. Expand and simplify (x + 4)(6x – 1).

a) 6x2 – 4

b) 6x2 + 23x – 4

c) 7x + 3

3. Factor 5x + 15y – 3xy – 9y2. d) 6x2 + 9x – 4

e) None of the above

a) (5 – 3y)(x – 3y)

b) (x + 3y)(x – 3y)(5 – 3y)

c) (5 – 3y)(x + 5)

4. Factor 4x2 – 9. d) (5 – 3y)(x + 3y)

e) None of the above

a) (2x – 3)(2x + 3)

b) (2x + 3)2 d) (2x – 3)2

e) None of the above

c) (2x + 4.5)(2x – 4.5)

a) { 3? ? ?? ?y :y R}

b) { 4? ? ?? ?y :y R} d) { 4? ? ?y 8:y?R}

e) None of the above

1. State the range of the graph shown on the right.

c) {??? ?? ?y :y R}

2. State the axis of symmetry of the graph shown on the right.

a) x = 1 d) y = –4

b) x = –1 e) None of the above

c) y = –3

3. State the x-intercepts of the quadratic y = (2x + 1)(5x – 3).

a) x = 1 and x = –3 d) x = –0.5 and x = 0.6

b) x = –1 and x = 3 e) None of the above

c) x = 0.5 and x = –0.6

4. Determine the y-intercept of the quadratic y = 3x(x + 1).

a) y = 0 d) Both a) and b)

b) y = -1 e) None of the above

c) y = 3

1. Graph the function y = 3(x + 5)2 – 4 on the grid below. State the vertex, axis of symmetry, direction of opening, max/min value, domain, and range.

Vertex

Axis of

Symmetry

Direction of Opening

Max/Min Value

Domain

Range

2. For the quadratic y = 2x2 + 24x + 40, complete the square and state the max/min value and where it occurs.

A

D

c)

B

E

1. Complete the table below for the following transformations:

Transformation Period Amplitude Vertical Shift Horizontal Shift Vertical

Stretch /

Compression/ Reflection

y = 3Sin(x + 30) – 1

y = - Sin(x – 45) + 2

2. Graph y = SinX and y??2sin(x?180)?3on the grid below. Include the table of values for the

original function and the transformed function.

1. Evaluate ? ?? ?75 ?3.

? ?

2.

Simplify using exponent rules and then evaluate ??12527 ??? .

?

3. Simplify each of the following using exponent laws. Evaluate your final answer.

(6 )5 4 ?(2)(2 )5 ??2

a) (6 )(6 )6 7 b) ?? 2?4 ??

For c, and d, state final answer with positive exponents.

9 12 d) ?5x y2 4?2?2x y5 4?

c) ?27x y ? 12 ?6

?10x y ?

1. Which of the following interest rates would result in an i value of 0.003?

a) 3%/annum, simple interest d) 3.5%/annum, compounded monthly

b) 1.095%/annum, compounded daily e) None of the above

c) 0.6%/annum, compounded semi-annually

2. Andrea invests $100 in an account that earns 3.6%/annum, simple interest, for 5 years. Which of the following values is NOT correct?

a) P = $100 c) n = 5 e) None of the above

b) i = 0.0072 d) All of the above

3. 3 years ago, Bobby invested some money in an account that earns 4.8%/annum, compounded quarterly, and now has $500. Which of the following values is NOT correct?

a) n = 12 c) P = 500 e) None of the above

b) i = 0.012 d) All of the above

4. Catherine invests $50 each month for 10 years into an account that earns 1.2%/annum, compounded monthly. Which of the following values is NOT correct? a) n = 120

b) R = 50

c) i = 0.001

d) All of the above

e) None of the above

5. Derek buys a $520000 home and makes weekly payments to pay off his mortgage that charges

7.8%/annum, compounded weekly, over a 25 year term. Which of the following values is NOT correct?

a) A = 520000

b) i = 0.0015

c) n = 1300

d) All of the above

e) None of the above

6. For each of the following, calculate the values of i and n in each row: [10 marks]

Investment Information i n

a) 5.11%/annum, compounded daily for 2 years

b) 6.6%/annum, compounded monthly for 5 years

c) 4.55 %/annum, compounded weekly, for 6 years

d) 2.2%/annum, compounded quarterly, for 13 years

e) 2.7%/annum, compounded semi-annually for 7 years

Exam Review: Part 2

1) Factor as fully as possible:

a) x2 + 5x + 4 b) 3x – 6xy + y – 2y2 c) 50x2 – 2y2

2) Find a simplified expression for the perimeter of a rectangle with width [2 – 3(x + 5)] units, and length (4x + 7) units. Include a diagram.

3) Find a simplified expression for the area of a rectangle with width (3x – 5) units and length (7x + 8) units. Include a diagram.

4) For f(x) = -5x2 + 10x + 5, find f(2) and f(-3).

5) Solve by factoring 2x2 – x – 3 = 0.

6) Solve using the quadratic formula 6x2 + 7x – 2 = 0. State exact and approximate answers.

7) A football follows a path modelled by the equation h = -0.5d2 + 3.5d + 4, where h is the height above ground in feet, and d is the horizontal distance from the player in feet. Calculate where the ball lands.

8) a) State the transformations for the parabola y? (x? ?3)2 7

b) State the max/min value and where it occurs.

9) Complete the square to write the quadratic in graphing form and state the vertex and axis of symmetry: y = –x2 – 8x + 1.

10) Solve for x. Round final answers to two decimal places.

.

11) Determine the centre line and amplitude of the sine function below, and then highlight the starting point for one cycle of the sine curve. Determine the equation of the graph.

Date:

You must show full solutions & show all your steps. Questions with only answers only will result in a zero marks. Exam Review: Basic Skills

1. Expand 3x(2x + 7).

a) 5x2 + 21x

b) 5x + 10 d) 6x + 7

e) None of the above

c) 6x2 + 21x

2. Expand and simplify (x + 4)(6x – 1).

a) 6x2 – 4

b) 6x2 + 23x – 4

c) 7x + 3

3. Factor 5x + 15y – 3xy – 9y2. d) 6x2 + 9x – 4

e) None of the above

a) (5 – 3y)(x – 3y)

b) (x + 3y)(x – 3y)(5 – 3y)

c) (5 – 3y)(x + 5)

4. Factor 4x2 – 9. d) (5 – 3y)(x + 3y)

e) None of the above

a) (2x – 3)(2x + 3)

b) (2x + 3)2 d) (2x – 3)2

e) None of the above

c) (2x + 4.5)(2x – 4.5)

a) { 3? ? ?? ?y :y R}

b) { 4? ? ?? ?y :y R} d) { 4? ? ?y 8:y?R}

e) None of the above

1. State the range of the graph shown on the right.

c) {??? ?? ?y :y R}

2. State the axis of symmetry of the graph shown on the right.

a) x = 1 d) y = –4

b) x = –1 e) None of the above

c) y = –3

3. State the x-intercepts of the quadratic y = (2x + 1)(5x – 3).

a) x = 1 and x = –3 d) x = –0.5 and x = 0.6

b) x = –1 and x = 3 e) None of the above

c) x = 0.5 and x = –0.6

4. Determine the y-intercept of the quadratic y = 3x(x + 1).

a) y = 0 d) Both a) and b)

b) y = -1 e) None of the above

c) y = 3

1. Graph the function y = 3(x + 5)2 – 4 on the grid below. State the vertex, axis of symmetry, direction of opening, max/min value, domain, and range.

Vertex

Axis of

Symmetry

Direction of Opening

Max/Min Value

Domain

Range

2. For the quadratic y = 2x2 + 24x + 40, complete the square and state the max/min value and where it occurs.

A

D

c)

B

E

1. Complete the table below for the following transformations:

Transformation Period Amplitude Vertical Shift Horizontal Shift Vertical

Stretch /

Compression/ Reflection

y = 3Sin(x + 30) – 1

y = - Sin(x – 45) + 2

2. Graph y = SinX and y??2sin(x?180)?3on the grid below. Include the table of values for the

original function and the transformed function.

1. Evaluate ? ?? ?75 ?3.

? ?

2.

Simplify using exponent rules and then evaluate ??12527 ??? .

?

3. Simplify each of the following using exponent laws. Evaluate your final answer.

(6 )5 4 ?(2)(2 )5 ??2

a) (6 )(6 )6 7 b) ?? 2?4 ??

For c, and d, state final answer with positive exponents.

9 12 d) ?5x y2 4?2?2x y5 4?

c) ?27x y ? 12 ?6

?10x y ?

1. Which of the following interest rates would result in an i value of 0.003?

a) 3%/annum, simple interest d) 3.5%/annum, compounded monthly

b) 1.095%/annum, compounded daily e) None of the above

c) 0.6%/annum, compounded semi-annually

2. Andrea invests $100 in an account that earns 3.6%/annum, simple interest, for 5 years. Which of the following values is NOT correct?

a) P = $100 c) n = 5 e) None of the above

b) i = 0.0072 d) All of the above

3. 3 years ago, Bobby invested some money in an account that earns 4.8%/annum, compounded quarterly, and now has $500. Which of the following values is NOT correct?

a) n = 12 c) P = 500 e) None of the above

b) i = 0.012 d) All of the above

4. Catherine invests $50 each month for 10 years into an account that earns 1.2%/annum, compounded monthly. Which of the following values is NOT correct? a) n = 120

b) R = 50

c) i = 0.001

d) All of the above

e) None of the above

5. Derek buys a $520000 home and makes weekly payments to pay off his mortgage that charges

7.8%/annum, compounded weekly, over a 25 year term. Which of the following values is NOT correct?

a) A = 520000

b) i = 0.0015

c) n = 1300

d) All of the above

e) None of the above

6. For each of the following, calculate the values of i and n in each row: [10 marks]

Investment Information i n

a) 5.11%/annum, compounded daily for 2 years

b) 6.6%/annum, compounded monthly for 5 years

c) 4.55 %/annum, compounded weekly, for 6 years

d) 2.2%/annum, compounded quarterly, for 13 years

e) 2.7%/annum, compounded semi-annually for 7 years

Exam Review: Part 2

1) Factor as fully as possible:

a) x2 + 5x + 4 b) 3x – 6xy + y – 2y2 c) 50x2 – 2y2

2) Find a simplified expression for the perimeter of a rectangle with width [2 – 3(x + 5)] units, and length (4x + 7) units. Include a diagram.

3) Find a simplified expression for the area of a rectangle with width (3x – 5) units and length (7x + 8) units. Include a diagram.

4) For f(x) = -5x2 + 10x + 5, find f(2) and f(-3).

5) Solve by factoring 2x2 – x – 3 = 0.

6) Solve using the quadratic formula 6x2 + 7x – 2 = 0. State exact and approximate answers.

7) A football follows a path modelled by the equation h = -0.5d2 + 3.5d + 4, where h is the height above ground in feet, and d is the horizontal distance from the player in feet. Calculate where the ball lands.

8) a) State the transformations for the parabola y? (x? ?3)2 7

b) State the max/min value and where it occurs.

9) Complete the square to write the quadratic in graphing form and state the vertex and axis of symmetry: y = –x2 – 8x + 1.

10) Solve for x. Round final answers to two decimal places.

.

11) Determine the centre line and amplitude of the sine function below, and then highlight the starting point for one cycle of the sine curve. Determine the equation of the graph.