toolkit.mathematicsmastery.orgtoolkit.mathematicsmastery.org/app/webroot/js/tiny_mce... · Web viewSimultaneous equations In this unit you will solve linear simultaneous equations

Pre-Learning Assessment

Year 9 Module 4: Equations and inequalities

Name: ………………………………………………………………….

Class: ……………………………………………………………………

Teacher: ……………………………………………………………….

What are we learning this half term?

You need: A Pen A Pencil A Ruler

Pre-Learning Assessment Mark:

50Teacher Comment:

Unit 12: Linear equations and inequalities In this unit you will consolidate earlier work on solving linear equations, using your algebraic skills from the

last two years and will also begin to solve simple linear inequalities.

Unit 13: Simultaneous equations In this unit you will solve linear simultaneous equations by drawing linear graphs for each equation. You will

have the chance to form equations from different contexts.

Unit 14: Quadratic and other graphs In this unit you will draw quadratic graphs and also work with exponential, reciprocal and piece-wise linear

graphs, using them to solve problems in a variety of contexts.

Unit 12

1. Solve:

(a) 3 x−4=47

x=¿¿(2)

(b) 3 (a+2 )=63

a=¿¿(2)(c) 4 b−3=2b+7

b=¿¿(2)

2. Samira has nbags of marbles. There are 22 marbles in each bag. Tina gives Samira 9 marbles.

(a) Write an expression for the number of marbles that Samira has.

_____________________________________________________________(2)(b) Samira now has a total of 119 marbles. Use this information to form an

equation.

_____________________________________________________________(2)(c) Solve this equation to find then number of bags that Samira has.

_____________________________________________________________(1)

3. Rectangle ABCD has width 2 x+1cm and length 3 x−2cm.

NOT DRAWN TO SCALE

(a) Write an expression, in terms of x ,for the perimeter of the rectangle.

_______________________(2)

The perimeter of the rectangle is 33 cm.

(b) Find the value of x .

x=¿¿(2)(c) Hence find the area of this rectangle.

Area = ______________ _______(2)

4. Sarah solves an inequality. He writes down the solution 4<x<−7.

Explain why her answer doesn’t make sense.

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________(1)

5. Solve the following inequality:

(a) 6>2x−8

______________________(2)

(b) Represent the solution to part (a) on the number line below.

(2)

(c) Solve the following inequality:9+4 x≤12

_________________________(2)

6. Write down all the integer values of n which satisfy the inequality −2<n≤1

___________________________________________________________________(2)

Unit 13

7.(a) On the axes below draw the graph of y=2x−3. You may use the table of

values below to help.

x 0 1 2 3 4 5y

(2)

(2)(b) On the same set of axes draw the graph of y=12−x.

(2)(c) Use your graphs to find the solution to the pair of simultaneous equations:

y=2x−3y=12−x

x=¿__________________ y=¿__________________(1)

8. By drawing the relevant graphs, solve the simultaneous equations:2 x+3 y=114 x−6 y=1

x=¿__________________

y=¿__________________

(4)

Unit 14

9. (a) Complete the table for y=x2+2 x−1 and draw the graph on the axes below.

x -4 -3 -2 -1 0 1 2y 2 -1 -1 7

(2)(b) Plot the graph of y=x2+2 x−1

(2)

(c) Use your graph to estimate the value of y when x=1.5 .

Give your estimate correct to one decimal place.

___________________________________________________________(1)

10.The graph below describes Carly’s journey to a job interview.

(a) How long does it take Carly to get to her job interview?

__________________________________________________________(1)

(b) For how long does Carly’s interview last?

___________________________________________________________(1)

(c) What was Carly’s speed on the way to the interview? Remember to give the correct units.

___________________________________________________________(2)

(d) Compare Carly’s speed when travelling to the interview and when travelling back home.

___________________________________________________________(1)

11.The graph below shows the growth of a population of birds over a number of years.

(a) Estimate the number of birds present when the count first began?

__________________________________________________________(1)

(b) How many birds were there three years after the count began?

__________________________________________________________(1)

(c) Approximately when did the number of birds first exceed 1000?

___________________________________________________________(1)

Number of birds

Number of years

Finishing Tasks

Fraction & percentage riddles

Karla is 20% heavier than Daniella. Daniella is 10% lighter than her sister. How much heavier is Karla than Daniella’s sister, as a percentage?

Daisy and Nila each had some money. Daisy gave Nila 12 of what she had.

Nila gave 50% of her money to Daisy. Finally, Daisy gave 12 of her money

back to Nila.By the end of this, Daisy had £96.00 and Nila had £228. How much money did they each have to begin with?