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Unit 4
Bonus Questions (1-4)
100
Write 2 to the power of 5 in expanded form a) 2x2x2x2x5 b) 2x2x2x5x5 c) 2x2x2x2x2 d) 2x5
The answer is: c) 2x2x2x2x2
100
Identify the Independent Variable and Dependent Variable in each pair. a) stress and heart rate b) income and level of education
a) The independent variable would be the stress and the dependent variable would be the heart rate. b) The independent variable would be the income and the dependent variable would be the level of education.
100
Is y= 2x+1 a linear equation? State why or why not.
Yes, y= 2x + 1 is a linear equation. A linear equation is an equation for a straight line.
100
What is the maximum area of a rectangle that has side lengths that are integers and has a perimeter of 32m? a) 8m b) 16m c) 4m d) 64m
P= 2(l+w) 32/2=16 8+8=16 The answer is 8m, with an area of 64m^2
100
What is the standard form of an equation?
The standard form of an equations is: ax + by + c = 0
200
Write 5^7 (5 to the power of 7) ÷ 5^4 (5 to the power of 4) in a single power a) 5^2 (5 to the power of 2) b) 5^74 (5 to the power of 74) c) 5^3 (5 to the power of 3) d) 5^28 (5 to the power of 28)
The answer is: 5^7-4 =5^3 (5 to the power of 3)
200
Identify if the relation is a direct variation, partial variation, or neither of them a) d = t^2 + 5 b) r = 3t + 6 c) c = 2.3m d) y= -8x + 3
a) neither b) partial c) direct d) partial Each answer is 50 points each.
200
What is the line perpendicular to the line y = 7x+3? a) y= 7/3x + 3 b) y= -7x +3 c) y= -1/7x + 3 d) none of the above
The answer is: perpendicular means a negative reciprocal y= -1/7x + 3
200
What is the volume of the cylinder that has a radius of 6cm and a height of 9cm? a) 54 cm^3 b) 1017 cm^3 c) 600 cm^3 d) none of the above
The answer is: b V= πr2^h = π(6^2)(9) = 1017 cm^3
200
Determine the radius of a golf ball that has a surface area of 324 cm^2. Round the answer to the nearest tenth. SA of a sphere: 4πr^2
SA of a sphere: 4πr^2 324= 4πr^2 324 ----- = r^2 4π 324/4π = 25.8 25.8/square 5.07 = 5.0 The radius is about 5 cm.
300
Which expression shows -4(x+10) expanded? a) -4x + 15 b) -4x + 10 c) -4x + 40 d) -4x - 40
The answer is: d -4x - 40
300
What is a 'curve of best fit'? What is a 'line of best fit'?A 'curve of best fit is a curve that passes through (or as near as possible) to the points on a scatter plot. A 'line of best fit' is a straight line that passes through (or as near as possible) to the points on a scatter plot.
A 'curve of best fit is a curve that passes through (or as near as possible) to the points on a scatter plot. A 'line of best fit' is a straight line that passes through (or as near as possible) to the points on a scatter plot.
300
Write an equation by those given points (6,9) and (2,3)
The answer is: x1 =6, y1=9, x2=2, y2=3 3 - 2 -6 -3 3 ------ = ------ = ----- = ----- ; m = 3/2 2 - 6 -4 -2 2 Equation: y= 3/2x + 9
300
A square-based decorated box has a volume of 600cm^3. What dimensions of the box have the least amount? a) 200cm by 200cm by 200cm b) 100cm by 100 cm by 100cmc) 8cm by 8cm by 8cm d) 50cm by 50cm by 50cm The answer is: c 8 x 8 x 8 = 512cm^3
The answer is: c 8 x 8 x 8 = 512cm^3
300
What is the root (of an equation)?
The value of the variable that makes an equation true. The same as the solution of an equation.
400
2k^4 + 3k + 6k is a a) monomial b) binomial c) trinomial d) polynomial
The answer is: c) trinomial
400
Mention the opposite of the hypothesises below a) Medicine improves your health b) In Ontario, more teenagers join basketball teams then soccer teams.
a) Medicine worsens your health b) In Ontario, the number of teenagers who join soccer teams are more than or equal to the number of teenagers who join basketball teams.
400
Express this equation '6x + 2y + 8= 0' in the form y= mx+b (slope-intercept form)
y= mx+b isolate 'y' 2y= 6 + 8 y = 6 ÷ 2x + 8 ÷ 2 y = 3x + 4
400
Which one of these have the maximum volume? a) 6cm by 2cm by 2cm b) 7 cm by 7cm by 7cm c) 9cm by 9cm by 9cm d) 10cm by 10 cm by 10cm
The answer is: d The diameter and height are the same.
400
A piece of land has a perimeter of 256 m. a) What are the dimensions of the land, if the land is a square? b) What are the dimensions of the land, if the land is in a rectangular shape and the length is twice the size of the width? The answer can be rounded to the nearest tenth.
a) 16m b) 11.3m (width) by 22.6m (length)
500
Solve for x: 6x +4 = 40 a) x = 5 b) x = 6 c) x = 10 d) x = 16 The answer is: 40-4=36 36÷6=6 x = 6
The answer is: 40-4=36 36÷6=6 x = 6
500
Rise= 6m Run = 10m Rise 6 ----- = ---- = 0.6 Run 10 The slope of the object is 0.6 m.
What is of the slope of an object with a rise of 6m and run of 10?m
500
The price charged to fix a computer is $56, plus $30/h a) Mention an equation representing this relationship; assume 'c' as the variable for the total cost. b) What is the total cost of repair that takes 2 hours?
a) C= $30h + 56 b) C= $30(2) + 56 = $60 + 56 = $116 The cost for 2 hours of repair is $116
500
A cylindrical can of coke holes 355mL and its diameter is 7 cm. Calculate the height of the can (to its nearest tenth of a centimetre) Volume formula : πr^2h
Volume: πr^2h Isolate 'h' πr^2 = 38.5 =355 ÷ 38.5 = 9.22 (9.2, to the nearest tenth) The height of the can is 9.2 cm
500
Alia's rate of pay is 10.75/h. If you made a table of values of Alia's earning, how would her hourly wage relate to the first differences?
Alia's hourly wage difference will be the same as the first difference. For example, if she works for 2 hours, her pay will be $21.50. 21.50-10.75 = 10.75 (the first difference). She is earning $10.75 per hour and the first difference is also $10.75.