Question 1:
Calculate the gradient of each line on the centimetre grids below.
Question 1(a): [1 mark]
What is the gradient of line A?
Answer type: Multiple choice type 1
A: - \dfrac{2}{3}
B: - 4
C: 1
D: \dfrac{3}{2}
ANSWER: D: \dfrac{3}{2}
WORKING: \dfrac{\text{change in} \, y}{\text{change in} \, x} = \dfrac{3}{2}
Question 1(b): [1 mark]
What is the gradient of line B?
Answer type: Multiple choice type 1
A: - \dfrac{2}{3}
B: - 4
C: 1
D: \dfrac{3}{2}
ANSWER: A: - \dfrac{2}{3}
WORKING: \dfrac{\text{change in} \, y}{\text{change in} \, x} = \dfrac{- 2}{3}
Question 1(c): [1 mark]
What is the gradient of line C?
Answer type: Multiple choice type 1
A: - \dfrac{2}{3}
B: - 4
C: 1
D: \dfrac{3}{2}
ANSWER: C: 1
WORKING: \dfrac{\text{change in} \, y}{\text{change in} \, x} = \dfrac{3}{3} = 1
Question 1(d): [1 mark]
What is the gradient of line D?
Answer type: Multiple choice type 1
A: - \dfrac{2}{3}
B: - 4
C: 1
D: \dfrac{3}{2}
ANSWER: B: - 4
WORKING: \dfrac{\text{change in} \, y}{\text{change in} \, x} = \dfrac{-4}{1} = - 4
Question 2:
The line below represents the heights a walker reached during a long trail.
Which section of the graph shows the following? Write your answers in CAPITAL LETTERS.
Question 2(a): [1 mark]
The steepest positive gradient?
Answer type: Simple text answer
ANSWER: E
Question 2(b): [1 mark]
The shallowest positive gradient?
Answer type: Simple text answer
ANSWER: G
Question 2(c): [1 mark]
The steepest negative gradient?
Answer type: Simple text answer
ANSWER: H
Question 2(d): [1 mark]
The shallowest negative gradient?
Answer type: Simple text answer
ANSWER: F
Question 3:
A and B are straight lines that intersect.
Question 3(a): [1 mark]
What is the gradient of line A?
Answer type: Fraction
ANSWER: \dfrac{4}{3}
WORKING: \dfrac{\text{change in} \, y}{\text{change in} \, x} = \dfrac{4}{3}
Question 3(b): [1 mark]
What is the gradient of line B?
Answer type: Simple text answer
ANSWER: 0
WORKING: No change in y with regards to x, so gradient is 0.
Question 4:
Calculate the gradients of lines X and Y below.
Question 4(a): [1 mark]
X
Answer type: Fraction
ANSWER: \dfrac{4}{3}
WORKING: \dfrac{\text{change in} \, y}{\text{change in} \, x} = \dfrac{4}{3}
Question 4(b): [1 mark]
Y
Answer type: Fraction
ANSWER: \dfrac{7}{2}
WORKING: \dfrac{\text{change in} \, y}{\text{change in} \, x} = \dfrac{7}{2}
Question 5(a): [2 marks]
The points (1,5) and (8,7) are on the same straight line. What is the gradient of the line?
Answer type: Fraction
ANSWER: \dfrac{2}{7}
WORKING: \dfrac{\text{change in} \, y}{\text{change in} \, x} = \dfrac{7 - 5}{8 - 1} = \dfrac{2}{7}
Question 5(b): [2 marks]
The points (3,6) and (7,-2) are on the same straight line. What is the gradient of the line?
Answer type: Simple text answer
ANSWER: - 2
WORKING: \dfrac{\text{change in} \, y}{\text{change in} \, x} = \dfrac{- 2 - 6}{7 - 3} = \dfrac{- 8}{4} = - 2
Question 6: [2 marks]
Points A (x , y) and B are on the same straight line.
The x-coordinate of B is three times the x-coordinate of A.
The y-coordinate of B is four times the y-coordinate of A.
What is the gradient of the line in terms of x and y?
Answer type: Multiple choice type 1
A: \dfrac{2x}{3y}
B: \dfrac{3y}{2x}
C: \dfrac{3x}{4y}
D: \dfrac{4y}{3x}
ANSWER: B: \dfrac{3y}{2x}
WORKING: \dfrac{\text{change in} \, y}{\text{change in} \, x} = \dfrac{4y - y}{3x - x} = \dfrac{3y}{2x}