These questions are from Section B of a final exam on Grade 8 math.

Show all your work since marks are given for your approach. No marks will be given for correct answers unless acceptable work is shown. Calculators may be used to work these out.

1) A men's wear store is having a sale with 40% off all clothing and shoes. Your dad decides to buy new shirts, socks and shoes at this sale. He buys 2 shirts, 3 pairs of socks and a pair of shoes. The pre-sale prices of these items are: $26 per shirt, $4 per pair of socks and $75 for the shoes. Once the 40% discount is deducted from the total, the store adds 15% sales tax. How much will your dad pay for the items he buys?

__________________________________________

2) Maria's recipe for 8 pancakes calls for 2 eggs, 100 mL milk and 100 mL flour. How many eggs, and how much milk and flour would she need to make 100 pancakes?

__________________________________________

3) It takes Georgina 18 minutes to walk the 1.5 kilometres to school. Demetrius walks at the same speed as Georgina. How many minutes will it take him to walk 2 kilometres to school?

__________________________________________

4) Because she missed the school bus one morning, Janice had to take a taxi. The taxi meter starts at $5.00 and then it costs $1.30 per kilometer travelled. If she lives 12 kilometres from school, and her mother gave her $20.00, will Janice have enough money to pay for the taxi? Explain.

__________________________________________

5) a) Find the simplified form of .....

b) Find the value of 2a + b² + 5c if a = 5.5, b = – 2, and c = – 4.

__________________________________________

6) Solve these equations:

a) 3(2x) + 5 – x = 2x + 17 .......... b)

__________________________________________

7) Triangle ABC has coordinates A(7, 12), B(7, 9) and C(14, 9). Find the coordinates of the 2 image triangles A'B'C' and A"B"C" after each of these transformations? (do each transformation separately on the original triangle ABC.)

a) t(0, – 8) ---> (x, y – 8).......... b) a rotation of + 90° about the origin (0, 0).

___________________________________________

8) Two regular hexagons with centres at A and B are attached along one side. The length of AB is 10.4 metres. The area of each hexagon is 93.6 m². What is the length of one of the equal sides?

___________________________________________

9) Three friends went biking on Monday, Tuesday and Wednesday. On Tuesday, they biked 5 km. more than three times the distance they biked on Monday. On Wednesday, they biked twice the distance they did on Tuesday. If they covered a total of 105 km over the 3 days, how many kilometres did they bike on Tuesday?

___________________________________________

10) A large parcel of land valued at $100 000 was divided into smaller lots. Ms. Jansen bought a lot that was of the large parcel and paid the corresponding amount. She made a down payment of $5000 and financed the rest at her bank.

If she paid 4% simple interest per year on the borrowed amount, how much did she pay in interest for 1 year?

___________________________________________

Solutions

1) 2 shirts @ $26 each = $52 ........ 3 pairs of socks @ $4 each = $12 and .....shoes = $75.

Total purchases before the 40% discount = $52 +$12 + $75 = $139.00

Total after the 40% discount = 60% of $139.00 = $83.40

Tax = 15% of $83.40 = $12.51, so Total bill = $83.40 + $12.51 = $95.91

The items cost your dad $95.91.

___________________________________________

2) 100 ÷ 8 = 12.5 so everything in the recipe gets multiplied by 12.5.

Maria will need 25 eggs, 1250 mL of milk and 1250 mL of flour.

___________________________________________

3) If it takes 18 minutes for 1.5 km, it takes 18 ÷ 1.5 = 12 minutes per kilometre.

It takes Demetrius 2 × 12 = 24 minutes to walk 2 km.

___________________________________________

4) The taxi must travel 12 km to get Janice to school so the cost of the taxi ride will be:

12($1.30) + $5.00 = $20.60 so Janice won't have enough to pay for the cab.

___________________________________________

5)a) First, divide by 2 to get 2(6x – 3) + x = 12x – 6 + x = 13x – 6

b) 2a + b² + 5c = 2(5.5) + (– 2)² + 5(– 4) = 11 + 4 – 20 = – 5

__________________________________________

6) a) 3(2x) + 5 – x = 2x + 17 becomes 6x + 5 – x = 2x + 17 so 5x + 5 = 2x + 17
when we collect like terms, we get 5x – 2x = 17 – 5 or 3x = 12 which makes x = 4

b) We cross multiply to get 3(x – 12) = 2x which becomes 3x – 36 = 2x so x = 36

__________________________________________

7) a) t(0, – 8) ---> (x, y – 8) doesn't change the x value and reduces the y value by 8, so triangle A'B'C' has coordinates A'(7, 4) B'(7, 1) C'(14, 1).

b) A rotation of 90° about the origin changes (x, y) into (– y, x)
so, A" is (–12, 7), B" is (–9, 7) and C" is (– 9, 14).

__________________________________________

8) There are 6 triangles in each hexagram, so the area of 1 triangle = 93.6 m² ÷ 6 = 15.6 m².
The height of the triangle is ½ (10.4) = 5.2, so we know that ½ s (5.2) = 15.6 m².
This makes s, the length of a side = 2 × 15.6 ÷ 5.2 = 6 m.

__________________________________________

9) If we let x be the distance they biked on Monday, then 3x + 5 = the distance they biked on Tuesday and 2(3x + 5) = the distance they biked on Wedneday. The total distance was 105 km, so our equation is x + 3x + 5 + 2(3x + 5) = 105 which becomes 10x + 15 = 105 or 10x = 90.

Since x = 9, they biked 3(9) + 5 or 32 km on Tuesday.

__________________________________________

10) Since and she made a down payment of $5000, she has $55 000 to finance at the bank. 4% of $55 000 = 0.04 × $55 000 = $2200 interest for 1 year.

__________________________________________

MathTub Index