Chapter 4 to 6 Review
Chapter
Chapter 6
Section
Chapter 4 to 6 Review
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Solutions 44 Videos

Use finite differences to determine whether each relation is linear, quadratic, or neither.

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Q1a

Use finite differences to determine whether each relation is linear, quadratic, or neither.

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Q1b

Sketch the graph of the quadratic relation. Describe the transformation from the graph of y = x^2.

\displaystyle y =x^2 + 2

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Q2a

Sketch the graph of the quadratic relation. Describe the transformation from the graph of y = x^2.

\displaystyle y = (x + 3)^2

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Q2b

Sketch the graph of the quadratic relation. Describe the transformation from the graph of y = x^2.

\displaystyle y =- \frac{1}{4}x^2

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Q2c

Dianne dove from the 10-m diving board. Her height h, in metres, above the water when she is x metres away from the end of the board is given by h = -(x - 1]^2 + 11.

a) Sketch a graph of her dive.

b) What was her maximum height above the water?

c) What horizontal distance had she travelled when she entered the water? Answer to the nearest tenth of a metre.

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Q3

Determine an equation to represent the parabola in the form y = a[x - r)(x - s).

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Q4

Evaluate.

2^{-4}

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Q5a

Evaluate.

(-3)^{-2}

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Q5b

Evaluate.

25^{0}

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Q5c

Evaluate.

8^{-1}

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Q5d

Evaluate.

(-1)^{12}

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Q5e

Evaluate.

(\frac{3}{4})^{-3}

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Q5f

Cobalt—60 is a radioactive element that is used to sterilize medical equipment.

Cobalt-60 decays to \frac{1}{2}, or 2^{-1}. of its original amount after every 5.2 years. Determine the remaining mass of 20 g of cobalt-60 after

a) 20.8 years

b) 36.4 years

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Q6

Write an algebraic expression to represent the area of the figure. Expand and simplify.

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Q7

Expand and simplify.

\displaystyle (n+ 3)(n -3)

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Q8a

Expand and simplify.

\displaystyle (h + 5)^2

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Q8b

Expand and simplify.

\displaystyle (d-4)(d-2)

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Q8c

Expand and simplify.

\displaystyle (m +3)(m + 7)

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Q8d

Expand and simplify.

\displaystyle (3t -5)(3t + 5)

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Q8e

Expand and simplify.

\displaystyle (x - 7)^2

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Q8f

Expand and simplify.

\displaystyle x(3x + 1)(2x - 5)

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Q9a

Expand and simplify.

\displaystyle (2k + 3)^2 -k(k+ 2)(k -2)

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Q9b

Expand and simplify.

\displaystyle 5(y-4)(3y + 1) + (3y -4)^2

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Q9c

Expand and simplify.

\displaystyle 3(2a + 3b)(3a -2b)

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Q9d

The area of a rectangle is given by the expression 8x^2 + 4x. Draw diagrams to show the possible rectangles, labelling the length and width of each.

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Q10

Factor, if possible.

\displaystyle y^2 + 12y + 27

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Q11a

Factor, if possible.

\displaystyle x^2 + 2x -3

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Q11b

Factor, if possible.

\displaystyle n^2 + 22n + 21

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Q11c

Factor, if possible.

\displaystyle p^2 -8p + 15

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Q11d

Factor, if possible.

\displaystyle x^2 + 2x - 15

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Q11e

Factor, if possible.

\displaystyle k^2 -5k + 24

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Q11f

Factor.

\displaystyle p^2 + 12p + 36

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Q12a

Factor.

\displaystyle 9d^2 -6d + 1

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Q12b

Factor.

\displaystyle x^2 - 49

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Q12c

Factor.

\displaystyle 4a^2 -20a + 25

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Q12d

Factor.

\displaystyle 8t^2 -18

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Q12e

Factor.

\displaystyle a^2 -4b^2

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Q12f

Find the value of k so that each trinomial can be factored over the integers.

\displaystyle m^2 + km + 10

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Q13a

Find the value of k so that each trinomial can be factored over the integers.

\displaystyle 9a^2 -a + 4

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Q13b

The area of a circle is given by the expression \pi(4x^2 + 36x + 81). What expression represents the diameter of this circle?

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Q14

A quadratic relation has roots 0 and -6 and a maximum at (-3, 4). Determine the equation of the relation.

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Q18

The perimeter of a rectangle is 8 m and its area is 2 m^2. Find the length and width of the rectangle to the nearest tenth of a metre.

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Q20

A ferry operator takes tourists to an island. The operator carries an average of 500 people per day for a round-trip fare of $20. The operator estimates that for each $1 increase in fare, 20 fewer people will take the trip. What fare will maximize the number of people taking the ferry?

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Q21