Ratios & Rates
Simplify 42:56
3:4
3/4 + 1/8
7/8
Simplify 5x+3x-2x
6x
Two angles on a straight line add to what?
180°
Convert 3.6km to metres.
3600m
Find the mean of 4,6,8,10,12
8
A drink uses powder and water in the ratio 1:8. How much water is needed for 75 g of powder?
600 g or approximately 600 mL of water.
Find 15% of 240
36
Solve 4x+7=31
x=6
Angles around a point total 360°. Three angles are 80°, 115° and 90°. Find the fourth angle.
75°
Find the area of a triangle with base 12cm and perpendicular height 7 cm.
1/2 x 12 x7 = 42 cm2
Find the median of 3,11,5,9,7,13,5.
7
Simplify 1.5m : 75 cm
150:75=2:1
A $160 jacket is discounted by 25%. What is the sale price?
$120
Expand 3(2x-5)
6x-15
Two parallel lines are crossed by a transversal. One corresponding angle is 68°. Find the other corresponding angle.
68°
A rectangular prism measures 5 cm x 4 cm x 3 cm. Find its volume.
60cm3
A fair six-sided die is rolled. What is the probability of rolling a prime number?
3/6 = 1/2
Share $84 in the ratio 3:4
7 parts; $12 per part, so $36 and $48.
Write 0.375 as a fraction in simplest form and as a percentage
37.5%
Solve 5(2x-1)=3x+16
10x-5=3x+16
so 7x=21, x=3.
Two co-interior angles between parallel lines are 3x° and 2x°. Find x and both angles.
3x+2x=180°, so x=36°. Angles are 108° and 72°
A circle has diameter 14 cm. Find its circumference in terms of π.
14π cm
A bag contains 5 red, 3 blue and 2 green counters. What is the probability of NOT selecting a blue counter?
7/10
A car travels 210 km in 2.5 hours. Calculate its average speed in km/h.
210/2.5=84 km/h
A price increases by 20% and then decreases by 20%. Does it return to its original price? Explain using an original price of $100.
No. $100 → $120 → $96. The decrease is calculated on the new price.
The perimeter of a rectangle is 54 cm. Its length is 3 cm more than twice its width. Find its dimensions.
Let width be w, length 2w+3. Then 2(w+2w+3)=54, so w=8 cm and length 19 cm.
An isosceles triangle has a vertex angle of 38°. Find each base angle and explain why they are equal.
(180-38)/2=71°. The base angles are equal because the triangle is isosceles.
A rectangular garden is 12 m long and 8 m wide. A path of uniform width 1 m runs inside the garden around all four edges. Find the area of the remaining grass.
10 m x 6 m; area 60 m2
The mean of five numbers is 12. Four numbers are 8,10,14,15. Find the fifth number.
Total = 5 x 12 = 60
Known total = 47
Missing number = 13