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Year 8 Maths TEST A Name: _____________ 2017
COORDINATE GEOMETRY, EQUATIONS AND PROBLEM SOLVING TEST
PART A: COORDINATE GEOMETRY
[22 marks]
Question 1: Use the set of axes below to answer the following questions.
a) i. On same set of axes (provided below), plot the following points:
A(1,3), B(-4,0), C(3, -2), D(0,5)
ii. What quadrant do Points A and C lie in?
[3 marks]
b) On the axes above, plot any point P which has a negative x and y coordinate. [1 mark]
Question 2: For each of the following equations fill in the provided table of values and draw the graph of the equation.
a) 𝑦 = 2𝑥 + 1.
𝒙 -2 -1 0 1 2
𝒚
Year 8 Maths TEST A Name: _____________ 2017
[3 marks]
b) 𝑦 = − !
!𝑥 + 2.
𝒙 -2 -1 0 1 2
𝒚
[3 marks]
Year 8 Maths TEST A Name: _____________ 2017
Question 3: Sarah is eating a block of chocolate over the weekend. On Saturday morning, she ate 4 squares from the block, and will eat 2 more squares of chocolate every hour over the weekend (she really likes chocolate). Let C be the total number of chocolate squares Sarah eats over the weekend. Let h be the number of hours Sarah has spent eating chocolate.
a) What are the independent and dependent variables?
[1 mark]
b) Complete the following table:
Time, h 0 1 2 3 4 5
Number of chocolate squares, C
[2 marks]
c) Plot the graph of C against h.
[2 marks]
d) Is the relationship between C and h linear?
[1 mark]
Year 8 Maths TEST A Name: _____________ 2017
e) How many squares of chocolate would Sarah have eaten after 8 hours?
[1 mark]
f) How many hours would it take Sarah to eat an entire block of chocolate (48 squares)?
[1 mark]
Question 4: a) Show that the point (2,4) lies on the line 𝑦 = 3𝑥 − 2.
[1 mark]
b) Determine whether the point (2,4) lies on the line 𝑦 = −𝑥 + 6.
[1 mark]
c) Plot the point (2,4) on the graph below. Explain your reasoning.
[2 marks]
𝑦 = 3𝑥 − 2
𝑦 = −𝑥 + 6
Year 8 Maths TEST A Name: _____________ 2017
COORDINATE GEOMETRY, EQUATIONS AND PROBLEM SOLVING TEST
PART B: EQUATIONS AND PROBLEM SOLVING
[21 marks] Question 5: Solve the following equations for x:
a) 𝑥 − 4 = 12.
[1 mark]
b) 2𝑥 + 3 = 11.
[2 marks]
c) 45− 3𝑥 = 3.
[2 marks]
d) !!!!!!
= 5.
[2 marks]
e) −7 2𝑥 + 4 = −21.
[2 marks]
f) 3𝑥 − 2 = 𝑥 + 4.
[3 marks]
Year 8 Maths TEST A Name: _____________ 2017
g) −2 𝑥 + 6 = 4𝑥 + 3(𝑥 + 1).
[3 marks]
Question 6: William is counting the number of Maths textbooks he owns. He has 3 suitcases full of textbooks and 2 textbooks on his desk. William has 38 Maths textbooks in total.
a) How many textbooks are in each suitcase? Assume each suitcase has the same number of textbooks.
[2 marks]
b) William decided to measure one of these textbooks.
i. Let the width of the textbook be 𝑥 cm. The length of the textbook is 4cm more than its width. What is the length of the book in terms of 𝑥?
[1 mark]
Maths Textbook Length
Width (𝑥 cm)
Year 8 Maths TEST A Name: _____________ 2017
ii. The perimeter of the book is 44cm. Use this information to make an equation and solve it to find the dimensions of the book.
[3 mark]
Year 8 Maths TEST B Name: _____________ 2017
COORDINATE GEOMETRY, EQUATIONS AND PROBLEM SOLVING TEST
PART A: COORDINATE GEOMETRY
[22 marks]
Question 1: Use the set of axes below to answer the following questions.
a) i. On same set of axes (provided below), plot the following points:
A(2,1), B(-6,0), C(5, -1), D(0,7)
ii. What quadrant do Points A and C lie in?
[3 marks]
b) On the axes above, plot any point P which has a negative x and y coordinate. [1 mark]
Question 2: For each of the following equations fill in the provided table of values and draw the graph of the equation.
a) 𝑦 = 2𝑥 − 1.
𝒙 -2 -1 0 1 2
𝒚
Year 8 Maths TEST B Name: _____________ 2017
[3 marks]
b) 𝑦 = !
!𝑥 − 1.
𝒙 -2 -1 0 1 2
𝒚
[3 marks]
Year 8 Maths TEST B Name: _____________ 2017
Question 3: Emily is eating a block of chocolate over the weekend. On Saturday morning, she ate 2 squares from the block, and will eat 3 more squares of chocolate every hour over the weekend (she really likes chocolate). Let C be the total number of chocolate squares Emily eats over the weekend. Let h be the number of hours Emily has spent eating chocolate.
a) What are the independent and dependent variables?
[1 mark]
b) Complete the following table:
Time, h 0 1 2 3 4 5
Number of chocolate squares, C
[2 marks]
c) Plot the graph of C against h.
[2 marks]
d) Is the relationship between C and h linear?
[1 mark]
Year 8 Maths TEST B Name: _____________ 2017
e) How many squares of chocolate would Emily have eaten after 7 hours?
[1 mark]
f) How many hours would it take Emily to eat an entire block of chocolate (48 squares)?
[1 mark]
Question 4: a) Show that the point (1,3) lies on the line 𝑦 = 2𝑥 + 1.
[1 mark]
b) Determine whether the point (1,3) lies on the line 𝑦 = −2𝑥 + 5.
[1 mark]
c) Plot the point (1,3) on the graph below. Explain your reasoning.
[2 marks]
𝑦 = 2𝑥 + 1
𝑦 = −2𝑥 + 5
Year 8 Maths TEST B Name: _____________ 2017
COORDINATE GEOMETRY, EQUATIONS AND PROBLEM SOLVING TEST
PART B: EQUATIONS AND PROBLEM SOLVING
[21 marks] Question 5: Solve the following equations for x:
a) 𝑥 − 3 = 15.
[1 mark]
b) 3𝑥 + 2 = 14.
[2 marks]
c) 46− 4𝑥 = 6.
[2 marks]
d) !!!!!!
= 7.
[2 marks]
e) −8 3𝑥 + 2 = −45.
[2 marks]
f) 2𝑥 − 4 = 4𝑥 + 3.
[3 marks]
Year 8 Maths TEST B Name: _____________ 2017
g) −3 𝑥 + 4 = 6𝑥 + 4(𝑥 + 5).
[3 marks]
Question 6: Simon is counting the number of Maths textbooks he owns. He has 2 suitcases full of textbooks and 4 textbooks on his desk. Simon has 40 Maths textbooks in total.
a) How many textbooks are in each suitcase? Assume each suitcase has the same number of textbooks.
[2 marks]
b) Simon decided to measure one of these textbooks.
i. Let the width of the textbook be 𝑥 cm. The length of the textbook is 6cm more than its width. What is the length of the book in terms of 𝑥?
[1 mark]
Maths Textbook Length
Width (𝑥 cm)
Year 8 Maths TEST B Name: _____________ 2017
ii. The perimeter of the book is 48cm. Use this information to make an equation and solve it to find the dimensions of the book.
[3 mark]
