|GRADE 8 MATH REVIEW|
When you do this review, make sure to:
List of Topics
|Pythagorean Theorem (right triangles)|
|Word Problems on Algebra and Geometry|
|- right triangle problem|
|- coin problem|
|- percent problem|
|- rectangle: area and diagonal problem|
|- 3 interest & discount problems|
|- distance, rate, time problem|
|- isometry: translation, rotation problem|
|- pentagon: area/apothem problem|
|- circle: arc length and area problem|
1/ Solve these equations:
|a) -3(x + 2) + 5(2x - 3) = 4(5 - 3x)||b)||c) -2(x + 5) = 2x + 7|
|a) 6x(5 - x) + 4x(x + 3) - 7(2x - x2)||b) (2x - 6) + 5(4 - 3x) - 9(2x + 3x2)|
|c) 3m (n3 + 3n - 2) - 2(mn3 - 9mn - 4m) - 7(-2mn3 + 5mn - 12)|
3/ Factor out the greatest common factor:
|a) tx2 - 4txy + 7 txy2||b) 4x + 8x2 y - 24xy3|
|c) -25 x3 y2 z7 + 50 x2 y z5 - 100 x2 y z3.||d) 18m2 n4 - 27m4 n2 - 81m3 n5.|
|e) -7a3 b3 + 14a7 b4 - 28a4 b7.|
4/ Find the missing side in these right triangles:
5/ A 15 m long ladder is placed against the wall of a building so that the foot of the
ladder is 3 m from the wall.
a) How high up the building will the ladder reach?
b) If each storey of the building is 3 m high, to which storey will the ladder reach?
6/ Jaclyn broke open her piggy bank and found $3.65 in pennies, nickels and dimes.
The number of nickels was 5 more than the number of pennies and the number of dimes
was 10 more than the number of pennies. How many of each coin did she have?
7/ A store owner paid $59 for a shirt which he intends to sell at a price which will give
him a profit of 25% of the cost (the price he paid).
a) What is the selling price of this shirt?
b) What is the total bill for a customer who buys this shirt if the PST is 7.5%
and the GST is 7%?
8/ A rectangle's width is 3 metres less than its length. The perimeter is 34 metres.
a) Find the dimensions of the rectangle.
b) Find the area of the rectangle.
c) Find the length of the diagonal.
9/ How much interest will I earn on an investment of $2500 at 5.3% per annum
if it is invested for 3 years and 6 months?
10) Find the difference in the amount Ryan will earn if he invests $10,000 at 4% per annum
compound interest for 3 years instead of investing the same amount at simple interest
of 4% per annum for 3 years.
11/ Norman bought some new sneakers which regularly cost $120 but were on sale at 35% off.
He also bought 2 new shirts at $23.50 each which were on sale at 15% off.
What was his total bill before taxes?
12/ Montreal is 500 km. from Toronto. If Mary leaves Toronto for Montreal at the same time as Charles leaves Montreal for Toronto, and if she averages 90 km/h while he averages 110 km/hr,
in how many hours will they meet? (make a diagram!!)
13/ Triangle ABC with coordinates A (-2, 7), B (5, 0) and C (-1, -3) is:
a) rotated 900 clockwise about the origin. What are the coordinates of the image?
b) reflected in the x-axis. What are the coordinates of the image?
c) translated through T:(x, y) t (x - 4, y + 6). What are the coordinates of the image?
d) Describe this translation in words.
14/ The Area of a regular pentagon is 75 cm2. If each side is 10 cm, how long is the apothem?
15/ An arc of 27.3 cm is cut off by a 45.6 o central angle in a circle.
a) What is the circumference of the circle?
b) What is the radius of the circle?
c) What is the area of the circle?
d) What is the area of the sector?