Sec 2 G2 Maths Coordinates and linear graphs worksheet with answers
A free Sec 2 G2 Maths worksheet on coordinates and linear graphs: 9 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.
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Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.
Section A
1
P is the point (2,−3) and Q is the point (2,4). Find the length of PQ.
Answerunits[1]
2
State whether the gradient of the line shown is positive, negative, zero or not defined.
Answer[1]
3
Find the gradient of the line −5x+4y=7.
Answer[2]
4
Write down the coordinates of the point E.
Answer[2]
5
The graph shows the height, y cm, of a candle x hours after it is lit. The candle burns at a steady rate. Find this rate, in cm per hour.
Answer[2]
6
The graph shows the taxi fare, $y, for a trip of x km. Assuming that the line continues in the same way, find the fare for a trip of 25 km.
Answer[3]
Section B
7
(a)State whether the gradient of the line shown is positive, negative, zero or not defined.
Answer (a)[1]
(b)P is the point (1,−5) and Q is the point (1,5). Find the length of PQ.
Answer (b)units[1]
(c)Complete the table of values for y=3x−2.
Answer (c)[3]
8
(a)The graph shows the taxi fare, $y, for a trip of x km. Use the graph to find the fare for a trip of 7 km.
Answer (a)[1]
(b)(i)Complete the table of values for y=4x+1.
Answer (b)(i)[3]
(b)(ii)Complete the table of values for 4x−y=−5.
Answer (b)(ii)[3]
9
(a)The graph shows the length, y cm, of a spring when a mass of x kg hangs from it. Use the graph to find the length of the spring when a mass of 5 kg hangs from it.
Answer (a)[1]
(b)Which point has coordinates (−1,4)?
Answer (b)[1]
(c)Find the gradient of the line 5x+5y=11.
Answer (c)[2]
(d)Complete the table of values for 2x+2y=−4.
Answer (d)[3]
END OF PAPER
Answers and worked solutions
Question 1
Answer: PQ=7 units[1]
P and Q have the same x-coordinate, so PQ is vertical.(4−(−3)=7 unitsPQ=7 units
Question 2
Answer: POSITIVE[1]
The line goes up from left to right.So the gradient is positive.
Question 3
Answer: m=45[2]
4y=5x+7y=45x+47m=45
Question 4
Answer: So E(5,2).[2]
x=5y=2So E(5,2).
Question 5
Answer: Rate: 2 cm per hour[2]
The line goes from (0,30) to (15,0).Rise: 0−30=−30; run: 15−0=15Gradient=15−30Gradient=−2Rate: 2 cm per hour
Question 6
Answer: Fare: $40.50[3]
Start=3The line goes from (0,3) to (10,18).Rise: 18−3=15; run: 10−0=10Rate=1.53+1.5×25=40.5Fare: $40.50
Question 7
(a)Answer: NEGATIVE[1]
The line goes down from left to right.So the gradient is negative.
(b)Answer: PQ=10 units[1]
P and Q have the same x-coordinate, so PQ is vertical.(5−(−5)=10 unitsPQ=10 units
(c)Answer: y=1[3]
When x=−1: y=3(−1)−2y=−5When x=0: y=3(0)−2y=−2When x=1: y=3(1)−2y=1
Question 8
(a)Answer: Fare: $18[1]
Fare: $18
(b)(i)Answer: y=9[3]
When x=−2: y=4(−2)+1y=−7When x=1: y=4(1)+1y=5When x=2: y=4(2)+1y=9