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- If 6 + 7|x + 4| = 48, then x could equal which of the following?

- -10
- -2
- 2
- 4
- 10

Answer: A, C

Subtract 6 from both sides:

7|x + 4| = 42

|x + 4| = 6

So, (x + 4) = 6 or (x +4) = −6

x = 2 OR -10

- A certain rectangle has an area of 36 and a perimeter of 26. What is the positive difference between the length and breadth of the rectangle?

- 4
- 5
- 6
- 9
- 13

Answer: B

Perimeter = 26 2(L + B) = 26

L = 13 – B

Area = 36

So, (13 – B)B = 36

B^{2} – 13B + 36 = 0

B^{2} – 9B – 4B + 36 = 0

B(B – 9) -4(B – 9) = 0

(B – 4) (B – 9) = 0

B= 4, 9

Positive Difference= 9-4 = 5

- If O is the centre of the circle and its radius of is 8, then what is the area of the shaded region?

- 32
- 64
- 16π – 16
- 32π – 16
- 16π − 32

Answer: E

The sector has a central angle of 90^{0} so it represents ¼ of the circle.

Area of sector = ¼ π (8)^{2} = 16 π

Area of isosceles right triangle AOB = ½ x 8 x 8 = 32

Area of shaded region = Area of sector – area of ΔAOB = 16 π – 32

- If 2
^{x+4}× 3^{y-1}= 576, where x and y are integers, what is x + y?

Answer: C

576 = 24^{2} and 24 = 2^{3} x 3

So, 576 = 2^{6} x 3^{2}

But 2^{x+4} × 3^{y-1} = 576 = 2^{6} x 3^{2}

x+4 = 6; x = 2

y – 1 = 2; y = 3

x+y = 5

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