GRADE 8 MATH REVIEW SOLUTIONS 
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List of Topics linked to Solutions
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1/ Solve these equations:
a) 3(x + 2) + 5(2x  3) = 4(5  3x) 3x  6 + 10x  15 = 20  12x 19x = 41 t x = 41/19 l 2.168 
b) x  4 =  21 x =  17 
c) 2(x + 5) = 2x + 7 2x  10 = 2x + 7  17 = 4x t x = 17/4 l  4.25 
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2/ Simplify:
a) 6x(5  x) + 4x(x + 3)  7(2x  x^{2}) 30x  6x² + 4x² + 12x  14x + 7x² = 5x² + 28x 
b) (2x  6) + 5(4  3x)  9(2x + 3x^{2}) 2x  6 + 20  15x  18x  27x² =  27x²  31x + 14 
c) 3m (n^{3} + 3n  2)  2(mn^{3}  9mn  4m)  7(2mn^{3} + 5mn  12) 3mn^{3} + 9mn  6m  2mn^{3} + 18mn + 8m + 14mn^{3}  35mn + 84 15mn^{3}  8mn + 2m + 84 
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3/ Factor out the greatest common factor:
a) tx^{2}  4txy + 7 txy² = tx (x  4y + 7y²)  b) 4x + 8x^{2} y  24xy³ = 4x ( 1 + 2xy  6y³ ) 
c) 25 x³ y^{2 }z^{7} + 50 x^{2 }y z^{5}  100 x^{2} y z³ 25 x² y z³ (xyz^{ 4}  2z² + 4) 
d) 18m^{2} n^{4}  27m^{4 }n^{2}  81m^{3} n^{5}. 9m²n² ( 2n²  3m²  9mn³ ) 
e) 7a^{3 }b^{3} + 14a^{7} b^{4}  28a^{4 }b^{7}.  7a³b³ ( 1  2a^{ 4} b + 4ab^{ 4} ) 
4/ Find the missing side in these right triangles:
a)  b) 
c)  d) this triangle is isosceles, ratio is 1: 1:

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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?
a)
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b) If each storey of the building is 3 m high, to which storey will the ladder reach?
14.7 + 3 = 4.9 storeys  or the 4th storey.
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6/ $3.65 in pennies, nickels and dimes. number of nickels  5 more than pennies; number of dimes  10 more than pennies. How many of each coin did she have?
Let p = the number of pennies
coin  number  value in cents 
pennies  p  p 
nickels  p + 5  5( p + 5) 
dimes  p + 10  10(p + 10) 
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7/ cost = $59  profit 25% of the cost (the price he paid).
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8/ A rectangle's width is 3 metres less than its length. The perimeter is 34 metres.
a) Find the dimensions of the rectangle.
We know the perimeter = 34 m so 2 ( x + x  3) = 34 t 4x = 40, so x = 10
b) Find the area of the rectangle. Area = 70 metres².
c) Find the length of the diagonal.
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9/ How much interest on $2500 at 5.3% per annum for 3 years and 6 months?
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10) difference in interest for $10,000 at 4% per annum compounded for 3 years and simple interest at 4% per annum for 3 years.
With compound interest, we calculate the total amount of money instead of just the interest. A = P (1 + r)^{ t} = 10,000 (1 + 0.04)^{ 3} = $11,248.64 which means I = $1,248.64 
For simple interest, we do the same as in the previous question. I = P $ r $ t = $10000 (0.04)( 3) = $1200 which means the difference = $48.64 
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11/ sneakers cost $120 on sale at 35% off. 2 shirts at $23.50 each at 15% off. total bill?
Sneakers cost 65% ($120) = $78; Shirts cost 85% ($23.50) % 2 = $39.95
Total bill = $78 + $39.95 = $117.95
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12/ Montreal is 500 km. from Toronto. Mary averages 90 km/h; Charles averages 110 km/hr,
in how many hours will they meet? (make a diagram!!)
Let t = the time they travel until they meet.
Since d = r t, and we know the sum of their distances must = 500 km.,
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13/ Triangle ABC with coordinates A (2, 7), B (5, 0) and C (1, 3) is:
question  solution 
a) rotated 90^{0} clockwise about the origin.  A' (7, 2); B' (0,  5); and C' ( 3, 1) 
b) reflected in the xaxis.  A' ' (2,  7); B'' (5, 0); and C'' ( 1, 3). 
c) translated with T:(x, y) t (x  4, y + 6).  A''' (6, 13); B''' (1, 6); and C''' ( 5, 3) 
d) Describe this translation in words.  The points moved 4 units left and 6 units up. 
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14/ The Area of a regular pentagon is 75 cm^{2}. If each side is 10 cm, how long is the apothem?
Since A = ½ n $ s $ a ; where n = number of sides, s = length of a side and a = apothem;
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15/ An arc of 27.3 cm is cut off by a 45.6^{ o} central angle in a circle.
a) We use a proportion since C = arc cut off by 360°
So,
b) What is the radius of the circle?
Since
c) What is the area of the circle?
d) What is the area of the sector?
So,
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