Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts

Pythagorean theorem wikipedia , lookup

Rational trigonometry wikipedia , lookup

Trigonometric functions wikipedia , lookup

Integer triangle wikipedia , lookup

Triangle wikipedia , lookup

Euclidean geometry wikipedia , lookup

Euler angles wikipedia , lookup

Transcript
```SOLUTIONS TO MATH REVIEW
Ch. 1
Ch. 2
1. 40 boys and 60 girls
1. a) 40.5
2. 120 gumballs and 130
chocolate bars
b) 11
c) 303
d) 332
3. 400 blue and 100 red
e) 138
4. \$250.
f) 30
5. 0.4 hours or 24 minutes.
g) 8
6. \$57.50
2.
24 (24 x 12 =288) packages of wieners
36 (36 x 8 =288) packages of buns
3.
Red: 10: 10, 20, 30, 40, 50, 60, 70, 80, 90
Con.: 25: 25, 50, 75, 100
S.S.: 15: 15, 30, 45, 60, 75, 90
7. a) 36%
b) 19%
No cars will be a red convertible with a built
in stereo system.
Ch. 5
1.
rectangle
Area = 80 cm²
Perimeter = 36 cm
triangle
Area = 25 m²
Perimeter = 40 m
parallelogram
Area = 30 cm²
Perimeter = 50 cm
trapezoid
Area = 210 m²
Perimeter = 48 m
right triangle
Area = 6 m²
Perimeter = 12 m
parallelogram
Area = 7.5 m²
Perimeter = 54 m
2. a) Perimeter: 36 cm
Area: 56 cm²
b)
She will have to pay \$28.
3. a) Perimeter: 124.7 m
Area: 900 m²
c)
He will have to pay \$9000.
Ch. 3
a)
120
100
80
60
40
20
0
0
1
2
3
4
5
Student
b) Student 7
c) Student 3, 5
d) 44
e) 75
f) 75
g) 74.5
6
7
8
9
Ch. 6
Ch. 8
1. -9
6. -16
1. \$10
2. -1
7. -10
2. \$12.50
3. 10
8. -12
3. \$9
4. -2
9. -31
4. \$210
5. -25
10. 19
5. # of stars = 4 x Figure #
–2
OR y = 4x – 2
6. 398 stars
Ch. 9
1.
a) >
b) >
c) <
d) >
e) Pat got the bigger piece because if you cut the cake into 5 slices, the pieces will
be bigger than is you cut a cake into 7 slices.
2.
a) <
b) <
c) Noah got the bigger piece.
4.
40 crabby patties have no lettuce.
5.
350 red seats =
117 red seats for children
150 grey seats =
60 grey seats for children
6.
** Note the fraction for green gumballs should have read
80 blue gumballs = 40 with dots and 40 without dots
60 red gumballs
60 green gumballs
15
12
and not
50
50
7.
a)
3
40
b)
31
40
c)
9
40
Ch. 10
1. A net is a 2D pattern that can fold into a 3D object.
2. Congruent means the same.
3. The intercept the point where 2 lines cross each other.
4. The 2 red lines are the diagonals of the rectangle and the black dot is the point of
intersection of the diagonals.
5. A quadrilateral is any shape with 4 sides that are straight lines.
6. An isosceles triangle has 2 sided that measure the same.
7. An equilateral triangle has all of its sides measuring the same.
8. Parallel lines go in the same direction and never touch.
9. Complementary angles are 2 angles that add up to 90˚
10. Supplementary angles are 2 angles that add up to 180˚
11. Vertically opposite angles are 2 angles are the same degree and the make an “X”.
12. Alternate interior angles are 2 angles are the same degree and the make an “Z”.
13. They can only be formed when there are 2 parallel lines.
14. a)
Angle
<1 = 90˚
<2 = 60˚
<3 = 30˚
<4 = 90˚
<5 = 60˚
Reason
Corner of a rectangle is 90˚
All angles in a triangle add up to 180˚ ( 30˚ + 90˚ + 60˚ = 180˚)
Alternate interior angle
Corner of a rectangle is 90˚
All angles in a triangle add up to 180˚ ( 30˚ + 90˚ + 60˚ = 180˚)
OR
Complementary angle (30˚ + 60˚ = 90˚)
b)
Angle
<1 = 120˚
<2 = 30˚
<3 = 30˚
<4 = 75˚
<5 = 60˚
Reason
Supplementary angle (60˚ + 120˚ = 180˚)
All angles in a triangle add up to 180˚ ( 30˚ + 120˚ + 30˚ = 180˚)
Alternate interior angle
Complementary angle (15˚ + 75˚ = 90˚)
All angles in a triangle add up to 180˚ ( 30˚ + 75˚ + 75˚ = 180˚)
Ch. 11
1. i) Length = 5 m
Width = 10dm = 1 m
Height = 220 cm = 2.2 m
Area = 36.4 m²
Volume = 11 m³
2. Box 1 will cost \$10 x 36.4 = \$364
Box 2 will cost \$10 x 62 = \$620
So box 1 will be cheaper to paint.
Ch. 12
4
11
4
b) P(M or T) =
11
c) P(N) = 0
1. a) P(a vowel) =
ii)
Length = 3 m
Width = 2 m
Height = 50 dm = 5 m
Area = 62 m²
Volume = 30 m³
2.
1st draw
2nd draw
100 tickets
2 prizes
99 tickets
1 prize
P(prize) =
2
1
=
100 50
P (prize, prize ) =
P(prize) =
1
99
1
1
1
X
=
is the probability of winning the 2 prizes
4950
50
99
3. a) Since you are the 1st person, you start with 50 lollipops in the bag.
1st draw
2nd draw
50 lollipops
20 red
20 blue
10 green
10 1
P(green) =
=
50 5
49 lollipops
20 red
20 blue
9 green
20
P(blue) =
49
P(green, blue) =
b)
1
20 20
4
X
=
=
is the probability of getting a green and a blue.
5
49 245 49
Since you are the 2st person, you start with 48 lollipops in the bag, because the 1st
person already took out 2 blue lollipops
1st draw
2nd draw
48 lollipops
20 red
18 blue
10 green
47 lollipops
20 red
18 blue
9 green
18
P(blue) =
47
P(green) =
10
5
=
48 24
P(green, blue) =
5
18
15
90
X
=
=
is the probability of getting a green and a blue.
24
47 1128 188
```