Symmetry and Surface Area
Scale factor and Similarity
Powers and Exponents
Rational Numbers
100
How many lines of symmetry does the image have?
5
100
Are the two triangles similar? Explain how you know
The two triangles are similar since when we compare the corresponding side lengths, they are proportional (the same)
Side length BC = 7.5/3 = 2.5, AB 5/2 = 2.5, AC 32.5/13 = 2.5
100
4 x 4 x 4 and (-5) x (-5) x (-5) x (-5) written in exponential form is....
Remember that exponential form is a shorter way of writing repeated multiplication.
4^3 since we have three 4's that are multiplying together we know the exponent will be 3
(-5)^4 since we have four (-5)'s that are multiplying together
100
Order the following rational numbers in ascending order
-1.5, 7/8, 8/10 -0.3, - 8/10
-1.5, -8/10, -0.3, 8/10, 7/8
200
Determine the order of rotation and angle of rotation for the following image
Remember that order of rotation is how many times the image rotates into itself before returning to the beginning.
Angle of rotation is the angle in how much I turn the image for it to fit in itself. We take 360 and divide it by the order of rotation.
Order of rotation 4 and 90 degrees since 360/4 = 90 degrees
200
If △ABC is similar to △DEF, determine the value of b. Show your work
Since the triangles are similar, we know that all side lengths are proportional
16/20 = 0.8, 20/25 = 0.8, b/15 = 0.8
We can solve this missing side length 15 x 0.8 = 12
Likewise you can solve it like this
20/16 = 1.25, 25/20 = 1.25, 15/b = 1.25
Solving for b, b = 15 /1.25 = 12
200
Rewrite the following as a single power and evaluate
a) (-3)2 x (-3)2
b) 26 ÷ 23
Remember that if we have the same bases multiplying we ADD the exponents
a) (-3)2 x (-3)2 = (-3)2+2 = (-3)4 = 81
Remember that if we have the same bases dividing we SUBTRACT the exponents
b) 26 ÷ 23 = 26-3 = 23 =8
200
Calculate the following. Show your work
-2.1 x 3.2 + 5.3 x (-0.5)
We still follow BEDMAS, we would multiply first
-6.72 + (-2.65) Multiply
-9.37 We add the two negatives together
300
Which example shoes a reflection of triangle X on the dotted line?
Example i is not since it does not reflect but just extends the line
Example ii is not since it flips over a different line of reflection
Example iii is not since it rotates 180 degrees instead
Example iv is
300
The two polygons are said to be similar. Find the length of ZY
Since the two polygons are similar. I know that the side lengths must be proportional.
ZY/1.8cm = 2/3
We multiply both sides by 1.8 we will get
ZY = (2/3) x 1.8 = 1.2cm
300
Write the following as two powers then evaluate
a) [3 x (-2)]2
b) (4/5)3
Remember that we can each factor in the product with the same exponent
a) [3 x (-2)]2 = 32 x (-2)2 = 9 x 4 = 36
Remember that if the exponent applies to the whole fraction, we can write the numerator and the denominator with the exponent
b) (4/5)3 = 43/53= 64 / 125
300
Determine each value.
a)-2/5(-2/3)
b)-2(1/6)-(1/3)
a) 4/15 since we multiply the two fractions straight across as the brackets mean we multiply
b)First we change to improper fraction
(-13/6)-(1/3) We then change to a common denominator
(-13/6)-(2/6) since we have common denominator and both numbers are negative we know that our answer will be negative and we add the numbers across
(-15/6)
400
This object is made using centimetre cubes. Determine its surface area.
In order to calculate the surface area, we need to calculate all the different faces.
Front and back
We need to split the front and back into two separate pieces. One which is 1x2=2 and the other which is 1x1=1. The total surface area then would be 3. We would multiply this by 2 since we have 2 faces which gets us to have 6 cm2
Top and bottom
it would be similar for how we do the top and bottom. 2 pieces split so that we have a 2x1=2 and 1x1=1. 2+1=3 and we have 2 faces which means 6 cm2
Sides
This would also be similar so we would have 2 pieces split so that we have a 2x1=2 and 1x1=1. 2+1=3 and we have 2 faces which means 6 cm2
We add the totals to get 6 + 6 + 6= 18 cm2
400
Determine if the following polygons are similar.
We need to determine if the side lengths are proportional (same).
top and bottom side length 4cm/2cm = 2cm
side side lengths 16cm/4cm = 4cm
As we can see, the side lengths are not proportional with the scale factor so the polygons are not the same.
400
Evaluate the following, show your work
a) -2(15-23) + 5
b) 6 - 2(23)
In each of these, we follow BEDMAS
a) -2(15-8) + 5 Solve whats in the brackets
-2 (7) +5 Brackets
-14 +5 Multiplication
9 Addition
b) 6 - 2(8) Brackets
6-16 Multiplication
-10 subtraction
400
Which of the following numbers is a perfect square and why?
64/121, 8/4, 0.81, 1.6
Remember that a perfect square can be expressed as the product (multiplication) of two equal (same value) of rational factors
64/121 can be multiplied by 8/11 x 8/11
and 0.81 can be multiplied by 0.9 x 0.9
8/4 and 1/6 are not perfect squares since there are not two numbers that are the same that are rational that can be multiplied together.
500
Write an expression that represents the volumes combined of a square with side length 3cm and side length 4cm. Then calculate what the total volume of the two cubes would be. (Draw it out if it helps)
Volume is length x width x height. Since the side lengths of a cube are all the same the volume of a cube will be sidelength3
The volume of first cube = 33
Volume of second cube = 43
Combined volume is 33 + 43 = 27 + 64 = 91
Combined volume is 91 cm3