-3x - 6 + 10x - 15 = 20 - 12x
19x = 41 t x = 41/19 l 2.168
x - 4 = - 21
x = - 17
-2x - 10 = 2x + 7
- 17 = 4x t x = -17/4 l - 4.25
| 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 - x2) 30x - 6x² + 4x² + 12x - 14x + 7x² = 5x² + 28x |
b) (2x - 6) + 5(4 - 3x) - 9(2x + 3x2) 2x - 6 + 20 - 15x - 18x - 27x² = - 27x² - 31x + 14 |
| c) 3m (n3 + 3n - 2) - 2(mn3 - 9mn - 4m) - 7(-2mn3 + 5mn - 12) 3mn3 + 9mn - 6m - 2mn3 + 18mn + 8m + 14mn3 - 35mn + 84 15mn3 - 8mn + 2m + 84 | |
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3/ Factor out the greatest common factor:
| a) tx2 - 4txy + 7 txy² = tx (x - 4y + 7y²) | b) 4x + 8x2 y - 24xy³ = 4x ( 1 + 2xy - 6y³ ) |
| c) -25 x³ y2 z7 + 50 x2 y z5 - 100 x2 y z³ -25 x² y z³ (xyz 4 - 2z² + 4) |
d) 18m2 n4 - 27m4 n2 - 81m3 n5. 9m²n² ( 2n² - 3m² - 9mn³ ) |
| e) -7a3 b3 + 14a7 b4 - 28a4 b7. - 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 900 clockwise about the origin. | A' (7, 2); B' (0, - 5); and C' (- 3, 1) |
| b) reflected in the x-axis. | 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 cm2. 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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