9 Maths Term 1 Revision

Index Laws

100

Simplify: y⁵ x y⁸

y¹³

200

Rewrite m^-14 with a positive index

1/m¹⁴

300

Simplify: (5a⁶b²)³ 

125a¹⁸b⁶

400

48x⁵y¹⁶a¹² ÷ 8x⁵y¹²a^-3

6y⁴a¹⁵

500

15a^-3b⁸y¹⁴ x 4a^-6b⁵y

60a^-9b¹³y¹⁵

Scientific Notation

100

Convert 2.3 x 10⁴ to a basic numeral

23 000

200

Convert 3.57 x 10^-3 to a basic numeral

0.00357

300

Convert 0.0000468 to Scientific Notation

4.68 x 10^-5

400

Convert 418200 to Scientific Notation

4.182 x 10⁵

500

Find the difference between 8.1 x 10⁴ and 5.7 x 10³.

Give your answer in Scientific Notation 

7.53 x 10⁴

Line Segments

100

Determine the midpoint between (5,3) and (1,8)

(3, 5.5)

200

Determine the midpoint between (-2,7) and (3,-4)

(0.5, 1.5)

300

Find the distance between the points (3, 9) and (7, 8)

√17 = 4.12

400

Find the distance between the points (-7, -10) and (-1, -1)

√ 117 = 10.82

500

The midpoint between (6, y) and (8, 11) is (7, 8).

Determine the missing y coordinate. 

y = 5

Trigonometry/Pythagoras

100

θ = sin^-1(10/15). 

Determine the value of θ to the nearest 0.1 degree. 

θ = 41.8 degrees

200

A right-angled triangle has an internal angle of θ = 62 degrees, and an adjacent length of 15cm. Determine the length of the hypotenuse, two decimal places.  

Hypotenuse = 31.95cm

300

A right-angled triangle has a hypotenuse length of 14m, and a short side length of 8m. Determine the length of the other short side. Give your answer to the nearest m. 

11m

400

A right-angled triangle has an internal angle of θ = 12 degrees, and hypotenuse length of 17.2m. Determine the length of the opposite side, rounded to one d.p.

θ = 3.6m

500

A right-angled triangle has an opposite side of 24mm and an adjacent side of 92mm. Determine the size of angle θ, to the nearest 1 d.p.

14.6 degrees

Measurement Error

100

A box was weighed and found to be 13.5kg. What is the absolute error?

0.05kg

200

The water in a vase was measured to be 625.57mL. What are the upper and lower bounds of this measurement?

UB: 625.575mL

LB: 625.565mL

300

The sound of a dog's bark was measured to be 85dB, to the nearest 5dB. Determine the upper and lower bounds of this measurement. 

UB: 87.5dB

LW: 82.5dB

400

Jim counted 462 ants in a colony. The true amount of ants in the colony was 474. Determine the percentage error, to the nearest percent. 

3%

500

A sack of flour was supposed to weigh 68kg. It actually weighed 61.5kg. Determine the percentage error, to the nearest 1 d.p.

10.6%