Grade 10 Quiz: Number System, Word Problems and Proportional Int

If $$\frac{a}{1}$$ is a rational number, which values can $$a$$ have? [2 Marks]

A : 1

B: $$-10$$  

C: $$\sqrt[]{2}$$  

D : $$2,1$$  

Which list of numbers represents a set of Integers? [2 Marks]

Between which two integers would $$\sqrt[]{30}$$  lie? Show all your working. [2 Marks]

The solution to the linear inequality $$-5x+10\le-2x+1;\ x\ \epsilon\ R$$  represented in interval notation is: [3 Marks]

Convert the recurring decimal, $$0.\overline{16}$$ ,to a common fraction in its simplest form. Show all working. [3 Marks]

What inequality does the following number line represent? [2 Marks]

A mother is three times as old as her daughter. The mother was six times her daughters age 15 years ago. If we let the daughters age $$=x$$ , which expression represents the mothers age 15 years ago? [2 Marks]

Zola bought six trays of lettuce plants for her vegetable garden but when she got home she saw that 16 plants were already dead. Sienna bought four trays of lettuce plants from the same nursery and all her plants were healthy. How many lettuce plants were in each tray if Zola and Sienna end up with the same number of plants? [3 Marks]

A square piece of paper is $$x\ cm$$ wide and $$\left(y+3\right)cm$$ long. If the perimeter of the paper is $$36cm$$  , Determine the values of $$x$$  and $$y$$ .[5 Marks]

The proportional intercept theorem states that: In ∆ ABC, if DE // BC then…. [1 Mark]

$$\frac{AD}{DB}=$$   $$\frac{AE}{ }$$  

(a)