Grade 8/9

Question 1

Terry measured the length and the width of a rectangle.
He measured the length to be 745 mm correct to the nearest 5 mm.
He measured the width to be 300 mm correct to the nearest 5 mm.
a) Calculate the lower bound for the area of this rectangle.
Give your answer correct to 3 significant figures.
b) Calculate the upper bound for the perimeter of the rectangle.

(206)

Answer 1

a) 742.5 x 297.5 = 220893.75 = 221000mm

b) 747.5 x 2 + 302.5 x 2 = 2100mm

Question 2

V = I x R

V = 217 ( correct to 3 significant figures)
R = 12.4 (correct to 3 significant figures) 

Find the lower bound of I

(206)

Answer 2

V / R = I
to get the LOWEST option you want to divide the LOWER BOUND by the UPPER BOUND
216.5 / 12.45 = 17.4

Question 3

Rationalise the denominator : 1 / √3

207

Answer 3

multiply by √3 -> 1√3 / 3 -> √3 /3

Question 4

Rationalise the denominator : 1/8√8

207

Answer 4

√8 / 64 -> 2√2 / 64

Question 5

(5 + √3) (5 - √3)
√22

(207)

Answer 5

Expand the brackets

25 + √15 - √15 - 3 -> 22

22/ √22 –> 22√22 / 22 –> √22