Patterns & Equations
Measurement of Circles
Transformations
Integer Operations
Angles and Triangles
100
What is the 11th term value in the following number sequence?
5, 12, 19, 26, ...
Answer: 75
100
What is the name of the chord that stretches from one end of a circle to the other AND passes through the center?
The diameter.
100
True or False:
A 90o clockwise rotation about the origin is the same as a 270o clockwise rotation about the origin.
False!
A 90o clockwise rotation about the origin is the same as a 270o counter-clockwise rotation about the origin.
100
True or False:
The product of three negative integers is always negative.
True!
E.g. (-2) x (-5) x (-7)
= (+10) x (-7) <-- First product is positive
= -70
100
Fill-in-the-blank:
A _______________ is a straight line that intersects two or more parallel lines.
Answer:
A transversal is a straight line that intersects two or more parallel lines.
200
Simplify the following expression:
4 (x + 3) - 5 (q - 4)
Answer: 4 (x + 3) - 5 (q - 4)
= 4x + 12 - 5q + 20
= -5q + 4x + 32
200
What are the formulas for the circumference and the area of a circle?
Circumference = Pi x d OR 2 x Pi x r
Area = Pi x r2
200
Describe the translation vector [5, -7] in words.
The translation vector [5, -7] means move 5 units to the right and 7 units down.
200
True or False:
Subtracting an integer is the same as adding its opposite.
True!
E.g. (-16) - (+12) = (-16) + (-12)
200
State a pair of co-interior angles in this diagram.
|
Answer:
i) Angles 3 & 6
ii) Angles 4 & 5
300
What is the solution to the following equation?
6 (n + 3) = -2(3 - n)
6n + 18 = -6 + 2n
6n - 2n = -6 - 18
4n = -24
n = -24/4
n = -6
300
A circle has an area of 14 cm2. What is the radius?
A = Pi x r2
r = sqrt(A ÷ Pi)
r = sqrt (14 cm2 ÷ Pi)
r = 2.11 cm (approx.)
300
A point has been reflected across the (diagonal) line represented by the equation y = x. The coordinates of the point are (6, 12).
What are the coordinates of the image point, AND in which quadrant is the image point located?
The coordinates of the image point are (12,6) and is located in quadrant 1.
300
Karen measures the temperature every day at 8:00 a.m. for one week. The temperatures for the week were:
4°C, -3°C, -7°C, -5°C, -4°C, 5°C, 3°C
What is the average weekly temperature?
Average (mean) = sum of numbers / # of numbers
= (+4) + (-3) + (-7) + (-5) + (-4) + (+5) + (+3) ÷ 7
= -7 ÷ 7
= -1
Therefore, the average weekly temperature is -1oC.
300
State a pair of corresponding angles in this diagram.
Answer:
i) Angles 1 & 6
ii) Angles 3 & 7
iii) Angles 2 & 5
iv) Angles 4 & 8
400
Solve the following inequality:
7 + 3x < 4 + 5 (x - 1)
7 + 3x < 4 + 5 (x - 1)
7 + 3x < 4 + 5x - 5
3x - 5x < 4 -5 -7
-2x < -8
x > -8/-2
x > 4
400
A size 7 ring has a diameter of 17.3 mm. A size 8 ring has a diameter of 18.2 mm.
How many times greater is the circumference of the size 8 ring compared to that of the size 7 ring.
Size 8 Ring: C = Pi x d
= Pi x (18.2 mm)
= 57.18 mm
Size 7 Ring: C = Pi x d
= Pi x (17.3 mm)
= 54.35 mm
Size Comparison: 57.18 mm ÷ 54.35 mm = 1.05
Therefore, the circumference of a size 8 ring is about 1.05 times greater than the circumference of a size 7 ring.
400
Select the two points that lie on the same horizontal line.
| a) (2, 1) and (2, 5) |
| b) (-3, 3) and (4, 3) |
Answer: b) (-3, 3) and (4, 3)
We know this because on a horizontal line, the y-values are all the same.
400
Evaluate using BEDMAS:
Solution:
= (26 + (-16) ÷ 2) / (3)(-2)
= (26 + (-8)) / (3)(-2)
= (26 + (-8)) / -6
= 18 / -6
= -3
400
What is the measure of angle c?
Answer: Angle c = 180o - (42o + 51o)
= 180o - (93o)
= 87o (opposite of angle c)
500
Joseph and Jordan play baseball. By the end of their season, Joseph made five more than twice the number of home runs compared to Jordan. Together, they made a total of 41 home runs.
How many home runs did each player make throughout their season?
Let n represent the number of home runs Jordan made
Let 2n + 3 represent the number of home runs Joseph made
n + 2n + 5 = 41
3n + 5 = 41
3n = 41 - 5
3n = 36
n = 36 / 3
n = 12
2n + 3 = 2(12) + 5
= 24 + 5
= 29
Therefore, Jordan made 12 home runs and Joseph made 29 home runs throughout their season.
500
A circular pool has a concrete walkway around the outside of the pool.
The concrete walkway is 1.5 m wide. The diameter of the pool and walkway together is 23 m.
Determine the area of the pool cover (The pool cover does not cover the walkway.)
1) Find the radius of the pool only:
Diameter of the pool = 23 m - 2 (1.5 m)
= 23 m - 3 m
= 20 m
Radius of the pool = d ÷ 2
= 20 m ÷ 2
= 10 m
2) Find the area of the pool to determine the area of the pool cover:
A = Pi x r2
= Pi x (10 m)2
= Pi x (100 m2)
= 314.16 m2 (approx.)
Therefore, the area of the pool cover is about 314.16 m2.
500
The quadrilateral ABCD has vertices at A(1, 1), B(1, 4), C(5, 4), and D(5, 1). Determine the coordinates of B" after a reflection in the x-axis, followed by a reflection in the y-axis.
Coordinates of B are (1, 4)
1) Reflection of B in the x-axis: B' (1, -4)
2) Reflection of B' in the y-axis: B" (-1, -4)
500
The sum of two integers is -5 and the difference is 13. What are the two integers?
Let x represent the larger integer
Let y represent the smaller integer
i) x + y = -5
ii) x - y = 13
-___________
2y = -18
y = -18 ÷ 2
y = -9 x + y = -5 x + (-9) = -5
x = -5 - (-9)
x = 4
Therefore the larger integer is 4 and the smaller integer is -9.
500
Name the types of angles used to solve for angle c.
Answer:
i) Supplementary angles
ii) Opposite angles