Math 9AName: ___________________

9A Midterm ReviewCh. 1-5

Below are all the vocabulary terms you should know the meaning of for the midterm. The review questions are going to be similar to what you will see on the midterm so make sure you understand how to do each type of question.

Important Vocabulary:

-rational number -integer -sum-difference -product -quotient-reciprocals -expression -equation-constant term -numerical coefficient -linear relation-independent variable -dependent variable -relation-extrapolation -interpolation -degree -perfect square -power -base-exponent -square number -square root-zero exponent law -power of ten -Pythagoras -binomial -monomial -trinomial-term -polynomial -permimeter-exponent law for a product of powers -exponent law for a quotient of powers-exponent law for a power of a power -exponent law for a power of a product-exponent law for a power of a quotient

Ch.1 Review Questions:

1. Use each diagram to determine the value of the square root.

a) √ 19 b) √0 .16

2. Which numbers below are perfect squares? How do you know?

a)25121 b) 2.89 c)

250 d) 0.004

3. Calculate the number whose square root is:

a)57 b) 1.6 c) 0.92 d)

109

Math 9AName: ___________________

4. Determine the value of each square root.

a) √22549 b) √ 9

25 c) √400324 d) √ 8

98

5. Determine the value of each square root.a) √6 .76 b) √327 .61 c) √0 . 0025 d) √0 . 0225

6. The area of a square garden is 12.25 m2.

a) Determine the perimeter of the garden. b)The owner decides to put a gravel pathway around the garden. This reduces the area of the garden by 4.96 m2. What is the new side length of the garden?

7. Use benchmarks to approximate each square root to the nearest tenth.

a) √11.6 b) √0 .39 c) √212 d) √11

52

8. In each triangle, determine the unknown length to the nearest tenth of a unit where necessary.

a) b)

Ch. 2 Review Questions:

1) Complete the table below.

Power Base Exponent Repeated Multiplication Standard Form

35

(–2)4

10 3

– (2 × 2 × 2 × 2 × 2 × 2)

2) Write each expression as a product or quotient of powers.

a) (2 × 3)5 _____ b)( 1

3 )2

_______

Math 9AName: ___________________

3) Write each expression as a single power, then evaluate it.

a)33 × 32 b) (–2)4 × (–2)0

c)511 ÷ 510 d) 108 × 102 ÷ 106

4) Evaluate. Show your work.a)[7 – (–3)]4 – (30 ÷ 6)4 b) [(4 – 10)3 × (3 + 3)5]0

c)(6 – 8)5 ÷ (–4) d) –40 – (8 – 3)3

e)24 × 21 – 23 × 22 f) 42 × 4 + 33 × 32

g)(–4)3 ÷ (–4)2 × (–4)0 + (–4)2 ÷ (–4) h) [(–3)3]3 × [(–4)0]3 – [(–3)5]0

i) [(–4) × (–5)]4 + [(–4)2]2 – [(–2)8 ÷ (–2)7]3

5) On a test, Randy used his calculator to evaluate this expression: The answer that was displayed was 162.a) Is this answer correct?b) If your answer is no, what error did Randy make?c) Show the solution to the problem to verify your answer in part a.

Chapter 3 Review Questions:

1) Sketch a number line and mark each rational number on it. Order the numbers from greatest to least.

–2.25, , –1.5, , 0.9

2) Determine each sum.

a) b)

c) d)

e) f)

Math 9AName: ___________________

3) Determine each difference. Describe the strategies you used.

a) b)

4) Two climbers leave base camp at the same time. Climber A ascends 20.4 m, while climber B descends 35.4 m. How far apart are the climbers? Write a subtraction statement using rational numbers to solve the problem.

5) Determine each product.

a) b)

c) d)e) f)

g) h)

6) Calculate each quotient.

a) b)

c) d)

e) f)

7) Evaluate.

a) b)

c) d)

e) f)

8) A formula for the area of a trapezoid is where b and c are the lengths of the parallel sides and a is the perpendicular distance between these sides. Use the formula to determine the area of a trapezoid with: cm, cm, cm.

Math 9AName: ___________________

Chapter 4 Review Questions:

1) In each equation, determine the value of A when n is 3.a) A = 2n + 1 b) A = 3n – 2c) A = 4n + 3 d) A = 30 – 2n

2) The pattern in each table below continues. For each table write an equation that relates v to t.

a) Term Number, t

Term Value, v b) Term Number,

t Term Value, v

1 8 1 34

2 13 2 31

3 18 3 28

4 23 4 253) Rachel takes care of homes during the summer while their owners are away on

vacation. She charges $8, plus $2.50 a day.

a) Create a table that shows the charges when the owners are away for up to 5 days.b) Write an equation that relates the charge, C dollars, to the number of days, n,

that the owners are away.c) What will the charge be when the owners are away for 14 days?d) How many days were the owners away when the charge was $33?

4) For each table of values below:i) Does it represent a linear relation?ii) If the relation is not linear, explain how you know.iii) If the relation is linear, describe it.

a) x y b) x y c) x y d) x y

1 5 1 1 4 11 –2 –12

2 12 3 3 2 14 –1 –5

3 19 5 7 0 17 0 0

4 26 7 13 –2

20 1 3

5 33 9 21 –4

23 2 4

Math 9AName: ___________________

5) Create a table of values for each linear relation and then graph the relation. Use values of x from –2 to 2.

a)y = x + 4 b) y = 2x + 1c) y = 5 – 2x

6) A computer repair company charges $80 for a service call, plus $50 an hour for labour.a) Create a table to show the relation between the time in hours for the service call and the total cost. b) Is this relation linear? Justify your answer.c) Let n represent the time in hours for the service call and C represent the total cost in dollars. Write an equation that relates C and n.d) How much will a 7-h service call cost?

7) Which equation below describes each graph?a) b)

i) x = 2 ii) x = –2iii) y = 2 iv) y = –2

8) a)Graph these equations on the same grid.x + y = 6 y = 1 x – y = –6

9) Match each equation with a graph on this grid. Justify your answers.a)x + y = 5b)x – y = 5c)x + y = –5

10) The graph shows how the cost of a long distance call changes with the time for the call.a) Estimate the cost of a 7-min call. Is this interpolation

or extrapolation? Explain.b) The cost of a call was $1.00. Estimate the time for the call.

c) The cost of a call was $1.50. Estimate the time for the call.

Math 9AName: ___________________

Chapter 5 Review Questions

1. Identify the polynomials in the following expressions.

a) 2m2 + 1 b) c) –4x d) e) 0.25y2

2. Name the coefficients, variable, degree, and constant term of each polynomial.a) –8y b) 12 c) –2b2 – b + 10 d) –4 – b

3. Identify each polynomial as a monomial, binomial, or trinomial.a) 19t b) g – 4g2 + 5 c) –1 + xy + y2 d) 4 – 11w

4. Write a polynomial to match the following conditions. Sketch them with algebra tilesa) Binomial, degree 1, with a constant term of 4b) 3 terms, degree 2, with the coefficient on the 2nd degree term –2

5. Use algebra tiles to model each polynomial, then combine like terms.Sketch the tiles for the simplified polynomial.a) 4 + x + 1 + 5x + 1 b) –3y2 + 3y – 2c) 2x2 + 8 – 11 – 4x2 + 5x2 d) 3y + 7y2 + 1 – y – 2y – 3y2

6. Simplify each polynomial.a) 3a2 – 2a – 4 + 2a – 3a2 + 5 b) 7z – z2 + 3 + z2 – 7c) d2 + 3d + 1 + 4d2 + 2 d) –6x2 + 10x – 4 + 4 – 12x – 7x2

7. Use algebra tiles to model each sum. Sketch your tile model. Record your answer symbolically.a) (– 4h + 1) + (6h + 3) b) (2a2 + a) + (–5a2 + 3a)c) (3y2 – 2y + 5) + (–y2 + 6y + 3) d) (3 – 2y + y2) + (–1 + y – 3y2)

8. Add these polynomials. Use algebra tiles if it helps.a) (x – 5) + (2x + 2) b) (b2 + 3b) + (b2 – 3b)c) (y2 + 6y) + (–7y2 + 2y) d) (5n2 + 5) + (–1 – 3n2)

9. a) For each shape below, write the perimeter as a sum of polynomials and in simplest form.i) ii)

iii) iv)

Math 9AName: ___________________

10. The sum of two polynomials is 4r + 5 – 3r2. One polynomial is –8 – 2r2 + 2r; what is the other polynomial? Explain how you found your answer.

11. Use algebra tiles to model find each difference. Sketch your tile model. Record your answer symbolically.a) (2s2 + 3s + 6) – (s2 + s + 2) b) (2s2 + 3s – 6) – (s2 + s – 2)c) (–2s2 + 3s + 6) – (–s2 + s + 2) d) (2s2 – 3s + 6) – (s2 – s + 2)

12. Use a personal strategy to subtract. Check your answers by adding.a) (2x + 3) – (5x + 4) b) (4 – 8w) – (7w + 1)c) (x2 + 2x – 4) – (4x2 + 2x – 2) d) (–9z2 – z – 2) – (3z2 – z – 3)

13. A student subtracted (3y2 + 5y + 2) – (4y2 + 3y + 2) like this:= 3y2 – 5y – 2 – 4y2 – 3y – 2= 3y2 – 4y2 – 5y – 3y – 2 – 2= –y2 – 8y – 4a) Explain why the student’s solution is incorrect.b) What is the correct answer? Show your work.

14. The difference between two polynomials is (5x + 3). One of the two polynomials is (4x + 1 – 3x2). What is the other polynomial? Explain how you found your answer.

15. Multiply. Sketch the tiles for one product.a) 2(3b) b) –2(6h) c) 4(2b2)d) –2(2x2) e) –2(–y2) f) –3(–2f)

16. Divide. Sketch the tiles for one division statement.a) 12d ÷ 4 b) –20d ÷ 5 c) 8d ÷ –4d) 12y2 ÷ 4 e) –14x2 ÷ 2 f) –10q ÷ –5

17. Determine each product.a) 4(3a + 2) b) (d2 + 2d)(–3)c) 2(4c2 – 2c + 3) d) (–2n2 + n – 1)(6)e) –3(–5m2 + 6m + 7)

18. Here is a student’s solution for a multiplication question.(–5k2 – k – 3)(–2)= –2(5k2) – 2(k) –2(3)= –10k2 – 2k – 6a) Explain why the student’s solution is incorrect.b) What is the correct answer? Show your work.

19. Determine each quotient. a) (16v + 16) ÷ (8) b) (25k2 – 15k) ÷ (5)

Math 9AName: ___________________

c) (20 – 8n) ÷ (–4) d) (18x2 – 6x + 6) ÷ (6)e) (7 – 7y + 14y2) ÷ (–7)

20. Write the multiplication sentence modelled by each set of algebra tiles.a) b)

21. For each set of algebra tiles in question 1, write a division sentence.

22. Write the multiplication sentence modelled by each rectangle.a) b)

23. For each rectangle in question 4, write a division sentence.

24. Multiply.a) v(3v + 1) b) 3c(5c + 2) c) (8 + 4y)(6y)d) 5p(–5 – 2p) e) (7k – 3)(–m) f) (–1 – 10r)( –r)

25. Divide.a) (6x + 3) ÷ 3 b) (14w – 7) ÷ –7 c) (–15 – 10q) ÷ 5d) (8z2 + 4z) ÷ 2z e) (12c2 – 6c) ÷ 3c f) (9xy – 6x) ÷ –3x

26. Here is a student’s solution for a division question.(–12x2 – 9x – 12xy) ÷ (–3x)

= = 4x2 – 3 + 4xya) Explain why the student’s solution is incorrect.

b) What is the correct answer?