EQUATIONS & ALGEBRA
A number is multiplied by 4 and then 7 is added. The result is 35. What is the number?
7
A cyclist travels at 18 km/h. How far will she travel in 20 minutes?
6 km
A rectangle is 3 times as long as it is wide. Its perimeter is 48 cm. Find its area.
108
Find the smallest positive number that is divisible by 4, 6 and 9.
36
A number is multiplied by 4 and then 7 is added. The result is 35. What is the number?
10 and 28
Two cyclists start from the same point at the same time. One travels at 14 km/h and the other at 20 km/h. How far apart will they be after 45 minutes?
4.5
A square has side length 18 cm. A smaller square with side length 6 cm is removed from one corner. What percentage of the original square remains?
88-89
A two-digit number has digits that add to 12. The tens digit is twice the units digit. What is the number?
84
Sarah has 4 times as many stickers as Emma. After Sarah gives 6 stickers to Emma, Sarah has twice as many stickers as Emma. How many stickers did each girl have originally?
Emma=9,Sarah=36
Two towns are 84 km apart. Two cyclists start from the towns at the same time and ride towards each other. One travels at 12 km/h and the other at 16 km/h. After how many hours do they meet, and how far has each cyclist travelled?
3 hours / 36 and 48 km
A rectangular garden is 30 m by 20 m. A path of equal width is built inside the garden along all four sides. The remaining grass has an area of 336 m². What is the width of the path?
3m
How many different three-digit numbers can be made using the digits 1, 2, 3, 4 and 5 without repeating a digit?
60
The perimeter of a rectangle is 76 cm. The length is 5 cm more than twice the width. Find the area of the rectangle.
297
Maya cycles to school at 12 km/h. If she cycles at 15 km/h, she arrives 12 minutes earlier. How far is the school from her home?
12
A square has side length 20 cm. A quarter-circle of radius 10 cm is drawn inside each corner, with the centre of each circle at the corner.
What area of the square is NOT inside any of the four quarter-circles?
Use π=3.14.
86
The sequence below follows a rule:
3, 6, 12, 24, 48,…
a) Find the 8th term.
b) Without calculating all the terms one by one, explain how you know the answer.
384
A number is chosen. It is multiplied by 3, then 8 is added. The result is the same as multiplying the original number by 5 and subtracting 14. Find the number.
11
Two runners start at the same point of a circular track and run in the same direction.
After how many seconds will A first catch B? How many laps will each runner have completed?
180 sec/ A — 4 laps, B — 3 laps.
A rectangle is 24 cm by 18 cm. A diagonal is drawn from one corner to the opposite corner.
What is the area of each of the two triangles formed?
4 times
A positive integer is less than 100.
When divided by 5, it leaves remainder 2.
When divided by 7, it leaves remainder 4.
What is the largest possible integer?
67