Math 10C Pre-IB final exam
1. A square has area 18 225 square feet. What is the perimeter of the square?
2. A cube has surface area 11 616 cm2. What is the edge length of the cube?
3. Evaluate each radical. Why do you not need a calculator?
3 6 4 81
a) √1000 b) √0.81 c) √64 d) √
625
4. Write each radical in simplest (i.e. mixed) form.
3 4
a) √150 b)√135 c) √112 d)√162
5. Write each mixed radical as an entire radical.
3 4
a) 6√5 b)3√14 c) 4√3 d)2√2
6. Express each power as a radical.
1
1 5
3 3
a) 124 b)(−50)3 c) 1.20.5 d)(8)
7. Express each radical as a power.
3
3 5 4 42
a) √1.4 b) √132 c) (√2.5) d) (√5)
, 8. Evaluate each power without using a calculator.
3
1 5
9 2
a) 160.25 b) 1.442 c) (−8)3 d) (16)
9. A company designs a container with the shape of a triangular prism to hold 500 mL of juice. The bases of
the prism are equilateral triangles with side length s centimetres. The height, h centimetres, of the prism is
given by the formula:
1
ℎ = 2000(3)−2 𝑠 −2
What is the height of a container with base side length 8.0 cm? Give your answer to the nearest tenth of a
centimetre.
10. Simplify. Show your work.
2
−2 1 −
4 2 𝑥2𝑦 2 6 −2 𝑟 3 𝑠−1 3
a) (3𝑚 𝑛) b)( −2 ) c) (16𝑎 𝑏 ) d) ( −2 −2 )
𝑦 𝑠 𝑟
11.Simplify. Show your work.
1 3
𝑎3 𝑥2𝑦
a) (a3b)(a–1b4) b)(𝑥 2 𝑦) (𝑥 2 𝑦 −2 ) c) 𝑎5 ⋅ 𝑎−3 d) 1
𝑥 2 𝑦 −2
12. Evaluate.
3 1 2 1 6 3
3 2 3 2 (−5.5)3 12 3 0.164
a) ( ) ( ) b) 4 c) [(− )] d) 1
2 2 5
(−5.5)−3 0.164
1. A square has area 18 225 square feet. What is the perimeter of the square?
2. A cube has surface area 11 616 cm2. What is the edge length of the cube?
3. Evaluate each radical. Why do you not need a calculator?
3 6 4 81
a) √1000 b) √0.81 c) √64 d) √
625
4. Write each radical in simplest (i.e. mixed) form.
3 4
a) √150 b)√135 c) √112 d)√162
5. Write each mixed radical as an entire radical.
3 4
a) 6√5 b)3√14 c) 4√3 d)2√2
6. Express each power as a radical.
1
1 5
3 3
a) 124 b)(−50)3 c) 1.20.5 d)(8)
7. Express each radical as a power.
3
3 5 4 42
a) √1.4 b) √132 c) (√2.5) d) (√5)
, 8. Evaluate each power without using a calculator.
3
1 5
9 2
a) 160.25 b) 1.442 c) (−8)3 d) (16)
9. A company designs a container with the shape of a triangular prism to hold 500 mL of juice. The bases of
the prism are equilateral triangles with side length s centimetres. The height, h centimetres, of the prism is
given by the formula:
1
ℎ = 2000(3)−2 𝑠 −2
What is the height of a container with base side length 8.0 cm? Give your answer to the nearest tenth of a
centimetre.
10. Simplify. Show your work.
2
−2 1 −
4 2 𝑥2𝑦 2 6 −2 𝑟 3 𝑠−1 3
a) (3𝑚 𝑛) b)( −2 ) c) (16𝑎 𝑏 ) d) ( −2 −2 )
𝑦 𝑠 𝑟
11.Simplify. Show your work.
1 3
𝑎3 𝑥2𝑦
a) (a3b)(a–1b4) b)(𝑥 2 𝑦) (𝑥 2 𝑦 −2 ) c) 𝑎5 ⋅ 𝑎−3 d) 1
𝑥 2 𝑦 −2
12. Evaluate.
3 1 2 1 6 3
3 2 3 2 (−5.5)3 12 3 0.164
a) ( ) ( ) b) 4 c) [(− )] d) 1
2 2 5
(−5.5)−3 0.164
