Ch1 to Ch3 Cumulative Review (pg 178)
Chapter
Chapter 3
Section
Ch1 to Ch3 Cumulative Review (pg 178)
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Solutions 35 Videos

Find the next three terms in each sequence. Describe how to find successive terms.

a) 1, 2, 4, 7

b) 1, 4, 9, 16

c) 17, 12, 7, 2

d) 2, 6, 12, 20

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Q1

Use the clues to find the value of E. Describe your strategy.

\displaystyle \begin{array}{llllllll} &A \times B = 80\\ &A \times C = 200\\ &B \times D = 36\\ &D \times E = 18\\ &C = 100 \end{array}

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Q2

You have three $5 bills, a $10 bill, and two $20 bills. How many different sums of money can you make?

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Q3

The area of this figure is 400 cm^2. What is its perimeter?

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Q4

Evaluate.

a) \displaystyle \frac{2}{3}- \frac{3}{4} \times \frac{1}{2}

b) \displaystyle (\frac{2}{3} - \frac{3}{4}) \times \frac{1}{2}

c) \displaystyle \frac{3}{4} - \frac{2}{3} \times \frac{1}{2}

\d) \displaystyle (\frac{3}{4} - \frac{2}{3}) \times \frac{1}{2}

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Q5

The daily high temperatures during one week in February were -6°C, 2°C, -8°C,- 5°C, 4°C, 1°C, and -9°C. What was the mean high temperature that week?

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Q6

A number is considered a perfect number if its factors (not including itself) add up to the number. For example, 6 is a perfect number because 1, 2, and 3 are factors of 6 and1+2+3+6.Findthenextperfect number. Describe the strategy that you used.

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Q7

How many breaths do you take in 1 year? Describe your strategy.

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Q8

Can you find five odd numbers that add up to 50? What about six numbers? Explain.

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Q9

Give a counter-example to prove that each statement is false.

a) The sum of two square numbers is always a square number.

b) The sum of two acute angles is an obtuse angle.

c) The sum of two prime numbers is a prime number.

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Q10

Claire is training for a half-marathon. The graph shows how her distance from home changed with time on a 14-km run. Write a description of her run.

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Q16

The area of one face of a cube is 64 cm^2.

a) What is the side length of the cube?

b) Determine the volume of the cube.

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Q17

Evaluate.

\displaystyle 3^2 + 2^3

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Q18a

Evaluate.

\displaystyle 5^2 -6^2 \div 2^2

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Q18b

Evaluate.

\displaystyle (4^3-3^3) + (2^5 \div 4^2)

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Q18c

Evaluate.

\displaystyle (\frac{3}{5})^2 \div \frac{9}{10}

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Q18d

Simplify.

\displaystyle n^2 \times n^3

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Q19a

Simplify.

\displaystyle d^8 \div d^2

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Q19b

Simplify.

\displaystyle (a^3)^4

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Q19c

Simplify.

\displaystyle 3 m^2n \times 4mn^3

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Q19d

Simplify.

\displaystyle 24 k^5 q^3 \div (2k^q)^2

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Q19e

In a quiz show, contestants receive 10 points for each correct answer but lose 5 points for each incorrect answer.

a) Write an expression for a contestant’s total score.

b) Theo answered 12 questions correctly and 5 questions incorrectly. Find his total score.

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Q20

Simplify.

4m + 8 -3m - 10

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Q21a

Simplify.

\displaystyle 3x^2 + 6x -3 -x^2 -5x -1

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Q21b

Simplify.

\displaystyle (h + 5)- (3h -8)

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Q21c

Simplify.

\displaystyle (4t+ 5w) + (t -2w)-(3t + 4w)

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Q21d

Expand and simplify.

\displaystyle 5(x + 3)

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Q22a

Expand and simplify.

\displaystyle k(2k - 1)

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Q22b

Expand and simplify.

\displaystyle 4(3y + 2) +3 (2y - 7)

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Q22c

Expand and simplify.

\displaystyle \frac{2}{3}(3a + 1) + \frac{1}{2}(4a -1)

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Q22d

a) Find a simplified expression for the perimeter of the triangle.

b) Determine the perimeter when n = 5.

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Q23