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) 5×2 + 21x

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

e) None of the above

c) 6×2 + 21x

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

a) 6×2 – 4

b) 6×2 + 23x – 4

c) 7x + 3

3. Factor 5x + 15y – 3xy – 9y2. d) 6×2 + 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 4×2 – 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 = 2×2 + 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) 50×2 – 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) = -5×2 + 10x + 5, find f(2) and f(-3).

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

6) Solve using the quadratic formula 6×2 + 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.

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